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Subject: 2. One-dimensional Steady-state Conduction - Heat and Mass Transfer, 2nd Edition
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<div id=3D"sbo-rt-content" style=3D"transform: none;"><div class=3D"annotat=
or-wrapper"><h2 id=3D"h20001" class=3D"EB04MainHeadClosedNum"><a id=3D"page=
_15"></a>2</h2>
<h2 id=3D"h20002" class=3D"EB04MainHeadClosedTitle">One-dimensional Steady-=
state Conduction</h2>
<p id=3D"p0001" class=3D"EB02BodyTextFullOut">Conduction heat transfer will=
 take place if there is a temperature gradient in a solid body. It will con=
tinue till the temperature is identical at every location in the body and i=
s associated with lattice vibration and free electron transport. In this ch=
apter, one-dimensional heat transfer analysis is carried out with the appli=
cation of Fourier's law.</p>
<h5 id=3D"h50001" class=3D"EB07SmallCapsMediumHead"><a id=3D"ch02lev1sec1">=
</a>2.1 FOURIER's LAW</h5>
<p id=3D"p0002" class=3D"EB02BodyTextFullOut">Fourier's law states that the=
 rate of heat transfer per unit surface area is proportional to the tempera=
ture gradient normal to the surface:</p>
<p id=3D"p0003" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0001" class=3D"imagewrap">
<img id=3D"img0296" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg15_img1.png" alt=3D"image" width=3D"331" hei=
ght=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg15_img1.png">
</div>
<p id=3D"p0004" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0005" class=3D"EB02BodyTextFullOut">where =E2=80=98<em>q</em>=E2=
=80=99 is the heat transfer rate and (<em>=E2=88=82T/=E2=88=82x</em>) is th=
e temperature difference in the flow direction.</p>
<p id=3D"p0006" class=3D"EB03BodyTextIndented">The proportionality sign is =
replaced by an equality sign with the introduction of the thermal conductiv=
ity =E2=80=98<em>k</em>=E2=80=99 of the material as</p>
<p id=3D"p0007" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0002" class=3D"imagewrap">
<img id=3D"img0297" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg15_img2.png" alt=3D"image" width=3D"344" hei=
ght=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg15_img2.png">
</div>
<p id=3D"p0008" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0009" class=3D"EB03BodyTextIndented">The negative sign is introdu=
ced to make the heat transfer rate positive in the flow direction.</p>
<h5 id=3D"h50002" class=3D"EB07SmallCapsMediumHead"><a id=3D"ch02lev1sec2">=
</a>2.2 GENERAL ENERGY EQUATION</h5>
<p id=3D"p0010" class=3D"EB02BodyTextFullOut"><em>Rectangular co-ordinates<=
/em></p>
<p id=3D"p0011" class=3D"EB02BodyTextFullOut">The three-dimensional time-de=
pendent general conduction equation with internal heat generation of now ho=
mogeneous material, i.e., the energy equation in cartesian co-ordinates (<a=
 href=3D"https://learning.oreilly.com/library/view/heat-and-mass/9789332515=
680/xhtml/chapter002.xhtml#figure2.1">Fig. 2.1</a>) is</p>
<p id=3D"p0012" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0003" class=3D"imagewrap">
<img id=3D"img0298" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg16_img1.png" alt=3D"Control Volume with Cart=
esian Co-ordinates" width=3D"288" height=3D"246" data-mfp-src=3D"/library/v=
iew/heat-and-mass/9789332515680/images/pg16_img1.png">
<p id=3D"p0013" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0014" class=3D"EB28InlineCaption"><strong><a id=3D"figure2.1"></a=
>Figure 2.1</strong> Control Volume with Cartesian Co-ordinates</p></div>
<p id=3D"p0015" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0004" class=3D"imagewrap">
<img id=3D"img0299" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg15_img3.png" alt=3D"image" width=3D"430" hei=
ght=3D"39" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg15_img3.png">
</div>
<p id=3D"p0016" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0017" class=3D"EB02BodyTextFullOut">where <em>T</em> is the tempe=
rature, <em>k</em> is the thermal conductivity, <em>q<sub class=3D"EBsub">g=
</sub></em> is the heat generation per unit volume, <em>=CF=81</em> is the =
density, <em>c</em> is the specific heat, and <em>t</em> is the time and <i=
mg id=3D"img0300" class=3D"Eq1" src=3D"https://learning.oreilly.com/library=
/view/heat-and-mass/9789332515680/images/pg15_img3a.png" alt=3D"image" widt=
h=3D"61" height=3D"44" data-mfp-src=3D"/library/view/heat-and-mass/97893325=
15680/images/pg15_img3a.png"> is the thermal diffusivity.</p>
<p id=3D"p0018" class=3D"EB03BodyTextIndented"><a id=3D"page_16"></a>The en=
ergy equation can also be written with Laplacian operator</p>
<p id=3D"p0019" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0005" class=3D"imagewrap">
<img id=3D"img0301" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg16_img2.png" alt=3D"image" width=3D"366" hei=
ght=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg16_img2.png">
</div>
<p id=3D"p0020" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0021" class=3D"EB03BodyTextIndented">The 3D steady-state conducti=
on equation with internal heat generation is</p>
<p id=3D"p0022" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0006" class=3D"imagewrap">
<img class=3D"Eq1" id=3D"img0007" src=3D"https://learning.oreilly.com/libra=
ry/view/heat-and-mass/9789332515680/images/pg16_img3.png" alt=3D"image" wid=
th=3D"159" height=3D"39" data-mfp-src=3D"/library/view/heat-and-mass/978933=
2515680/images/pg16_img3.png"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(or)
</div>
<p id=3D"p0023" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0007" class=3D"imagewrap">
<img id=3D"img0302" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg16_img3a.png" alt=3D"image" width=3D"428" he=
ight=3D"32" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg16_img3a.png">
</div>
<p id=3D"p0024" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0025" class=3D"EB03BodyTextIndented">The 3D unsteady conduction e=
quation without internal heat generation is</p>
<p id=3D"p0026" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0008" class=3D"imagewrap">
<img class=3D"Eq1" id=3D"img0009" src=3D"https://learning.oreilly.com/libra=
ry/view/heat-and-mass/9789332515680/images/pg16_img4.png" alt=3D"image" wid=
th=3D"155" height=3D"39" data-mfp-src=3D"/library/view/heat-and-mass/978933=
2515680/images/pg16_img4.png"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(or)
</div>
<p id=3D"p0027" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0009" class=3D"imagewrap">
<img id=3D"img0303" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg16_img4a.png" alt=3D"image" width=3D"421" he=
ight=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg16_img4a.png">
</div>
<p id=3D"p0028" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0029" class=3D"EB03BodyTextIndented">The 3D steady-state conducti=
on equation without internal heat generation is</p>
<p id=3D"p0030" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0010" class=3D"imagewrap">
<img class=3D"Eq1" id=3D"img0011" src=3D"https://learning.oreilly.com/libra=
ry/view/heat-and-mass/9789332515680/images/pg16_img5.png" alt=3D"image" wid=
th=3D"128" height=3D"39" data-mfp-src=3D"/library/view/heat-and-mass/978933=
2515680/images/pg16_img5.png">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(or)
</div>
<p id=3D"p0031" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0011" class=3D"imagewrap">
=E2=96=BD<sup class=3D"EBsup">2</sup><em>T</em> =3D 0 (Laplace equation).&n=
bsp;&nbsp;&nbsp;&nbsp; (2.7)</div>
<p id=3D"p0032" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0033" class=3D"EB03BodyTextIndented">The simplest form is the ste=
ady-state one-dimensional heat transfer without heat generation which is</p=
>
<p id=3D"p0034" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0012" class=3D"imagewrap"><a id=3D"page_17"></a>
<img id=3D"img0304" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg17_img1.png" alt=3D"image" width=3D"53" heig=
ht=3D"36" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/=
pg17_img1.png">
</div>
<p id=3D"p0035" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0036" class=3D"EB02BodyTextFullOut"><em>Cylindrical co-ordinates<=
/em></p>
<p id=3D"p0037" class=3D"EB02BodyTextFullOut">The general equation is</p>
<p id=3D"p0038" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0013" class=3D"imagewrap">
<img id=3D"img0305" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg17_img2.png" alt=3D"image" width=3D"445" hei=
ght=3D"45" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg17_img2.png">
</div>
<p id=3D"p0039" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0040" class=3D"EB03BodyTextIndented">Steady-state one-dimensional=
 (radial direction) heat transfer (<a href=3D"https://learning.oreilly.com/=
library/view/heat-and-mass/9789332515680/xhtml/chapter002.xhtml#figure2.2">=
Fig. 2.2</a>) is given by</p>
<p id=3D"p0041" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0014" class=3D"imagewrap">
<img id=3D"img0306" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg17_img3.png" alt=3D"Heat Conduction in a Sol=
id Element =E2=80=93 Cylindrical Co-ordinate System" width=3D"357" height=
=3D"339" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/p=
g17_img3.png">
<p id=3D"p0042" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0043" class=3D"EB28InlineCaption"><strong><a id=3D"figure2.2"></a=
>Figure 2.2</strong> Heat Conduction in a Solid Element =E2=80=93 Cylindric=
al Co-ordinate System</p></div>
<p id=3D"p0044" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0015" class=3D"imagewrap">
<img id=3D"img0307" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg17_img4.png" alt=3D"image" width=3D"124" hei=
ght=3D"35" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg17_img4.png">
</div>
<p id=3D"p0045" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0046" class=3D"EB02BodyTextFullOut"><em>Spherical co-ordinates</e=
m></p>
<p id=3D"p0047" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0016" class=3D"imagewrap">
<img id=3D"img0308" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg17_img5.png" alt=3D"image" width=3D"518" hei=
ght=3D"36" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg17_img5.png">
</div>
<p id=3D"p0048" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0049" class=3D"EB03BodyTextIndented">If the heat flow is steady a=
nd in one-dimensional (radial direction) without heat source (<a href=3D"ht=
tps://learning.oreilly.com/library/view/heat-and-mass/9789332515680/xhtml/c=
hapter002.xhtml#figure2.3">Fig. 2.3</a>), then the equation becomes</p>
<p id=3D"p0050" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0017" class=3D"imagewrap">
<img id=3D"img0309" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg18_img1.png" alt=3D"Heat Conduction in a Sol=
id Element =E2=80=93 Spherical Co-ordinate System" width=3D"333" height=3D"=
348" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/pg18_=
img1.png">
<p id=3D"p0051" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0052" class=3D"EB28InlineCaption"><strong><a id=3D"figure2.3"></a=
>Figure 2.3</strong> Heat Conduction in a Solid Element =E2=80=93 Spherical=
 Co-ordinate System</p></div>
<p id=3D"p0053" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0018" class=3D"imagewrap">
<img id=3D"img0310" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg17_img6.png" alt=3D"image" width=3D"98" heig=
ht=3D"42" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/=
pg17_img6.png">
</div>
<div id=3D"div0019" class=3D"BoxHead">
<h5 id=3D"h50003" class=3D"EB08ExtraFeatureHead">KEY CONCEPTS</h5></div>
<div id=3D"div0020" class=3D"BoxText">
<ul id=3D"ul0001" class=3D"BulletCircle">
<li id=3D"li0001" class=3D"EB23ListFirst"><a id=3D"page_18"></a><p id=3D"p0=
054" class=3D"EB02BodyTextFullOut">Thermal diffusivity is the material prop=
erty governing heat flow when the temperature varies with time</p></li>
<li id=3D"li0002" class=3D"EB24List"><p id=3D"p0055" class=3D"EB02BodyTextF=
ullOut">It is closely related to thermal conductivity.</p></li>
<li id=3D"li0003" class=3D"EB24List"><p id=3D"p0056" class=3D"EB02BodyTextF=
ullOut">Multiplying together thermal diffusivity, density and specific heat=
 capacity of a material gives its thermal conductivity</p></li>
<li id=3D"li0004" class=3D"EB25ListLast"><p id=3D"p0057" class=3D"EB02BodyT=
extFullOut">Thermal diffusivity can be measured on small samples of a few m=
illimeters in size, up to very high temperatures.</p></li>
</ul>
</div>
<h5 id=3D"h50004" class=3D"EB07SmallCapsMediumHead"><a id=3D"ch02lev1sec3">=
</a>2.3 PLANE WALL (SLAB): CONSTANT SURFACE TEMPERATURE WITHOUT HEAT GENERA=
TION</h5>
<p id=3D"p0058" class=3D"EB02BodyTextFullOut"><a href=3D"https://learning.o=
reilly.com/library/view/heat-and-mass/9789332515680/xhtml/chapter002.xhtml#=
figure2.4">Figure 2.4</a> shows a slab and the general conduction equation =
is reduced to one-dimensional equation as</p>
<p id=3D"p0059" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0021" class=3D"imagewrap">
<img id=3D"img0311" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg19_img1.png" alt=3D"One-dimensional Heat Con=
duction in the Slab" width=3D"196" height=3D"251" data-mfp-src=3D"/library/=
view/heat-and-mass/9789332515680/images/pg19_img1.png">
<p id=3D"p0060" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0061" class=3D"EB28InlineCaption"><strong><a id=3D"figure2.4"></a=
>Figure 2.4</strong> One-dimensional Heat Conduction in the Slab</p></div>
<p id=3D"p0062" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0022" class=3D"imagewrap"><a id=3D"eq2.10"></a>
<img id=3D"img0312" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg18_img2.png" alt=3D"image" width=3D"334" hei=
ght=3D"36" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg18_img2.png">
</div>
<p id=3D"p0063" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0064" class=3D"EB03BodyTextIndented">The boundary conditions are<=
/p>
<ol id=3D"ol0001" class=3D"LowerRoman">
<li id=3D"li0005" class=3D"EB23ListFirst"><em>x</em> =3D 0; <em>T</em> =3D =
<em>T</em><sub class=3D"EBsub">1</sub> and</li>
<li id=3D"li0006" class=3D"EB25ListLast"><em>x</em> =3D <em>L</em>; <em>T</=
em> =3D <em>T</em><sub class=3D"EBsub">2</sub></li>
</ol>
<p id=3D"p0065" class=3D"EB03BodyTextIndented"><a id=3D"page_19"></a>To get=
 the temperature distribution in the slab, integrate <a href=3D"https://lea=
rning.oreilly.com/library/view/heat-and-mass/9789332515680/xhtml/chapter002=
.xhtml#eq2.10">Equation (2.10)</a></p>
<p id=3D"p0066" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0023" class=3D"imagewrap">
<img class=3D"Eq1" id=3D"img0021" src=3D"https://learning.oreilly.com/libra=
ry/view/heat-and-mass/9789332515680/images/pg19_img2.png" alt=3D"image" wid=
th=3D"50" height=3D"35" data-mfp-src=3D"/library/view/heat-and-mass/9789332=
515680/images/pg19_img2.png"> and <em>T</em> =3D <em>C</em><sub class=3D"EB=
sub">1</sub><em>x</em> + <em>C</em><sub class=3D"EBsub">2</sub>.
</div>
<p id=3D"p0067" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0068" class=3D"EB03BodyTextIndented">Applying the boundary condit=
ions, <em>C</em><sub class=3D"EBsub">2</sub> =3D <em>T</em><sub class=3D"EB=
sub">1</sub> and <img id=3D"img0313" class=3D"Eq1" src=3D"https://learning.=
oreilly.com/library/view/heat-and-mass/9789332515680/images/pg19_img3.png" =
alt=3D"image" width=3D"79" height=3D"33" data-mfp-src=3D"/library/view/heat=
-and-mass/9789332515680/images/pg19_img3.png"></p>
<p id=3D"p0069" class=3D"EB03BodyTextIndented">Substituting <em>C</em><sub =
class=3D"EBsub">1</sub> and <em>C</em><sub class=3D"EBsub">2</sub>, the tem=
perature distribution is</p>
<p id=3D"p0070" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0024" class=3D"imagewrap">
<a id=3D"eq2.11"></a><img id=3D"img0314" src=3D"https://learning.oreilly.co=
m/library/view/heat-and-mass/9789332515680/images/pg19_img4.png" alt=3D"ima=
ge" width=3D"367" height=3D"41" data-mfp-src=3D"/library/view/heat-and-mass=
/9789332515680/images/pg19_img4.png">
</div>
<p id=3D"p0071" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0072" class=3D"EB03BodyTextIndented">The rate of heat transfer th=
rough the slab is</p>
<p id=3D"p0073" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0025" class=3D"imagewrap">
<img id=3D"img0315" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg19_img5.png" alt=3D"image" width=3D"81" heig=
ht=3D"35" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/=
pg19_img5.png">
</div>
<p id=3D"p0074" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0075" class=3D"EB03BodyTextIndented">From <a href=3D"https://lear=
ning.oreilly.com/library/view/heat-and-mass/9789332515680/xhtml/chapter002.=
xhtml#eq2.11">Equation (2.11)</a>,</p>
<p id=3D"p0076" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0026" class=3D"imagewrap">
<img id=3D"img0316" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg19_img6.png" alt=3D"image" width=3D"87" heig=
ht=3D"35" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/=
pg19_img6.png">
</div>
<p id=3D"p0077" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0027" class=3D"imagewrap">
<img id=3D"img0317" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg19_img6a.png" alt=3D"image" width=3D"358" he=
ight=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg19_img6a.png">
</div>
<p id=3D"p0078" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0079" class=3D"EB02BodyTextFullOut"><em>Electrical analogy</em></=
p>
<p id=3D"p0080" class=3D"EB02BodyTextFullOut">As per Ohm's law, the flow of=
 current <em>i</em> for the potential driving force =CE=94<em>e</em> for a =
resistance <em>R</em> is as shown in <a href=3D"https://learning.oreilly.co=
m/library/view/heat-and-mass/9789332515680/xhtml/chapter002.xhtml#figure2.5=
">Fig. 2.5</a>.</p>
<p id=3D"p0081" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0028" class=3D"imagewrap">
<img id=3D"img0318" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg20_img1.png" alt=3D"Electrical Analogy" widt=
h=3D"273" height=3D"154" data-mfp-src=3D"/library/view/heat-and-mass/978933=
2515680/images/pg20_img1.png">
<p id=3D"p0082" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0083" class=3D"EB28InlineCaption"><strong><a id=3D"figure2.5"></a=
>Figure 2.5</strong> Electrical Analogy</p></div>
<p id=3D"p0084" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0029" class=3D"imagewrap">
<img id=3D"img0319" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg19_img7.png" alt=3D"image" width=3D"362" hei=
ght=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg19_img7.png">
</div>
<p id=3D"p0085" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0086" class=3D"EB03BodyTextIndented"><a id=3D"page_20"></a>The im=
portance of the electrical analogy is that the electrical circuit analysis =
technique can be used to solve the one-dimensional steady-state heat conduc=
tion problems.</p>
<p id=3D"p0087" class=3D"EB03BodyTextIndented">Then 1<em>/R</em> is called =
thermal conductance. Similar to electrical system, the heat transfer can be=
 written as</p>
<p id=3D"p0088" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0030" class=3D"imagewrap">
<img id=3D"img0320" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg20_img2.png" alt=3D"image" width=3D"122" hei=
ght=3D"53" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg20_img2.png">
</div>
<p id=3D"p0089" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0090" class=3D"EB02BodyTextFullOut">where <em>R</em> is called th=
ermal resistance <img id=3D"img0321" class=3D"Eq1" src=3D"https://learning.=
oreilly.com/library/view/heat-and-mass/9789332515680/images/pg20_img2a.png"=
 alt=3D"image" width=3D"36" height=3D"41" data-mfp-src=3D"/library/view/hea=
t-and-mass/9789332515680/images/pg20_img2a.png">.</p>
<h4 id=3D"h40001" class=3D"EB10SmallHead"><a id=3D"ch02lev2sec1"></a>2.3.1 =
In a Slab With Convection Boundaries</h4>
<p id=3D"p0091" class=3D"EB02BodyTextFullOut">If the slab is surrounded on =
both sides by fluid at different temperatures as shown in <a href=3D"https:=
//learning.oreilly.com/library/view/heat-and-mass/9789332515680/xhtml/chapt=
er002.xhtml#figure2.6">Fig. 2.6</a> such that</p>
<p id=3D"p0092" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0031" class=3D"imagewrap">
<img id=3D"img0322" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg20_img3.png" alt=3D"One-dimensional Conducti=
on Heat Transter Through a Slab with Convection Boundaries at Both Sides" w=
idth=3D"568" height=3D"214" data-mfp-src=3D"/library/view/heat-and-mass/978=
9332515680/images/pg20_img3.png">
<p id=3D"p0093" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0094" class=3D"EB28InlineCaption"><strong><a id=3D"figure2.6"></a=
>Figure 2.6</strong> One-dimensional Conduction Heat Transfer Through a Sla=
b with Convection Boundaries at Both Sides</p></div>
<p id=3D"p0095" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0032" class=3D"imagewrap"><em>T<sub class=3D"EBsub">h</sub></=
em> &gt; <em>T</em><sub class=3D"EBsub">1</sub> &gt; <em>T</em><sub class=
=3D"EBsub">2</sub> &gt; <em>T<sub class=3D"EBsub">c</sub></em></div>
<p id=3D"p0096" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0097" class=3D"EB02BodyTextFullOut">where <em>T<sub class=3D"EBsu=
b">h</sub></em> is the temperature of hot fluid, which supplies heat to the=
 slab and <em>T<sub class=3D"EBsub">c</sub></em> is the temperature of the =
cold fluid, which receives heat from the slab. The steady-state one-dimensi=
onal heat transfer equation then becomes</p>
<p id=3D"p0098" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0033" class=3D"imagewrap"><a id=3D"page_21"></a>
<img id=3D"img0323" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg21_img1.png" alt=3D"image" width=3D"445" hei=
ght=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg21_img1.png">
</div>
<p id=3D"p0099" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0100" class=3D"EB03BodyTextIndented">From this equation, we can w=
rite</p>
<p id=3D"p0101" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0034" class=3D"imagewrap">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;(<em>T</em><sub class=3D"EBsub">h</sub> =E2=80=93 <em>T</em><sub cla=
ss=3D"EBsub">1</sub>) =3D <em>q</em>/<em>h</em>, <em>A</em></div>
<div id=3D"div0035" class=3D"imagewrap">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;(<em>T</em><sub class=3D"EBsub">1</sub> =E2=80=93 <em>T</em><sub cla=
ss=3D"EBsub">2</sub>) =3D <em>Lq</em> / <em>kA</em></div>
<div id=3D"div0036" class=3D"imagewrap">and (<em>T</em><sub class=3D"EBsub"=
>2</sub> =E2=80=93 <em>T<sub class=3D"EBsub">e</sub></em>) =3D <em>q</em> /=
 <em>h<sub class=3D"EBsub">c</sub> A</em></div>
<p id=3D"p0102" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0103" class=3D"EB03BodyTextIndented">Adding the above equation, t=
he final form is</p>
<p id=3D"p0104" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0037" class=3D"imagewrap">
<img id=3D"img0324" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg21_img2b.png" alt=3D"image" width=3D"219" he=
ight=3D"58" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg21_img2b.png">
</div>
<p id=3D"p0105" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0106" class=3D"EB02BodyTextFullOut">where <em>R<sub class=3D"EBsu=
b">h</sub></em> and <em>R<sub class=3D"EBsub">c</sub></em> are the convecti=
ve thermal resistances and <em>R</em><sub class=3D"EBsub">1</sub> is the co=
nduction thermal resistance.</p>
<p id=3D"p0107" class=3D"EB03BodyTextIndented">The electrical equivalent th=
ermal network for this condition is also shown in <a href=3D"https://learni=
ng.oreilly.com/library/view/heat-and-mass/9789332515680/xhtml/chapter002.xh=
tml#figure2.6">Fig. 2.6</a>.</p>
<h4 id=3D"h40002" class=3D"EB10SmallHead"><a id=3D"ch02lev2sec2"></a>2.3.2 =
One-dimensional Steady-state conduction Through a Composite Slab</h4>
<p id=3D"p0108" class=3D"EB02BodyTextFullOut">Consider a composite slab mad=
e up of two layers as shown in <a href=3D"https://learning.oreilly.com/libr=
ary/view/heat-and-mass/9789332515680/xhtml/chapter002.xhtml#figure2.7">Fig.=
 2.7</a>.</p>
<p id=3D"p0109" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0038" class=3D"imagewrap">
<img id=3D"img0325" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg21_img3.png" alt=3D"(a) Composite Slab; (b) =
Electrical Analogy" width=3D"601" height=3D"237" data-mfp-src=3D"/library/v=
iew/heat-and-mass/9789332515680/images/pg21_img3.png">
<p id=3D"p0110" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0111" class=3D"EB28InlineCaption"><strong><a id=3D"figure2.7"></a=
>Figure 2.7</strong> (a) Composite Slab; (b) Electrical Analogy</p></div>
<p id=3D"p0112" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0113" class=3D"EB03BodyTextIndented">The thermal resistance of th=
e first and second layers are</p>
<p id=3D"p0114" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0039" class=3D"imagewrap">
<img id=3D"img0326" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg21_img5.png" alt=3D"image" width=3D"168" hei=
ght=3D"37" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg21_img5.png">
</div>
<p id=3D"p0115" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0116" class=3D"EB03BodyTextIndented">If the composite wall consis=
ts of =E2=80=98<em>N=E2=80=99</em> slabs, then</p>
<p id=3D"p0117" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0040" class=3D"imagewrap">
<img id=3D"img0327" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg21_img6.png" alt=3D"image" width=3D"89" heig=
ht=3D"56" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/=
pg21_img6.png">
</div>
<p id=3D"p0118" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0119" class=3D"EB03BodyTextIndented">If the condition occurs in a=
 section with two different materials placed in parallel, as shown in <a hr=
ef=3D"https://learning.oreilly.com/library/view/heat-and-mass/9789332515680=
/xhtml/chapter002.xhtml#figure2.8">Fig. 2.8</a> with thermal circuit, heat =
transfer is given by</p>
<p id=3D"p0120" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0041" class=3D"imagewrap">
<img id=3D"img0328" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg22_img1.png" alt=3D"Materials Connected in P=
arallel (a); Thermal Circuit (b)" width=3D"547" height=3D"220" data-mfp-src=
=3D"/library/view/heat-and-mass/9789332515680/images/pg22_img1.png">
<p id=3D"p0121" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0122" class=3D"EB28InlineCaption"><strong><a id=3D"figure2.8"></a=
>Figure 2.8</strong> Materials Connected in Parallel (a); Thermal Circuit (=
b)</p></div>
<p id=3D"p0123" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0042" class=3D"imagewrap"><a id=3D"page_22"></a>
<img id=3D"img0329" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg22_img2.png" alt=3D"image" width=3D"217" hei=
ght=3D"37" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg22_img2.png">
</div>
<p id=3D"p0124" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0125" class=3D"EB03BodyTextIndented">If the composite slab is exp=
osed to convection environment with <em>T<sub class=3D"EBsub">h</sub></em> =
&gt; <em>T</em><sub class=3D"EBsub">1</sub> &gt; <em>T</em><sub class=3D"EB=
sub">2</sub> &gt; <em>T</em><sub class=3D"EBsub">3</sub> &gt; <em>T<sub cla=
ss=3D"EBsub">c</sub></em>, then the convection resistances are <img id=3D"i=
mg0330" class=3D"Eq1" src=3D"https://learning.oreilly.com/library/view/heat=
-and-mass/9789332515680/images/pg22_img2b.png" alt=3D"image" width=3D"71" h=
eight=3D"46" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg22_img2b.png"> and <img id=3D"img0331" class=3D"Eq1" src=3D"https://le=
arning.oreilly.com/library/view/heat-and-mass/9789332515680/images/pg22_img=
2a.png" alt=3D"image" width=3D"78" height=3D"46" data-mfp-src=3D"/library/v=
iew/heat-and-mass/9789332515680/images/pg22_img2a.png"></p>
<p id=3D"p0126" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0043" class=3D"imagewrap">
The heat transfer <img class=3D"Eq1" id=3D"img0040" src=3D"https://learning=
.oreilly.com/library/view/heat-and-mass/9789332515680/images/pg22_img3.png"=
 alt=3D"image" width=3D"375" height=3D"58" data-mfp-src=3D"/library/view/he=
at-and-mass/9789332515680/images/pg22_img3.png">
</div>
<p id=3D"p0127" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0128" class=3D"EB02BodyTextFullOut">where <em>R<sub class=3D"EBsu=
b">t</sub></em> =3D <em>R<sub class=3D"EBsub">h</sub></em> + <em>R</em><sub=
 class=3D"EBsub">l</sub> + <em>R</em><sub class=3D"EBsub">2</sub> + <em>R<s=
ub class=3D"EBsub">c</sub>.</em>, and <em>h<sub class=3D"EBsub">h</sub></em=
>, <em>h<sub class=3D"EBsub">c</sub></em> and <em>T<sub class=3D"EBsub">h</=
sub></em>, <em>T<sub class=3D"EBsub">c</sub></em> are the heat transfer coe=
fficients and temperatures at the hot and cold sides, respectively.</p>
<h4 id=3D"h40003" class=3D"EB10SmallHead"><a id=3D"ch02lev2sec3"></a>2.3.3 =
A Slab With Heat Generation and Uniform Thermal Conductivity</h4>
<p id=3D"p0129" class=3D"EB02BodyTextFullOut">In this case, heat transfer a=
nd heat generation are considered together as shown in <a href=3D"https://l=
earning.oreilly.com/library/view/heat-and-mass/9789332515680/xhtml/chapter0=
02.xhtml#figure2.9">Fig. 2.9</a> and the governing equation is</p>
<p id=3D"p0130" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0044" class=3D"imagewrap">
<img id=3D"img0332" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg23_img1.png" alt=3D"Slab with Heat Generatio=
n" width=3D"460" height=3D"313" data-mfp-src=3D"/library/view/heat-and-mass=
/9789332515680/images/pg23_img1.png">
<p id=3D"p0131" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0132" class=3D"EB28InlineCaption"><strong><a id=3D"figure2.9"></a=
>Figure 2.9</strong> Slab with Heat Generation</p></div>
<p id=3D"p0133" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0045" class=3D"imagewrap">
<img id=3D"img0333" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg22_img4.png" alt=3D"image" width=3D"84" heig=
ht=3D"36" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/=
pg22_img4.png">
</div>
<p id=3D"p0134" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0135" class=3D"EB03BodyTextIndented">The integrations of the equa=
tion give</p>
<p id=3D"p0136" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0046" class=3D"imagewrap"><a id=3D"eq2.15"></a>
<img id=3D"img0334" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg22_img5.png" alt=3D"image" width=3D"453" hei=
ght=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg22_img5.png">
</div>
<p id=3D"p0137" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0138" class=3D"EB02BodyTextFullOut"><a id=3D"page_23"></a><strong=
>Case (a) Different wall temperatures</strong></p>
<p id=3D"p0139" class=3D"EB02BodyTextFullOut">The boundary conditions are</=
p>
<ol id=3D"ol0002" class=3D"LowerRoman">
<li id=3D"li0007" class=3D"EB23ListFirst">at <em>x</em> =3D 0; <em>T</em> =
=3D <em>T</em><sub class=3D"EBsub">1</sub> and</li>
<li id=3D"li0008" class=3D"EB25ListLast">at <em>x</em> =3D <em>L</em>; <em>=
T</em> =3D <em>T</em><sub class=3D"EBsub">2</sub>.</li>
</ol>
<p id=3D"p0140" class=3D"EB03BodyTextIndented">Using these conditions in <a=
 href=3D"https://learning.oreilly.com/library/view/heat-and-mass/9789332515=
680/xhtml/chapter002.xhtml#eq2.15">Equation (2.15)</a>, we get</p>
<p id=3D"p0141" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0047" class=3D"imagewrap">
<img id=3D"img0335" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg23_img2.png" alt=3D"image" width=3D"211" hei=
ght=3D"36" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg23_img2.png">
</div>
<p id=3D"p0142" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0143" class=3D"EB03BodyTextIndented">The temperature distribution=
 becomes</p>
<p id=3D"p0144" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0048" class=3D"imagewrap">
<img id=3D"img0336" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg23_img3.png" alt=3D"image" width=3D"419" hei=
ght=3D"109" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg23_img3.png">
</div>
<p id=3D"p0145" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0049" class=3D"imagewrap">
<img id=3D"img0337" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg23_img4.png" alt=3D"image" width=3D"247" hei=
ght=3D"73" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg23_img4.png">
</div>
<p id=3D"p0146" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0147" class=3D"EB03BodyTextIndented"><a id=3D"page_24"></a>In the=
 dimensionless form,</p>
<p id=3D"p0148" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0050" class=3D"imagewrap">
<img id=3D"img0338" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg24_img1.png" alt=3D"image" width=3D"262" hei=
ght=3D"47" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg24_img1.png">
</div>
<p id=3D"p0149" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0150" class=3D"EB02BodyTextFullOut"><strong>Case (b) Wall surface=
s at same temperature</strong></p>
<p id=3D"p0151" class=3D"EB02BodyTextFullOut">If the both walls are at same=
 temperature (<em>T</em><sub class=3D"EBsub">1</sub> =3D <em>T</em><sub cla=
ss=3D"EBsub">2</sub> =3D <em>T<sub class=3D"EBsub">w</sub></em>), then <a h=
ref=3D"https://learning.oreilly.com/library/view/heat-and-mass/978933251568=
0/xhtml/chapter002.xhtml#eq2.15">Equation (2.15)</a> becomes</p>
<p id=3D"p0152" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0051" class=3D"imagewrap">
<img id=3D"img0339" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg24_img2.png" alt=3D"image" width=3D"178" hei=
ght=3D"113" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg24_img2.png">
</div>
<p id=3D"p0153" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0154" class=3D"EB03BodyTextIndented">The maximum temperature occu=
rs at the center plane <img id=3D"img0340" class=3D"Eq1" src=3D"https://lea=
rning.oreilly.com/library/view/heat-and-mass/9789332515680/images/pg24_img2=
a.png" alt=3D"image" width=3D"50" height=3D"38" data-mfp-src=3D"/library/vi=
ew/heat-and-mass/9789332515680/images/pg24_img2a.png"> and the distribution=
 of temperature is parabolic about the mid-plane:</p>
<p id=3D"p0155" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0052" class=3D"imagewrap">
<img id=3D"img0341" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg24_img3.png" alt=3D"image" width=3D"106" hei=
ght=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg24_img3.png">
</div>
<p id=3D"p0156" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0157" class=3D"EB03BodyTextIndented">Heat transfer from one side =
of the wall is given by</p>
<p id=3D"p0158" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0053" class=3D"imagewrap">
<img id=3D"img0342" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg24_img4.png" alt=3D"image" width=3D"193" hei=
ght=3D"41" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg24_img4.png">
</div>
<p id=3D"p0159" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0160" class=3D"EB03BodyTextIndented">For both sides, <em>Q</em> =
=3D <em>ALq<sub class=3D"EBsub">g</sub></em> =3D heat generated in the wall=
. If heat is transferred to surrounding atmosphere at temperature (<em>T<su=
b class=3D"EBsub">a</sub></em>) from the wall, then</p>
<p id=3D"p0161" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0054" class=3D"imagewrap">
<img id=3D"img0343" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg24_img5.png" alt=3D"image" width=3D"227" hei=
ght=3D"36" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg24_img5.png">
</div>
<p id=3D"p0162" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0163" class=3D"EB02BodyTextFullOut">then heat transfer <img id=3D=
"img0344" class=3D"Eq1" src=3D"https://learning.oreilly.com/library/view/he=
at-and-mass/9789332515680/images/pg24_img6.png" alt=3D"image" width=3D"173"=
 height=3D"39" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/im=
ages/pg24_img6.png"></p>
<h4 id=3D"h40004" class=3D"EB10SmallHead"><a id=3D"ch02lev2sec4"></a>2.3.4 =
One-dimensional Steady-state Heat Conduction in a Slab With Variable Therma=
l Conductivity</h4>
<p id=3D"p0164" class=3D"EB02BodyTextFullOut">Let the variation in thermal =
conductivity be linear with temperature as</p>
<p id=3D"p0165" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0055" class=3D"imagewrap"><em>k</em>(<em>T</em>) =3D <em>k<su=
b class=3D"EBsub">o</sub></em>(1 + <em>CT</em>)</div>
<p id=3D"p0166" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0167" class=3D"EB02BodyTextFullOut">where <em>k</em><sub class=3D=
"EBsub">0</sub> and <em>C</em> are constants. The governing equation is</p>
<p id=3D"p0168" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0056" class=3D"imagewrap">
<img id=3D"img0345" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg25_img1.png" alt=3D"Slab with Variable Therm=
al Conductivity" width=3D"226" height=3D"286" data-mfp-src=3D"/library/view=
/heat-and-mass/9789332515680/images/pg25_img1.png">
<p id=3D"p0169" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0170" class=3D"EB28InlineCaption"><strong><a id=3D"figure2.10"></=
a>Figure 2.10</strong> Slab with Variable Thermal Conductivity</p></div>
<p id=3D"p0171" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0057" class=3D"imagewrap"><a id=3D"page_25"></a>
<img id=3D"img0346" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg25_img2.png" alt=3D"image" width=3D"366" hei=
ght=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg25_img2.png">
</div>
<p id=3D"p0172" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0173" class=3D"EB03BodyTextIndented">Integrating and substituting=
 the boundary conditions, we get</p>
<p id=3D"p0174" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0058" class=3D"imagewrap"><em>x</em> =3D 0 &nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;<em>T</em> =3D <em>T</em><sub class=3D"EBsub">1</sub></div>=20
<div id=3D"div0059" class=3D"imagewrap"><em>x</em> =3D <em>L</em> &nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;<em>T</em> =3D <em>T</em><sub class=3D"EBsub">2</sub><=
/div>=20
<p id=3D"p0175" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0060" class=3D"imagewrap">
<img id=3D"img0347" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg25_img3.png" alt=3D"image" width=3D"200" hei=
ght=3D"122" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg25_img3.png">
</div>
<p id=3D"p0176" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0177" class=3D"EB02BodyTextFullOut">where <em>k<sub class=3D"EBsu=
b">m</sub></em>  =3D (1 + <em>CT<sub class=3D"EBsub">m</sub></em>)<em>k</em=
><sub class=3D"EBsub">o</sub> =3D mean thermal conductivity of material and=
 <img class=3D"Eq1" id=3D"img0056" src=3D"https://learning.oreilly.com/libr=
ary/view/heat-and-mass/9789332515680/images/pg25_img3a.png" alt=3D"image" w=
idth=3D"83" height=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/97893=
32515680/images/pg25_img3a.png"></p>
<h5 id=3D"h50005" class=3D"EB07SmallCapsMediumHead"><a id=3D"ch02lev1sec4">=
</a>2.4 A HOLLOW CYLINDER WITHOUT HEAT GENERATION</h5>
<p id=3D"p0178" class=3D"EB02BodyTextFullOut">Consider a hollow cylinder as=
 shown in <a href=3D"https://learning.oreilly.com/library/view/heat-and-mas=
s/9789332515680/xhtml/chapter002.xhtml#figure2.11">Fig. 2.11</a>. If the en=
tire inner and outer surfaces of the hollow cylinder are maintained at cons=
tant temperatures of <em>T</em><sub class=3D"EBsub">1</sub> and <em>T</em><=
sub class=3D"EBsub">2</sub>, then the heat transfer can take place only in =
the radial direction. The governing equation for this one-dimensional stead=
y-state problem is</p>
<p id=3D"p0179" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0061" class=3D"imagewrap">
<a id=3D"eq2.20"></a><img id=3D"img0348" src=3D"https://learning.oreilly.co=
m/library/view/heat-and-mass/9789332515680/images/pg26_img1.png" alt=3D"Hol=
low Cylinder" width=3D"498" height=3D"323" data-mfp-src=3D"/library/view/he=
at-and-mass/9789332515680/images/pg26_img1.png">
<p id=3D"p0180" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0181" class=3D"EB28InlineCaption"><strong><a id=3D"figure2.11"></=
a>Figure 2.11</strong> Hollow Cylinder</p></div>
<p id=3D"p0182" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0062" class=3D"imagewrap">
<img id=3D"img0349" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg25_img4.png" alt=3D"image" width=3D"427" hei=
ght=3D"41" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg25_img4.png">
</div>
<p id=3D"p0183" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0184" class=3D"EB03BodyTextIndented"><a id=3D"page_26"></a>The bo=
undary conditions are</p>
<ol id=3D"ol0003" class=3D"LowerRoman">
<li id=3D"li0009" class=3D"EB23ListFirst"><em>r</em> =3D <em>r</em><sub cla=
ss=3D"EBsub">1</sub> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<em>T</em> =3D <em>T</em=
><sub class=3D"EBsub">1</sub> and</li>
<li id=3D"li0010" class=3D"EB25ListLast"><em>r</em> =3D <em>r</em><sub clas=
s=3D"EBsub">2</sub> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<em>T</em> =3D <em>=
T</em><sub class=3D"EBsub">2</sub>.</li>
</ol>
<p id=3D"p0185" class=3D"EB03BodyTextIndented">Integrating <a href=3D"https=
://learning.oreilly.com/library/view/heat-and-mass/9789332515680/xhtml/chap=
ter002.xhtml#eq2.20">Equation (2.20)</a>, we get</p>
<p id=3D"p0186" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0063" class=3D"imagewrap">
<img id=3D"img0350" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg26_img2.png" alt=3D"image" width=3D"198" hei=
ght=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg26_img2.png">
</div>
<p id=3D"p0187" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0188" class=3D"EB03BodyTextIndented">Applying the above boundary =
conditions, the equation for the temperature distribution in the radial dir=
ection is given as</p>
<p id=3D"p0189" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0064" class=3D"imagewrap">
<img id=3D"img0351" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg26_img3.png" alt=3D"image" width=3D"522" hei=
ght=3D"37" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg26_img3.png">
</div>
<p id=3D"p0190" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0191" class=3D"EB03BodyTextIndented">Heat transfer rate</p>
<p id=3D"p0192" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0065" class=3D"imagewrap">
<img id=3D"img0352" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg26_img4.png" alt=3D"image" width=3D"222" hei=
ght=3D"118" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg26_img4.png">
</div>
<p id=3D"p0193" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0194" class=3D"EB02BodyTextFullOut">where <em>R</em> is the therm=
al resistance and is equal to <img id=3D"img0353" class=3D"Eq1" src=3D"http=
s://learning.oreilly.com/library/view/heat-and-mass/9789332515680/images/pg=
26_img4a.png" alt=3D"image" width=3D"78" height=3D"46" data-mfp-src=3D"/lib=
rary/view/heat-and-mass/9789332515680/images/pg26_img4a.png"></p>
<h4 id=3D"h40005" class=3D"EB10SmallHead"><a id=3D"page_27"></a><a id=3D"ch=
02lev2sec5"></a>2.4.1 A Hollow Cylinder With Convection Boundaries</h4>
<p id=3D"p0195" class=3D"EB02BodyTextFullOut">The heat transfer equations f=
or cylinder with convection is</p>
<p id=3D"p0196" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0066" class=3D"imagewrap">
<img id=3D"img0354" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg27_img1.png" alt=3D"image" width=3D"307" hei=
ght=3D"65" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg27_img1.png">
</div>
<p id=3D"p0197" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0198" class=3D"EB03BodyTextIndented">Simplifying the equation</p>
<p id=3D"p0199" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0067" class=3D"imagewrap">
<img id=3D"img0355" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg27_img1a.png" alt=3D"image" width=3D"164" he=
ight=3D"84" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg27_img1a.png">
</div>
<p id=3D"p0200" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0201" class=3D"EB02BodyTextFullOut">where <em>A<sub class=3D"EBsu=
b">h</sub></em> =3D 2=CF=80<em>r</em><sub class=3D"EBsub">l</sub> <em>L</em=
>, <em>A<sub class=3D"EBsub">c</sub></em> =3D 2=CF=80<em>r</em><sub class=
=3D"EBsub">2</sub><em>L</em>.</p>
<p id=3D"p0202" class=3D"EB02BodyTextFullOut">The electrical analogy of thi=
s case is shown in <a href=3D"https://learning.oreilly.com/library/view/hea=
t-and-mass/9789332515680/xhtml/chapter002.xhtml#figure2.12">Fig. 2.12</a>.<=
/p>
<p id=3D"p0203" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0068" class=3D"imagewrap">
<img id=3D"img0356" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg27_img1b.png" alt=3D"Electrical analogy" wid=
th=3D"175" height=3D"45" data-mfp-src=3D"/library/view/heat-and-mass/978933=
2515680/images/pg27_img1b.png">
<p id=3D"p0204" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0205" class=3D"EB28InlineCaption"><strong><a id=3D"figure2.12"></=
a>Figure 2.12</strong> Electrical analogy</p></div>
<p id=3D"p0206" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0069" class=3D"imagewrap">
<img id=3D"img0357" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg27_img1c.png" alt=3D"image" width=3D"165" he=
ight=3D"38" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg27_img1c.png">
</div>
<h4 id=3D"h40006" class=3D"EB10SmallHead"><a id=3D"ch02lev2sec6"></a>2.4.2 =
A Solid Cylinder With Heat Generation</h4>
<p id=3D"p0207" class=3D"EB02BodyTextFullOut">The governing equation for th=
is case is</p>
<p id=3D"p0208" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0070" class=3D"imagewrap">
<img id=3D"img0358" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg27_img2.png" alt=3D"image" width=3D"433" hei=
ght=3D"41" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg27_img2.png">
</div>
<p id=3D"p0209" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0210" class=3D"EB03BodyTextIndented">Integrating the above equati=
on, we get</p>
<p id=3D"p0211" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0071" class=3D"imagewrap">
<img id=3D"img0359" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg27_img3.png" alt=3D"image" width=3D"281" hei=
ght=3D"38" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg27_img3.png">
</div>
<p id=3D"p0212" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0213" class=3D"EB03BodyTextIndented">Substituting the following b=
oundary conditions:</p>
<ol id=3D"ol0004" class=3D"LowerRoman">
<li id=3D"li0011" class=3D"EB23ListFirst"><em>r</em> =3D 0; <img id=3D"img0=
360" class=3D"Eq1" src=3D"https://learning.oreilly.com/library/view/heat-an=
d-mass/9789332515680/images/pg27_img3b.png" alt=3D"image" width=3D"49" heig=
ht=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/=
pg27_img3b.png"></li>
<li id=3D"li0012" class=3D"EB25ListLast">at <em>r</em> =3D <em>R</em>; <em>=
T</em> =3D <em>T<sub class=3D"EBsub">w</sub></em>, the values of constants =
are <em>C</em><sub class=3D"EBsub">1</sub>, =3D 0 and <img id=3D"img0361" c=
lass=3D"Eq1" src=3D"https://learning.oreilly.com/library/view/heat-and-mass=
/9789332515680/images/pg27_img3c.png" alt=3D"image" width=3D"100" height=3D=
"38" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/pg27_=
img3c.png"></li>
</ol>
<p id=3D"p0214" class=3D"EB03BodyTextIndented">Thus the temperature distrib=
ution is</p>
<p id=3D"p0215" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0072" class=3D"imagewrap">
<img id=3D"img0362" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg27_img3d.png" alt=3D"image" width=3D"374" he=
ight=3D"32" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg27_img3d.png">
</div>
<p id=3D"p0216" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0217" class=3D"EB03BodyTextIndented">The maximum occurs at the ce=
nter and its value is given by</p>
<p id=3D"p0218" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0073" class=3D"imagewrap">
<img id=3D"img0363" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg27_img4.png" alt=3D"image" width=3D"108" hei=
ght=3D"32" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg27_img4.png">
</div>
<p id=3D"p0219" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0220" class=3D"EB03BodyTextIndented"><a id=3D"page_28"></a>Then t=
he dimensionless form of the temperature distribution becomes</p>
<p id=3D"p0221" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0074" class=3D"imagewrap">
<img id=3D"img0364" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg28_img1.png" alt=3D"image" width=3D"122" hei=
ght=3D"43" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg28_img1.png">
</div>
<p id=3D"p0222" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0223" class=3D"EB03BodyTextIndented">If the generated heat within=
 the rod is transferred to the surroundings (<em>T<sub class=3D"EBsub">a</s=
ub></em>) by convection, then</p>
<p id=3D"p0224" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0075" class=3D"imagewrap">(=CF=80<em>R</em><sup class=3D"EBsu=
p">2</sup> <em>L</em>)<em>q<sub class=3D"EBsub">g</sub></em> =3D 2 =CF=80 <=
em>hRL</em>(<em>T<sub class=3D"EBsub">w</sub></em> =E2=80=93 <em>T<sub clas=
s=3D"EBsub">a</sub></em>)</div>
<p id=3D"p0225" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0076" class=3D"imagewrap">
<img id=3D"img0365" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg28_img2.png" alt=3D"image" width=3D"123" hei=
ght=3D"35" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg28_img2.png">
</div>
<h5 id=3D"h50006" class=3D"EB07SmallCapsMediumHead"><a id=3D"ch02lev1sec5">=
</a>2.5 A HOLLOW SPHERE WITHOUT HEAT GENERATION</h5>
<p id=3D"p0226" class=3D"EB02BodyTextFullOut">Consider a sphere as shown in=
 <a href=3D"https://learning.oreilly.com/library/view/heat-and-mass/9789332=
515680/xhtml/chapter002.xhtml#figure2.13">Fig. 2.13</a>. According to Fouri=
er's Law, the heat transfer in the radial direction is given by</p>
<p id=3D"p0227" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0077" class=3D"imagewrap">
<img id=3D"img0366" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg28_img3.png" alt=3D"Hollow Sphere" width=3D"=
402" height=3D"189" data-mfp-src=3D"/library/view/heat-and-mass/97893325156=
80/images/pg28_img3.png">
<p id=3D"p0228" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0229" class=3D"EB28InlineCaption"><strong><a id=3D"figure2.13"></=
a>Figure 2.13</strong> Hollow Sphere</p></div>
<p id=3D"p0230" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0078" class=3D"imagewrap">
<img id=3D"img0367" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg28_img4.png" alt=3D"image" width=3D"376" hei=
ght=3D"94" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg28_img4.png">
</div>
<p id=3D"p0231" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0232" class=3D"EB03BodyTextIndented">Integrating these equations,=
 we get</p>
<p id=3D"p0233" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0079" class=3D"imagewrap">
<img id=3D"img0368" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg28_img5.png" alt=3D"image" width=3D"192" hei=
ght=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg28_img5.png">
</div>
<p id=3D"p0234" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0235" class=3D"EB03BodyTextIndented">Using the following boundary=
 conditions:</p>
<ol id=3D"ol0005" class=3D"LowerRoman">
<li id=3D"li0013" class=3D"EB23ListFirst"><em>r</em> =3D <em>r</em><sub cla=
ss=3D"EBsub">1</sub> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<em>T</em> =3D <em>T</em=
><sub class=3D"EBsub">1</sub></li>
<li id=3D"li0014" class=3D"EB25ListLast"><em>r</em> =3D <em>r</em><sub clas=
s=3D"EBsub">2</sub> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<em>T</em> =3D <em>T</em>=
<sub class=3D"EBsub">2</sub></li>
</ol>
<p id=3D"p0236" class=3D"EB03BodyTextIndented">we obtain the following rela=
tions:</p>
<p id=3D"p0237" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0080" class=3D"imagewrap">
<img id=3D"img0369" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg28_img6.png" alt=3D"image" width=3D"173" hei=
ght=3D"37" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg28_img6.png">
</div>
<p id=3D"p0238" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0081" class=3D"imagewrap"><a id=3D"page_29"></a>
<img id=3D"img0370" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg29_img1.png" alt=3D"image" width=3D"345" hei=
ght=3D"240" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg29_img1.png">
</div>
<p id=3D"p0239" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0240" class=3D"EB03BodyTextIndented">The values of the constants =
are</p>
<p id=3D"p0241" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0082" class=3D"imagewrap">
<img class=3D"Eq1" id=3D"img0080" src=3D"https://learning.oreilly.com/libra=
ry/view/heat-and-mass/9789332515680/images/pg29_img1a.png" alt=3D"image" wi=
dth=3D"102" height=3D"37" data-mfp-src=3D"/library/view/heat-and-mass/97893=
32515680/images/pg29_img1a.png"> and <em>C</em><sub class=3D"EBsub">2</sub>=
 =3D <em>T</em><sub class=3D"EBsub">1</sub> + [(<em>T</em><sub class=3D"EBs=
ub">1</sub> =E2=88=92 <em>T</em><sub class=3D"EBsub">2</sub>)(<em>r</em><su=
b class=3D"EBsub">1</sub><em>r</em><sub class=3D"EBsub">2</sub>)/<em>r</em>=
<sub class=3D"EBsub">1</sub>(<em>r</em><sub class=3D"EBsub">1</sub> =E2=88=
=92 <em>r</em><sub class=3D"EBsub">2</sub>)].
</div>
<p id=3D"p0242" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0243" class=3D"EB03BodyTextIndented">Substituting the values of c=
onstants, the temperature distribution becomes</p>
<p id=3D"p0244" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0083" class=3D"imagewrap">
<img id=3D"img0371" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg29_img1b.png" alt=3D"image" width=3D"278" he=
ight=3D"394" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg29_img1b.png">
</div>
<p id=3D"p0245" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0246" class=3D"EB03BodyTextIndented">In non-dimensional form,</p>
<p id=3D"p0247" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0084" class=3D"imagewrap">
<img id=3D"img0372" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg29_img1c.png" alt=3D"image" width=3D"122" he=
ight=3D"43" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg29_img1c.png">
</div>
<p id=3D"p0248" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0249" class=3D"EB03BodyTextIndented">Then the heat transfer is gi=
ven by the expression</p>
<p id=3D"p0250" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0085" class=3D"imagewrap"><a id=3D"page_30"></a>
<img id=3D"img0373" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg29_img2.png" alt=3D"image" width=3D"162" hei=
ght=3D"41" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg29_img2.png">
</div>
<p id=3D"p0251" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0252" class=3D"EB03BodyTextIndented">Simplifying this, we get</p>
<p id=3D"p0253" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0086" class=3D"imagewrap">
<img id=3D"img0374" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg29_img2c.png" alt=3D"image" width=3D"150" he=
ight=3D"65" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg29_img2c.png">
</div>
<p id=3D"p0254" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0255" class=3D"EB02BodyTextFullOut">where <em>R</em> is the resis=
tance and is equal to <img id=3D"img0375" class=3D"Eq1" src=3D"https://lear=
ning.oreilly.com/library/view/heat-and-mass/9789332515680/images/pg29_img2b=
.png" alt=3D"image" width=3D"86" height=3D"46" data-mfp-src=3D"/library/vie=
w/heat-and-mass/9789332515680/images/pg29_img2b.png"></p>
<h4 id=3D"h40007" class=3D"EB10SmallHead"><a id=3D"ch02lev2sec7"></a>2.5.1 =
A Hollow Sphere with Convection Heat Transfer and Without Heat Generation</=
h4>
<p id=3D"p0256" class=3D"EB02BodyTextFullOut">Similar to plain wall and hol=
low cylinder equations, the heat transfer in a hollow sphere with convectio=
n heat transfer (<a href=3D"https://learning.oreilly.com/library/view/heat-=
and-mass/9789332515680/xhtml/chapter002.xhtml#figure2.14">Fig. 2.14</a>) is=
 given by</p>
<p id=3D"p0257" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0087" class=3D"imagewrap">
<img id=3D"img0376" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg30_img1.png" alt=3D"Hollow Sphere with Conve=
ction Heat Transter" width=3D"355" height=3D"219" data-mfp-src=3D"/library/=
view/heat-and-mass/9789332515680/images/pg30_img1.png">
<p id=3D"p0258" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0259" class=3D"EB28InlineCaption"><strong><a id=3D"figure2.14"></=
a>Figure 2.14</strong> Hollow Sphere with Convection Heat Transfer</p></div=
>
<p id=3D"p0260" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0088" class=3D"imagewrap">
<img id=3D"img0377" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg30_img3.png" alt=3D"image" width=3D"81" heig=
ht=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/=
pg30_img3.png">
</div>
<p id=3D"p0261" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0262" class=3D"EB02BodyTextFullOut">where <em>R<sub class=3D"EBsu=
b">t</sub></em> =3D <em>R<sub class=3D"EBsub">h</sub></em>, + <em>R</em><su=
b class=3D"EBsub">1</sub>, + <em>R<sub class=3D"EBsub">c</sub></em>;</p>
<p id=3D"p0263" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0089" class=3D"imagewrap">
<img id=3D"img0378" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg30_img4.png" alt=3D"image" width=3D"413" hei=
ght=3D"48" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg30_img4.png">
</div>
<h4 id=3D"h40008" class=3D"EB10SmallHead"><a id=3D"ch02lev2sec8"></a>2.5.2 =
A Hollow Composite Sphere Without Heat Generation</h4>
<p id=3D"p0264" class=3D"EB02BodyTextFullOut">Considering a two-layer compo=
site sphere as shown in <a href=3D"https://learning.oreilly.com/library/vie=
w/heat-and-mass/9789332515680/xhtml/chapter002.xhtml#figure2.14">Fig. 2.14<=
/a>, and adopting the usual procedure we get the following equation:</p>
<p id=3D"p0265" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0090" class=3D"imagewrap"><a id=3D"page_31"></a>
<img id=3D"img0379" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg31_img01.png" alt=3D"image" width=3D"274" he=
ight=3D"58" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg31_img01.png">
</div>
<p id=3D"p0266" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0091" class=3D"imagewrap">
<img id=3D"img0380" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg31_img02.png" alt=3D"image" width=3D"394" he=
ight=3D"60" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg31_img02.png">
</div>
<p id=3D"p0267" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0268" class=3D"EB03BodyTextIndented">If there are =E2=80=98<em>n<=
/em>=E2=80=99 layers, then</p>
<p id=3D"p0269" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0092" class=3D"imagewrap">
<img id=3D"img0381" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg31_img03.png" alt=3D"image" width=3D"231" he=
ight=3D"61" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg31_img03.png">
</div>
<p id=3D"p0270" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0271" class=3D"EB03BodyTextIndented">Then, the above equation wit=
h our convection can be written as</p>
<p id=3D"p0272" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0093" class=3D"imagewrap">
<img id=3D"img0382" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg31_img04.png" alt=3D"image" width=3D"124" he=
ight=3D"62" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg31_img04.png">
</div>
<h4 id=3D"h40009" class=3D"EB10SmallHead"><a id=3D"ch02lev2sec9"></a>2.5.3 =
Solid Sphere With Heat Generation</h4>
<p id=3D"p0273" class=3D"EB02BodyTextFullOut">Let a solid sphere of radius =
(<em>R</em>) be subjected with heat generation (<em>q<sub class=3D"EBsub">g=
</sub></em>) and surface temperature (<em>T<sub class=3D"EBsub">w</sub></em=
>).</p>
<p id=3D"p0274" class=3D"EB03BodyTextIndented">The controlling equation is =
<img class=3D"Eq1" id=3D"img0093" src=3D"https://learning.oreilly.com/libra=
ry/view/heat-and-mass/9789332515680/images/pg31_img05.png" alt=3D"image" wi=
dth=3D"122" height=3D"36" data-mfp-src=3D"/library/view/heat-and-mass/97893=
32515680/images/pg31_img05.png"></p>
<p id=3D"p0275" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0094" class=3D"imagewrap">
<img id=3D"img0383" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg31_img05f.png" alt=3D"image" width=3D"166" h=
eight=3D"44" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg31_img05f.png">
</div>
<p id=3D"p0276" class=3D"EB02BodyTextFullOut">&nbsp;</p>

<p id=3D"p0277" class=3D"EB03BodyTextIndented">Integrating the above equati=
on, we get</p>
<p id=3D"p0278" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0095" class=3D"imagewrap">
<img id=3D"img0384" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg31_img05a.png" alt=3D"image" width=3D"127" h=
eight=3D"35" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg31_img05a.png">
</div>
<p id=3D"p0279" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0280" class=3D"EB03BodyTextIndented">Using the boundary condition=
, i.e., <em>r</em> =3D 0; <img id=3D"img0385" class=3D"Eq1" src=3D"https://=
learning.oreilly.com/library/view/heat-and-mass/9789332515680/images/pg31_i=
mg05b.png" alt=3D"image" width=3D"46" height=3D"34" data-mfp-src=3D"/librar=
y/view/heat-and-mass/9789332515680/images/pg31_img05b.png"> and <em>r</em> =
=3D <em>R</em>; <em>T</em> =3D <em>T<sub class=3D"EBsub">w</sub></em>.</p>
<p id=3D"p0281" class=3D"EB02BodyTextFullOut">we get <em>C</em><sub class=
=3D"EBsub">1</sub> =3D 0; and <img id=3D"img0386" class=3D"Eq1" src=3D"http=
s://learning.oreilly.com/library/view/heat-and-mass/9789332515680/images/pg=
31_img05c.png" alt=3D"image" width=3D"99" height=3D"38" data-mfp-src=3D"/li=
brary/view/heat-and-mass/9789332515680/images/pg31_img05c.png"></p>
<p id=3D"p0282" class=3D"EB03BodyTextIndented">Therefore, the temperature d=
istribution is given by</p>
<p id=3D"p0283" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0096" class=3D"imagewrap">
<img id=3D"img0387" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg31_img05d.png" alt=3D"image" width=3D"168" h=
eight=3D"47" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg31_img05d.png">
</div>
<p id=3D"p0284" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0285" class=3D"EB03BodyTextIndented"><a id=3D"page_32"></a>The te=
mperature distribution is parabolic and the maximum temperature occurs at t=
he center (<em>r</em> =3D 0).</p>
<p id=3D"p0286" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0097" class=3D"imagewrap">
<img id=3D"img0388" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg32_img01.png" alt=3D"image" width=3D"124" he=
ight=3D"38" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg32_img01.png">
</div>
<p id=3D"p0287" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0288" class=3D"EB03BodyTextIndented">In non-dimensional form,</p>
<p id=3D"p0289" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0098" class=3D"imagewrap">
<img id=3D"img0389" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg32_img02.png" alt=3D"image" width=3D"122" he=
ight=3D"44" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg32_img02.png">
</div>
<p id=3D"p0290" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0291" class=3D"EB03BodyTextIndented">Therefore the heat transfer<=
/p>
<p id=3D"p0292" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0099" class=3D"imagewrap">
<img id=3D"img0390" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg32_img03.png" alt=3D"image" width=3D"206" he=
ight=3D"39" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg32_img03.png">
</div>
<p id=3D"p0293" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0294" class=3D"EB03BodyTextIndented">The wall temperature in term=
s of the ambient temperature (<em>T<sub class=3D"EBsub">a</sub></em>):</p>
<p id=3D"p0295" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0100" class=3D"imagewrap">
<img id=3D"img0391" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg32_img04.png" alt=3D"image" width=3D"314" he=
ight=3D"36" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg32_img04.png">
</div>
<h4 id=3D"h40010" class=3D"EB10SmallHead"><a id=3D"ch02lev2sec10"></a>2.5.4=
 Logarithmic Mean Area for Hollow Cylinder and Sphere</h4>
<p id=3D"p0296" class=3D"EB02BodyTextFullOut">The heat transfer through a h=
ollow cylinder and sphere can be written in a form such that it is equivale=
nt to heat transfer through a plane wall having the thickness of (<em>r</em=
><sub class=3D"EBsub">2</sub> =E2=80=93<em>r</em><sub class=3D"EBsub">1</su=
b>) and area of <em>A<sub class=3D"EBsub">m</sub></em> with the same temper=
ature difference and thermal conductivity.</p>
<p id=3D"p0297" class=3D"EB03BodyTextIndented">The heat transfer through a =
cylinder is given by</p>
<p id=3D"p0298" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0101" class=3D"imagewrap">
<img id=3D"img0392" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg32_img05.png" alt=3D"image" width=3D"372" he=
ight=3D"37" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg32_img05.png">
</div>
<p id=3D"p0299" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0300" class=3D"EB03BodyTextIndented">The heat transfer through a =
plane wall is given by</p>
<p id=3D"p0301" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0102" class=3D"imagewrap">
<img id=3D"img0393" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg32_img06.png" alt=3D"image" width=3D"369" he=
ight=3D"37" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg32_img06.png">
</div>
<p id=3D"p0302" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0303" class=3D"EB03BodyTextIndented">Equating <a href=3D"https://=
learning.oreilly.com/library/view/heat-and-mass/9789332515680/xhtml/chapter=
002.xhtml#Eq2.29">Equations (2.29)</a> and <a href=3D"https://learning.orei=
lly.com/library/view/heat-and-mass/9789332515680/xhtml/chapter002.xhtml#Eq2=
.29">(2.30)</a>, we get</p>
<p id=3D"p0304" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0103" class=3D"imagewrap">
<a id=3D"Eq2.29"></a><img id=3D"img0394" src=3D"https://learning.oreilly.co=
m/library/view/heat-and-mass/9789332515680/images/pg32_img07.png" alt=3D"im=
age" width=3D"212" height=3D"101" data-mfp-src=3D"/library/view/heat-and-ma=
ss/9789332515680/images/pg32_img07.png">
</div>
<p id=3D"p0305" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0306" class=3D"EB03BodyTextIndented">This area <em>A<sub class=3D=
"EBsub">m</sub></em> is called the logarithmic mean area of the hollow cyli=
nder.</p>
<p id=3D"p0307" class=3D"EB03BodyTextIndented">Similarly, for a hollow sphe=
re, we get</p>
<p id=3D"p0308" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0104" class=3D"imagewrap">
<img id=3D"img0395" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg32_img08.png" alt=3D"image" width=3D"187" he=
ight=3D"37" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg32_img08.png">
</div>
<p id=3D"p0309" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0105" class=3D"imagewrap"><a id=3D"page_33"></a>
<img id=3D"img0396" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg33_img01.png" alt=3D"image" width=3D"140" he=
ight=3D"22" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg33_img01.png">
</div>
<p id=3D"p0310" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0311" class=3D"EB02BodyTextFullOut">where <em>A<sub class=3D"EBsu=
b">m</sub></em> is the geometric mean area of the sphere.</p>
<h4 id=3D"h40011" class=3D"EB10SmallHead"><a id=3D"ch02lev2sec11"></a>2.5.5=
 Thermal Contact Resistance</h4>
<p id=3D"p0312" class=3D"EB02BodyTextFullOut">Consider two solid bars are b=
rought into contact as shown in <a href=3D"https://learning.oreilly.com/lib=
rary/view/heat-and-mass/9789332515680/xhtml/chapter002.xhtml#figure2.15">Fi=
g. 2.15</a>. The sides of the bars are insulated so that the heat flows alo=
ng the axial direction. At steady-state conditions, the heat flow is consta=
nt. But there is no temperature drop in the contact plane between the two r=
ods. This drop is mainly due to resistance offered by gases entrapped in th=
e void spaces created by the contact. The resistance due to these gases is =
called the thermal contact resistance.</p>
<p id=3D"p0313" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0106" class=3D"imagewrap">
<img id=3D"img0397" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg33_img02.png" alt=3D"Thermal Contact Resista=
nce in a Slab" width=3D"392" height=3D"228" data-mfp-src=3D"/library/view/h=
eat-and-mass/9789332515680/images/pg33_img02.png">
<p id=3D"p0314" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0315" class=3D"EB28InlineCaption"><strong><a id=3D"figure2.15"></=
a>Figure 2.15</strong> Thermal Contact Resistance in a Slab</p></div>
<p id=3D"p0316" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0317" class=3D"EB03BodyTextIndented">Heat flux <img id=3D"img0398=
" class=3D"Eq1" src=3D"https://learning.oreilly.com/library/view/heat-and-m=
ass/9789332515680/images/pg33_img03.png" alt=3D"image" width=3D"313" height=
=3D"39" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/pg=
33_img03.png"></p>
<p id=3D"p0318" class=3D"EB03BodyTextIndented">where <em>h<sub class=3D"EBs=
ub">c</sub></em> is called the contact coefficients and <img id=3D"img0399"=
 class=3D"Eq1" src=3D"https://learning.oreilly.com/library/view/heat-and-ma=
ss/9789332515680/images/pg33_img03a.png" alt=3D"image" width=3D"25" height=
=3D"37" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/pg=
33_img03a.png"> is called the contact thermal resistance.</p>
<h5 id=3D"h50007" class=3D"EB07SmallCapsMediumHead"><a id=3D"ch02lev1sec6">=
</a>2.6 CRITICAL THICKNESS OF INSULATION</h5>
<p id=3D"p0319" class=3D"EB02BodyTextFullOut">Insulation is usually provide=
d around a system (<a href=3D"https://learning.oreilly.com/library/view/hea=
t-and-mass/9789332515680/xhtml/chapter002.xhtml#figure2.16">Fig. 2.16</a>) =
to reduce the heat transfer. But it actually increases the heat flow upto a=
 certain thickness of insulation in the case of cylinders and spheres.</p>
<p id=3D"p0320" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0107" class=3D"imagewrap">
<img id=3D"img0400" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg34_img01.png" alt=3D"(a) Insulated Cylinder;=
 (b) Heat Loss as a Function of Insulation Thickness" width=3D"310" height=
=3D"549" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/p=
g34_img01.png">
<p id=3D"p0321" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0322" class=3D"EB28InlineCaption"><strong><a id=3D"figure2.16"></=
a>Figure 2.16</strong> (a) Insulated Cylinder; (b) Heat Loss as a Function =
of Insulation Thickness</p></div>
<p id=3D"p0323" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0108" class=3D"imagewrap">
<img id=3D"img0401" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg33_img04.png" alt=3D"image" width=3D"251" he=
ight=3D"58" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg33_img04.png">
</div>
<p id=3D"p0324" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0109" class=3D"imagewrap">
<img id=3D"img0402" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg33_img05.png" alt=3D"image" width=3D"194" he=
ight=3D"43" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg33_img05.png">
</div>
<p id=3D"p0325" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0326" class=3D"EB03BodyTextIndented"><a id=3D"page_34"></a>Consid=
er a cylindrical insulation around a cylinder of length <em>L</em> with inn=
er radius <em>r</em><sub class=3D"EBsub">1</sub> and outer radius <em>r</em=
><sub class=3D"EBsub">2</sub>. The temperature at the inner surface is <em>=
T</em><sub class=3D"EBsub">1</sub> and at the outer surface is <em>T</em><s=
ub class=3D"EBsub">2</sub>. If the convection heat transfer coefficient on =
the outer surface is <em>h</em><sub class=3D"EBsub">2</sub> and thermal con=
ductivity of the insulating material is <em>k</em>, then the heat loss over=
 the insulation in the radial direction can be given as</p>
<p id=3D"p0327" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0110" class=3D"imagewrap">
<img id=3D"img0403" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg34_img03.png" alt=3D"image" width=3D"385" he=
ight=3D"56" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg34_img03.png">
</div>
<p id=3D"p0328" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0329" class=3D"EB02BodyTextFullOut">where <em>T<sub class=3D"EBsu=
b">a</sub></em> is the surrounding temperature.</p>
<p id=3D"p0330" class=3D"EB03BodyTextIndented">To determine the maximum hea=
t loss with respect to <em>r</em><sub class=3D"EBsub">2</sub>, keeping all =
other parameters constants, we differentiate w.r.t. =E2=80=98<em>r</em><sub=
 class=3D"EBsub">2</sub>=E2=80=99 and equate the derivative equal to zero:<=
/p>
<p id=3D"p0331" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0111" class=3D"imagewrap">
<img id=3D"img0404" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg34_img04.png" alt=3D"image" width=3D"186" he=
ight=3D"46" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg34_img04.png">
</div>
<p id=3D"p0332" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0112" class=3D"imagewrap"><a id=3D"page_35"></a>
<img id=3D"img0405" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg35_img01.png" alt=3D"image" width=3D"174" he=
ight=3D"37" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg35_img01.png">
</div>
<p id=3D"p0333" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0113" class=3D"imagewrap">
<img id=3D"img0406" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg35_img02.png" alt=3D"image" width=3D"397" he=
ight=3D"37" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg35_img02.png">
</div>
<p id=3D"p0334" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0335" class=3D"EB03BodyTextIndented">The maximum heat loss occurs=
 at <img id=3D"img0407" class=3D"Eq1" src=3D"https://learning.oreilly.com/l=
ibrary/view/heat-and-mass/9789332515680/images/pg35_img03.png" alt=3D"image=
" width=3D"43" height=3D"36" data-mfp-src=3D"/library/view/heat-and-mass/97=
89332515680/images/pg35_img03.png"> and thereafter it decreases. This value=
 of <em>r<sub class=3D"EBsub">c</sub></em> is known as critical radius. The=
 thickness of the insulation should be always greater than the critical thi=
ckness.</p>
<p id=3D"p0336" class=3D"EB03BodyTextIndented">For a hollow sphere, the cri=
tical insulation thickness is given by</p>
<p id=3D"p0337" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0114" class=3D"imagewrap">
<img id=3D"img0408" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg35_img04.png" alt=3D"image" width=3D"334" he=
ight=3D"37" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg35_img04.png">
</div>
<h5 id=3D"h50008" class=3D"EB07SmallCapsMediumHead"><a id=3D"ch02lev1sec7">=
</a>2.7 FINS</h5>
<p id=3D"p0338" class=3D"EB02BodyTextFullOut">The extended solid surfaces t=
hat are used in order to increase the heat transfer by increasing the surfa=
ce area are known as fins. Fins are of different sizes, shapes, and dimensi=
ons. The commonly used shapes are shown in <a href=3D"https://learning.orei=
lly.com/library/view/heat-and-mass/9789332515680/xhtml/chapter002.xhtml#fig=
ure2.17">Fig. 2.17</a>. Fins are used in air-cooled engines, compressors, e=
lectric motor bodies, automobile radiators, and transformers.</p>
<p id=3D"p0339" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0115" class=3D"imagewrap">
<img id=3D"img0409" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg36_img01.png" alt=3D"(a) Rectangular Fin; (b=
) Circular or Annular Fin; (c) Triangular Fin" width=3D"423" height=3D"841"=
 data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/pg36_img0=
1.png">
<p id=3D"p0340" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0341" class=3D"EB28InlineCaption"><strong><a id=3D"figure2.17"></=
a>Figure 2.17</strong> (a) Rectangular Fin; (b) Circular or Annular Fin; (c=
) Triangular Fin</p></div>
<h4 id=3D"h40012" class=3D"EB10SmallHead"><a id=3D"ch02lev2sec12"></a>2.7.1=
 Rectangular Fin</h4>
<p id=3D"p0342" class=3D"EB02BodyTextFullOut">Consider a rectangular fin as=
 shown in <a href=3D"https://learning.oreilly.com/library/view/heat-and-mas=
s/9789332515680/xhtml/chapter002.xhtml#figure2.17">Fig. 2.17(a)</a> and the=
 control volume of a small element represented by =CE=B4<em>x</em>. The ene=
rgy balance in the control volume, for a steady-state condition, is given b=
y the heat conducted into the element is equal to the sum of heat conducted=
 out of the element and the heat convected out of the element:</p>
<p id=3D"p0343" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0116" class=3D"imagewrap">
<img id=3D"img0410" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg35_img05.png" alt=3D"image" width=3D"439" he=
ight=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg35_img05.png">
</div>
<p id=3D"p0344" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0117" class=3D"imagewrap">
<img id=3D"img0411" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg35_img06.png" alt=3D"image" width=3D"154" he=
ight=3D"35" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg35_img06.png">
</div>
<p id=3D"p0345" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0346" class=3D"EB02BodyTextFullOut">where <img id=3D"img0412" cla=
ss=3D"Eq1" src=3D"https://learning.oreilly.com/library/view/heat-and-mass/9=
789332515680/images/pg35_img07.png" alt=3D"image" width=3D"82" height=3D"34=
" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/pg35_img=
07.png"></p>
<p id=3D"p0347" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0118" class=3D"imagewrap">
<img id=3D"img0413" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg35_img08.png" alt=3D"image" width=3D"230" he=
ight=3D"36" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg35_img08.png">
</div>
<p id=3D"p0348" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0119" class=3D"imagewrap"><a id=3D"eq2.48"></a><img id=3D"img=
0414" src=3D"https://learning.oreilly.com/library/view/heat-and-mass/978933=
2515680/images/pg35_img09.png" alt=3D"image" width=3D"376" height=3D"36" da=
ta-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/pg35_img09.p=
ng">
</div>
<p id=3D"p0349" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0350" class=3D"EB02BodyTextFullOut">where <em>P</em> is the perim=
eter of the small element, <em>k</em> is the thermal conductivity of the fi=
n material, and <em>T<sub class=3D"EBsub">a</sub></em> is the atmospheric t=
emperature. The above equation can be rewritten as</p>
<p id=3D"p0351" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0120" class=3D"imagewrap"><a id=3D"eq2.49"></a><a id=3D"page_=
36"></a>
<img id=3D"img0415" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg35_img10.png" alt=3D"image" width=3D"354" he=
ight=3D"36" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg35_img10.png">
</div>
<p id=3D"p0352" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0353" class=3D"EB03BodyTextIndented"><a id=3D"page_37"></a><a hre=
f=3D"https://learning.oreilly.com/library/view/heat-and-mass/9789332515680/=
xhtml/chapter002.xhtml#eq2.49">Equation (2.49)</a> is called the one-dimens=
ional fin equation for a uniform cross-section,</p>
<p id=3D"p0354" class=3D"EB02BodyTextFullOut">where <img id=3D"img0416" cla=
ss=3D"Eq1" src=3D"https://learning.oreilly.com/library/view/heat-and-mass/9=
789332515680/images/pg37_img01.png" alt=3D"image" width=3D"163" height=3D"3=
4" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/pg37_im=
g01.png"></p>
<p id=3D"p0355" class=3D"EB03BodyTextIndented">The second-order <a href=3D"=
https://learning.oreilly.com/library/view/heat-and-mass/9789332515680/xhtml=
/chapter002.xhtml#eq2.49">equation (2.49)</a> has a general solution in the=
 form of</p>
<p id=3D"p0356" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0121" class=3D"imagewrap"><a id=3D"eq2.50"></a><em>=CE=B8</em=
> =3D <em>B</em><sub class=3D"EBsub">1</sub> e <sup class=3D"EBsup"><em>mx<=
/em></sup> + <em>B</em><sub class=3D"EBsub">2</sub> e <sup class=3D"EBsup">=
=E2=88=92<em>mx</em></sup> =3D <em>C</em><sub class=3D"EBsub">1</sub> cos <=
em>h</em><sub class=3D"EBsub">mx</sub> + <em>C</em><sub class=3D"EBsub">2</=
sub> sin <em>h</em><sub class=3D"EBsub">mx</sub>&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp; (2.50)</div>
<p id=3D"p0357" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0358" class=3D"EB02BodyTextFullOut">where <em>B</em><sub class=3D=
"EBsub">1</sub>, <em>B</em><sub class=3D"EBsub">2</sub>, <em>C</em><sub cla=
ss=3D"EBsub">1</sub>, and <em>C</em><sub class=3D"EBsub">2</sub> are consta=
nts. It is necessary to specify the boundary conditions to evaluate the con=
stants based on the physical situation. The boundary condition and temperat=
ure distributions are given in the following cases.</p>
<p id=3D"p0359" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0360" class=3D"EB02BodyTextFullOut"><strong>Case (a) The end of t=
he fin is insulated [negligible heat loss at the tip]</strong></p>
<p id=3D"p0361" class=3D"EB02BodyTextFullOut">In this case, the tip of the =
fin is assumed to be insulated.</p>
<p id=3D"p0362" class=3D"EB03BodyTextIndented">The boundary conditions for =
this case are</p>
<ol id=3D"ol0006" class=3D"LowerRoman">
<li id=3D"li0015" class=3D"EB23ListFirst">at <em>x</em> =3D 0, <em>T</em> =
=3D <em>T<sub class=3D"EBsub">b</sub></em>; &nbsp;&nbsp;&nbsp;&nbsp;and <em=
>=CE=B8</em> =3D <em>=CE=B8<sub class=3D"EBsub">b</sub></em> =3D <em>T<sub =
class=3D"EBsub">b</sub></em> =E2=88=92 <em>T<sub class=3D"EBsub">a</sub></e=
m> and</li>
<li id=3D"li0016" class=3D"EB25ListLast">at <em>x</em> =3D <em>L;</em> <img=
 id=3D"img0417" class=3D"Eq1" src=3D"https://learning.oreilly.com/library/v=
iew/heat-and-mass/9789332515680/images/pg37_img04.png" alt=3D"image" width=
=3D"47" height=3D"38" data-mfp-src=3D"/library/view/heat-and-mass/978933251=
5680/images/pg37_img04.png"></li>
</ol>
<p id=3D"p0363" class=3D"EB02BodyTextFullOut">where <em>T<sub class=3D"EBsu=
b">b</sub></em> is the base temperature of the fin. Applying these boundary=
 conditions in <a href=3D"https://learning.oreilly.com/library/view/heat-an=
d-mass/9789332515680/xhtml/chapter002.xhtml#eq2.50">Equation (2.50)</a> and=
 solving for constants <em>C</em><sub class=3D"EBsub">1</sub> and <em>C</em=
><sub class=3D"EBsub">2</sub>, we get <em>C</em><sub class=3D"EBsub">1</sub=
> =3D <em>=CE=B8<sub class=3D"EBsub">b</sub></em> and <em>C</em><sub class=
=3D"EBsub">2</sub> =3D =E2=88=92<em>=CE=B8<sub class=3D"EBsub">b</sub></em>=
 =C2=B7 tanh <em>mL</em>.. The temperature variation is=EF=80=A0</p>
<p id=3D"p0364" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0122" class=3D"imagewrap"><a id=3D"eq2.51"></a>
<img id=3D"img0418" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg37_img06.png" alt=3D"image" width=3D"376" he=
ight=3D"36" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg37_img06.png">
</div>
<p id=3D"p0365" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0366" class=3D"EB03BodyTextIndented"><a id=3D"page_38"></a>The he=
at transfer rate of the fin is calculated from <a href=3D"https://learning.=
oreilly.com/library/view/heat-and-mass/9789332515680/xhtml/chapter002.xhtml=
#eq2.51">Equation (2.51)</a> as</p>
<p id=3D"p0367" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0123" class=3D"imagewrap">
<img id=3D"img0419" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg37_img07.png" alt=3D"image" width=3D"320" he=
ight=3D"42" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg37_img07.png">
</div>
<p id=3D"p0368" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0124" class=3D"imagewrap">
<img id=3D"img0420" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg37_img08.png" alt=3D"image" width=3D"257" he=
ight=3D"21" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg37_img08.png">
</div>
<p id=3D"p0369" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0370" class=3D"EB02BodyTextFullOut"><strong>Case (b) Fin with con=
vention heat transfer at the end</strong></p>
<p id=3D"p0371" class=3D"EB02BodyTextFullOut">The boundary conditions are</=
p>
<ol id=3D"ol0007" class=3D"LowerRoman">
<li id=3D"li0017" class=3D"EB23ListFirst">at <em>x</em> =3D 0, <em>T</em> =
=3D <em>T<sub class=3D"EBsub">b</sub></em>; and <em>=CE=B8</em> =3D <em>=CE=
=B8<sub class=3D"EBsub">b</sub></em> =3D <em>T<sub class=3D"EBsub">b</sub><=
/em> =E2=88=92 <em>T<sub class=3D"EBsub">a</sub></em> and</li>
<li id=3D"li0018" class=3D"EB25ListLast">at <em>x</em> =3D <em>L</em>, =E2=
=80=93 <em>kA</em> <img id=3D"img0421" class=3D"Eq1" src=3D"https://learnin=
g.oreilly.com/library/view/heat-and-mass/9789332515680/images/pg37_img04a.p=
ng" alt=3D"image" width=3D"21" height=3D"33" data-mfp-src=3D"/library/view/=
heat-and-mass/9789332515680/images/pg37_img04a.png"> =3D <em>h=CE=B8<sub cl=
ass=3D"EBsub">L</sub></em> =3D <em>hA</em>(<em>T<sub class=3D"EBsub">L</sub=
></em> =E2=80=93 <em>T<sub class=3D"EBsub">a</sub></em>) i.e., =E2=80=93<em=
>k</em> <img id=3D"img0422" class=3D"Eq1" src=3D"https://learning.oreilly.c=
om/library/view/heat-and-mass/9789332515680/images/pg37_img04a.png" alt=3D"=
image" width=3D"21" height=3D"33" data-mfp-src=3D"/library/view/heat-and-ma=
ss/9789332515680/images/pg37_img04a.png"> =3D <em>h=CE=B8<sub class=3D"EBsu=
b">L</sub></em>.</li>
</ol>
<p id=3D"p0372" class=3D"EB03BodyTextIndented">Applying these boundary cond=
itions in <a href=3D"https://learning.oreilly.com/library/view/heat-and-mas=
s/9789332515680/xhtml/chapter002.xhtml#eq2.50">Equation (2.50)</a>, the tem=
perature variation is obtained as</p>
<p id=3D"p0373" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0125" class=3D"imagewrap">
<img id=3D"img0423" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg37_img11.png" alt=3D"image" width=3D"368" he=
ight=3D"38" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg37_img11.png">
</div>
<p id=3D"p0374" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0375" class=3D"EB03BodyTextIndented">The heat transfer rate of th=
e fin is</p>
<p id=3D"p0376" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0126" class=3D"imagewrap">
<img id=3D"img0424" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg38_img01.png" alt=3D"image" width=3D"385" he=
ight=3D"39" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg38_img01.png">
</div>
<p id=3D"p0377" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0378" class=3D"EB03BodyTextIndented">For a rectangular fin having=
 width (<em>w</em>) and thickness (<em>t</em>), then</p>
<p id=3D"p0379" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0127" class=3D"imagewrap">
<img class=3D"Eq1" id=3D"img0133" src=3D"https://learning.oreilly.com/libra=
ry/view/heat-and-mass/9789332515680/images/pg38_img02.png" alt=3D"image" wi=
dth=3D"187" height=3D"39" data-mfp-src=3D"/library/view/heat-and-mass/97893=
32515680/images/pg38_img02.png"> (<em>t</em> is small compared to <em>w</em=
>).
</div>
<p id=3D"p0380" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0381" class=3D"EB03BodyTextIndented">For a circular fin (pin-fin)=
</p>
<p id=3D"p0382" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0128" class=3D"imagewrap">
<img id=3D"img0425" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg38_img03.png" alt=3D"image" width=3D"109" he=
ight=3D"39" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg38_img03.png">=20
</div>
<p id=3D"p0383" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0384" class=3D"EB02BodyTextFullOut"><strong>Case (c) Fin tip at s=
pecific temperature</strong></p>
<p id=3D"p0385" class=3D"EB02BodyTextFullOut">If the end of the fin is expo=
sed to a specific temperature, then the boundary conditions are</p>
<ol id=3D"ol0008" class=3D"LowerRoman">
<li id=3D"li0019" class=3D"EB23ListFirst"><em>x</em> =3D 0, <em>T</em> =3D =
<em>T<sub class=3D"EBsub">b</sub></em>; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<em>=
=CE=B8</em> =3D <em>=CE=B8<sub class=3D"EBsub">b</sub></em> =3D <em>T<sub c=
lass=3D"EBsub">b</sub></em> =E2=80=93 <em>T<sub class=3D"EBsub">a</sub></em=
> and</li>
<li id=3D"li0020" class=3D"EB25ListLast"><em>x</em> =3D <em>L</em>, <em>T</=
em> =3D <em>T<sub class=3D"EBsub">L</sub></em>; &nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;=E2=88=B4 <em>=CE=B8</em> =3D <em>=CE=B8<sub class=3D"EBsub">L</sub></em=
> =3D <em>T<sub class=3D"EBsub">L</sub></em> =E2=80=93 <em>T<sub class=3D"E=
Bsub">a</sub></em></li>
</ol>
<p id=3D"p0386" class=3D"EB03BodyTextIndented">Applying these boundary cond=
itions in <a href=3D"https://learning.oreilly.com/library/view/heat-and-mas=
s/9789332515680/xhtml/chapter002.xhtml#eq2.50">Equation (2.50)</a>, the tem=
perature variation is given by</p>
<p id=3D"p0387" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0129" class=3D"imagewrap">
<img id=3D"img0426" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg38_img06.png" alt=3D"image" width=3D"385" he=
ight=3D"35" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg38_img06.png">
</div>
<p id=3D"p0388" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0389" class=3D"EB03BodyTextIndented">The heat transfer rate of th=
e fin is</p>
<p id=3D"p0390" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0130" class=3D"imagewrap">
<img id=3D"img0427" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg38_img07.png" alt=3D"image" width=3D"385" he=
ight=3D"39" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg38_img07.png">
</div>
<p id=3D"p0391" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0392" class=3D"EB02BodyTextFullOut"><strong>Case (d) Fin tip at f=
luid temperature (infinite long fin)</strong></p>
<p id=3D"p0393" class=3D"EB02BodyTextFullOut">If the fin is sufficiently lo=
ng, then the temperature of its tip reaches a value equal to the temperatur=
e of the surrounding fluid.</p>
<p id=3D"p0394" class=3D"EB03BodyTextIndented">The boundary conditions are<=
/p>
<ol id=3D"ol0009" class=3D"LowerRoman">
<li id=3D"li0021" class=3D"EB23ListFirst">at <em>x</em> =3D 0, &nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;<em>T</em> =3D <em>T<sub class=3D"EBsub">b</sub></em>; &n=
bsp;&nbsp;&nbsp;&nbsp;=E2=88=B4 <em>=CE=B8</em> =3D <em>=CE=B8<sub class=3D=
"EBsub">b</sub></em></li>
<li id=3D"li0022" class=3D"EB25ListLast">at <em>x</em> =3D <em>=CE=B1</em>,=
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<em>T</em> =3D <em>T<sub class=3D"EBsub">a</=
sub></em>; &nbsp;&nbsp;&nbsp;&nbsp;=E2=88=B4 <em>=CE=B8</em> =3D 0.</li>
</ol>
<p id=3D"p0395" class=3D"EB03BodyTextIndented">Applying these boundary cond=
itions in <a href=3D"https://learning.oreilly.com/library/view/heat-and-mas=
s/9789332515680/xhtml/chapter002.xhtml#eq2.50">Equation (2.50)</a>, the val=
ues of constants <em>C</em><sub class=3D"EBsub">1</sub> =3D <em>=CE=B8<sub =
class=3D"EBsub">b</sub></em> and <em>C</em><sub class=3D"EBsub">1</sub> =3D=
 <em>=CE=B8<sub class=3D"EBsub">b</sub></em> Co + <em>hmL</em>. Then the te=
mperature distribution</p>
<p id=3D"p0396" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0131" class=3D"imagewrap"><em>=CE=B8</em> =3D <em>=CE=B8<sub =
class=3D"EBsub">b</sub></em> [cos <em>h</em>(<em>mx</em>) =E2=80=93 cos <em=
>h</em>(<em>mL</em>) =C2=B7sin <em>h</em>(<em>mx</em>)] &nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
p;(2.57)</div>
<p id=3D"p0397" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0398" class=3D"EB03BodyTextIndented">The heat transfer rate of th=
e fin is <img id=3D"img0428" class=3D"Eq1" src=3D"https://learning.oreilly.=
com/library/view/heat-and-mass/9789332515680/images/pg38_img13.png" alt=3D"=
image" width=3D"211" height=3D"39" data-mfp-src=3D"/library/view/heat-and-m=
ass/9789332515680/images/pg38_img13.png"></p>
<p id=3D"p0399" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0132" class=3D"imagewrap"><a id=3D"page_39"></a>
<img id=3D"img0429" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg39_img01.png" alt=3D"image" width=3D"354" he=
ight=3D"21" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg39_img01.png">
</div>
<h4 id=3D"h40013" class=3D"EB10SmallHead"><a id=3D"ch02lev2sec13"></a>2.7.2=
 Triangular Fin</h4>
<p id=3D"p0400" class=3D"EB02BodyTextFullOut">In the triangular fin shown i=
n <a href=3D"https://learning.oreilly.com/library/view/heat-and-mass/978933=
2515680/xhtml/chapter002.xhtml#figure2.18">Fig. 2.18 (c)</a>, the area of t=
he cross section of the fin varies in the <em>x</em> direction.</p>
<p id=3D"p0401" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0133" class=3D"imagewrap">
<img id=3D"img0430" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg40_img02.png" alt=3D"Fin Area" width=3D"520"=
 height=3D"198" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/i=
mages/pg40_img02.png">
<p id=3D"p0402" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0403" class=3D"EB28InlineCaption"><strong><a id=3D"figure2.18"></=
a>Figure 2.18</strong> Fin Area</p></div>
<p id=3D"p0404" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0405" class=3D"EB03BodyTextIndented"><a href=3D"https://learning.=
oreilly.com/library/view/heat-and-mass/9789332515680/xhtml/chapter002.xhtml=
#eq2.48">Equation (2.48)</a> becomes</p>
<p id=3D"p0406" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0134" class=3D"imagewrap">
<a id=3D"eq2.59"></a><img id=3D"img0431" src=3D"https://learning.oreilly.co=
m/library/view/heat-and-mass/9789332515680/images/pg39_img02.png" alt=3D"im=
age" width=3D"385" height=3D"38" data-mfp-src=3D"/library/view/heat-and-mas=
s/9789332515680/images/pg39_img02.png">
</div>
<p id=3D"p0407" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0408" class=3D"EB03BodyTextIndented">In terms of non-dimensional =
temperature <em>=CE=B8</em> =3D (<em>T</em> =E2=80=93 <em>T<sub class=3D"EB=
sub">a</sub></em>), <a href=3D"https://learning.oreilly.com/library/view/he=
at-and-mass/9789332515680/xhtml/chapter002.xhtml#eq2.59">equation (2.59)</a=
> becomes</p>
<p id=3D"p0409" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0135" class=3D"imagewrap">
<img id=3D"img0432" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg39_img03.png" alt=3D"image" width=3D"385" he=
ight=3D"40" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg39_img03.png">
</div>
<p id=3D"p0410" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0411" class=3D"EB03BodyTextIndented">Let <img id=3D"img0433" clas=
s=3D"Eq1" src=3D"https://learning.oreilly.com/library/view/heat-and-mass/97=
89332515680/images/pg39_img04.png" alt=3D"image" width=3D"172" height=3D"42=
" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/pg39_img=
04.png"></p>
<p id=3D"p0412" class=3D"EB03BodyTextIndented">The <a href=3D"https://learn=
ing.oreilly.com/library/view/heat-and-mass/9789332515680/xhtml/chapter002.x=
html#eq2.59">equation (2.59)</a> becomes</p>
<p id=3D"p0413" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0136" class=3D"imagewrap">
<img id=3D"img0434" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg39_img05.png" alt=3D"image" width=3D"378" he=
ight=3D"35" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg39_img05.png">
</div>
<p id=3D"p0414" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0415" class=3D"EB02BodyTextFullOut">where <img id=3D"img0435" cla=
ss=3D"Eq1" src=3D"https://learning.oreilly.com/library/view/heat-and-mass/9=
789332515680/images/pg39_img06.png" alt=3D"image" width=3D"61" height=3D"34=
" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/pg39_img=
06.png"> This is a modified Bessel equation.</p>
<p id=3D"p0416" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0137" class=3D"imagewrap">
<img id=3D"img0436" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg39_img07.png" alt=3D"image" width=3D"159" he=
ight=3D"36" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg39_img07.png">
</div>
<p id=3D"p0417" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0418" class=3D"EB03BodyTextIndented">The solution to this equatio=
n gives the temperature distribution as</p>
<p id=3D"p0419" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0138" class=3D"imagewrap">
<img id=3D"img0437" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg39_img08.png" alt=3D"image" width=3D"385" he=
ight=3D"23" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg39_img08.png">
</div>
<p id=3D"p0420" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0421" class=3D"EB02BodyTextFullOut">where <em>I<sub class=3D"EBsu=
b">o</sub></em> and <em>K<sub class=3D"EBsub">0</sub></em> are the Bessel f=
unctions and <em>B</em><sub class=3D"EBsub">1</sub>, and <em>B</em><sub cla=
ss=3D"EBsub">2</sub> are constants.</p>
<h4 id=3D"h40014" class=3D"EB10SmallHead"><a id=3D"ch02lev2sec14"></a>2.7.3=
 Efficiency of Fin</h4>
<p id=3D"p0422" class=3D"EB02BodyTextFullOut">Efficiency of the fin is defi=
ned as the ratio of the actual heat transfer to the maximum possible heat t=
ransfer under ideal condition. The maximum possible heat transfer occurs if=
 the entire surface temperature of the fin is equal to the base temperature=
:</p>
<p id=3D"p0423" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0139" class=3D"imagewrap">
<img id=3D"img0438" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg39_img09.png" alt=3D"image" width=3D"343" he=
ight=3D"37" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg39_img09.png">
</div>
<p id=3D"p0424" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0425" class=3D"EB02BodyTextFullOut">where <em>Q</em><sub class=3D=
"EBsub">max</sub> =3D <em>hA<sub class=3D"EBsub">s</sub></em> (<em>T<sub cl=
ass=3D"EBsub">b</sub></em> =E2=80=93 <em>T<sub class=3D"EBsub">a</sub></em>=
) =3D <em>hA<sub class=3D"EBsub">s</sub></em> <em>=CE=B8<sub class=3D"EBsub=
">b</sub></em> and <em>T<sub class=3D"EBsub">b</sub></em> is the base tempe=
rature and <em>T<sub class=3D"EBsub">a</sub></em> is the atmospheric temper=
ature.</p>
<p id=3D"p0426" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0140" class=3D"imagewrap">=E2=88=B4 <em>Q</em><sub class=3D"E=
Bsub">actual</sub> =3D <em>=CE=B7</em><sub class=3D"EBsub"><em>f</em></sub>=
 <em>A<sub class=3D"EBsub">s</sub></em><em>h=CE=B8<sub class=3D"EBsub">b</s=
ub></em>.</div>
<p id=3D"p0427" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0428" class=3D"EB02BodyTextFullOut"><em>=CE=B7</em><em><sub class=
=3D"EBsub">f</sub></em> is taken from the graph <em>=CE=B7</em> version <im=
g id=3D"img0439" class=3D"Eq1" src=3D"https://learning.oreilly.com/library/=
view/heat-and-mass/9789332515680/images/pg39_img12.png" alt=3D"image" width=
=3D"61" height=3D"18" data-mfp-src=3D"/library/view/heat-and-mass/978933251=
5680/images/pg39_img12.png"> based on fin geometries.</p>
<h4 id=3D"h40015" class=3D"EB10SmallHead"><a id=3D"page_40"></a><a id=3D"ch=
02lev2sec15"></a>2.7.4 Effectiveness of Fin</h4>
<p id=3D"p0429" class=3D"EB02BodyTextFullOut">Effectiveness of the fin is d=
efined as the ratio of heat transfer with fin to the heat transfer at the b=
ase without fin (<a href=3D"https://learning.oreilly.com/library/view/heat-=
and-mass/9789332515680/xhtml/chapter002.xhtml#figure2.18">Fig. 2.18</a>)</p=
>
<p id=3D"p0430" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0141" class=3D"imagewrap">
<img id=3D"img0440" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg40_img01.png" alt=3D"image" width=3D"385" he=
ight=3D"35" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg40_img01.png">
</div>
<p id=3D"p0431" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0432" class=3D"EB02BodyTextFullOut">where <em>A<sub class=3D"EBsu=
b">b</sub></em> is the fin base area <em>A<sub class=3D"EBsub">s</sub></em>=
 is the total surface area of fins, <em>T<sub class=3D"EBsub">b</sub></em> =
is the base temperature, and <em>T<sub class=3D"EBsub">a</sub></em> is the =
atmospheric temperature. The effectiveness of fins must always be greater t=
han 1 to prove their addition of surfaces.</p>
<h5 id=3D"h50009" class=3D"EB07SmallCapsMediumHead"><a id=3D"ch02lev1sec8">=
</a>2.8 CONCLUSIONS</h5>
<p id=3D"p0433" class=3D"EB02BodyTextFullOut">Thermal resistance is the res=
istance of a metal for flow of heat through it. It is similar to electrical=
 resistance. Thermal conductance is the reciprocal of the thermal resistanc=
e.</p>
<p id=3D"p0434" class=3D"EB03BodyTextIndented">Materials used to reduce the=
 heat transfer between an enclosure and its surroundings are called insulat=
ing materials. Examples are rock wool, glass wool for low temperature insul=
ation and asbestos, magnesia are for high-temperature insulation. Refractor=
y materials are used in applications in which it is desired to have a mater=
ial capable of withstanding high temperature without any physical deteriora=
tion. Examples are fire clay bricks, magnesite, chrome, etc. Insulation mat=
erials used in the storage and transport cryogenic liquids maintained aroun=
d 25K are known as super insulators. Thermal conductivity is about 0.3 mW/m=
=C2=B0C. Examples are glass fibers, foams. All real surfaces are not perfec=
tly smooth and has some surface roughness. When two surfaces are made to ha=
ve physical contact, the joint is not 100% perfect and this is due to rough=
ness of the surfaces. Contact points are interspersed with air gaps. The ai=
r gaps add additional resistance to the heat flow between the surfaces and =
that is referred as contact resistance. Thermal contact resistance depends =
on the surface roughness, material properties, pressure at the interface, a=
nd the nature of the interface fluid.</p>
<p id=3D"p0435" class=3D"EB03BodyTextIndented">A composite system is one th=
at will have a number of layers with different thicknesses and thermal cond=
uctivities.</p>
<p id=3D"p0436" class=3D"EB03BodyTextIndented">If the temperature of a medi=
um does not changes with time, then the heat flow is named as a steady-stat=
e heat transfer. If the temperature of a medium changes with respect to tim=
e, then the heat flow is named as an unsteady-state heat transfer.</p>
<p id=3D"p0437" class=3D"EB03BodyTextIndented">Fins are extended surfaces f=
rom the base or primary surface and they are used to increase the heat tran=
sfer surface area available for convection heat transfer. Applications for =
fins are in radiators, <a id=3D"page_41"></a>in automobiles, air-cooled IC =
engines, air-cooled compressors, electrical motors and transformers, coolin=
g and condenser coils in refrigerators and air conditioners.</p>
<p id=3D"p0438" class=3D"EB03BodyTextIndented">General assumptions for the =
heat transfer analysis for fins are that the heat transfer coefficient is u=
niform, thermal conductivity of the material is constant, one-dimensional h=
eat transfer, negligible radiation and contact resistance and steady-state =
conditions, and no heat generation within fin.</p>
<p id=3D"p0439" class=3D"EB03BodyTextIndented">Fins are made as uniform str=
aight fin, tapered straight fin, annular fin and pin-fins (splines). They a=
re more effective with materials of large thermal conductivity. All though =
copper is having high thermal conductivity than aluminum, due to light weig=
ht and low cost, aluminum fins are generally used. They are are classified =
based on the boundary conditions such as (i) long fins (when end temperatur=
e is equal to ambient temperature); (ii) short fins (with end is insulated =
or end heat transfer is small) and short fins with convection (convection h=
eat transfer at the end).</p>
<p id=3D"p0440" class=3D"EB03BodyTextIndented">Fin efficiency is defined as=
 the ratio of the actual rate of heat transfer with the fin to the rate of =
heat transfer from the fin that could be obtained when the entire fin surfa=
ce is mentioned at the base temperature.</p>
<p id=3D"p0441" class=3D"EB03BodyTextIndented">Fin effectiveness is defined=
 as the ratio of the rate of heat transfer with the fin to that of without =
the fin. It increases with decrease in heat transfer coefficient. In boilin=
g and condensation, heat transfer coefficient is very high, and therefore u=
se of fins may actually produce a reduction in heat transfer.</p>
<div id=3D"div0142" class=3D"BoxHead">
<h5 id=3D"h50010" class=3D"EB08ExtraFeatureHead">KEY CONCEPTS</h5>
</div>
<div id=3D"div0143" class=3D"BoxText">
<ul id=3D"ul0002" class=3D"BulletCircle">
<li id=3D"li0023" class=3D"EB23ListFirst"><p id=3D"p0442" class=3D"EB02Body=
TextFullOut">Heat transfer rate increase relates to <strong><em>h</em></str=
ong> and to <em>A</em>, or both simultaneously.</p></li>
<li id=3D"li0024" class=3D"EB24List"><p id=3D"p0443" class=3D"EB02BodyTextF=
ullOut">The simplest method of increasing <em>Q</em> is to increase the are=
a of the</p></li>
<li id=3D"li0025" class=3D"EB24List"><p id=3D"p0444" class=3D"EB02BodyTextF=
ullOut">plate but this is limited by the fact that the spreading resistance=
 also increases.</p></li>
<li id=3D"li0026" class=3D"EB24List"><p id=3D"p0445" class=3D"EB02BodyTextF=
ullOut">The best way to increase contact surface area between fluid and sol=
id is to use fins, and the vast majority of coolers are provided with such.=
</p></li>
<li id=3D"li0027" class=3D"EB24List"><p id=3D"p0446" class=3D"EB02BodyTextF=
ullOut">Rather than adding surface area while spreading out horizontally, i=
t is done vertically.</p></li>
<li id=3D"li0028" class=3D"EB24List"><p id=3D"p0447" class=3D"EB02BodyTextF=
ullOut">On the practical and theoretical side, the effectiveness of a fin w=
ill primarily depend on its thickness and height.</p></li>
<li id=3D"li0029" class=3D"EB24List"><p id=3D"p0448" class=3D"EB02BodyTextF=
ullOut">Each part of the fin surface will not exchange the same amount of h=
eat, since the temperature decreases from the base to the top of the fin.</=
p></li>
<li id=3D"li0030" class=3D"EB24List"><p id=3D"p0449" class=3D"EB02BodyTextF=
ullOut">This results in a coefficient (efficiency, ranging between 0 and 1)=
 which will balance the fin=E2=80=93fluid contact surface area, so that the=
 fin's heat transfer with the fluid occurs on an effective area smaller tha=
n the real contact area.</p></li>
<li id=3D"li0031" class=3D"EB24List"><p id=3D"p0450" class=3D"EB02BodyTextF=
ullOut">Generally, beyond the point where the temperature of the fin is nea=
rly identical to that of the fluid, the remainder of surface exchanges virt=
ually no heat to the fluid and is thus useless.</p></li>
<li id=3D"li0032" class=3D"EB24List"><p id=3D"p0451" class=3D"EB02BodyTextF=
ullOut">Moreover, the higher the fin, the more the volume of the cooler, an=
d if the flow rate is constant, the.n its velocity decreases, also the ther=
mal convection.</p></li>
<li id=3D"li0033" class=3D"EB25ListLast"><p id=3D"p0452" class=3D"EB02BodyT=
extFullOut">It is a matter of compromises, as in most situations.</p></li>
</ul>
</div>
<h5 id=3D"h50011" class=3D"EB07SmallCapsMediumHead"><a id=3D"ch02lev1sec9">=
</a>EXAMPLE PROBLEMS</h5>
<p id=3D"p0453" class=3D"EB26SmallTextHangingIndent"><a id=3D"page_42"></a>=
2.1. <em>A composite wall is made up of two slabs with outermost surface te=
mperatures maintained at (T<sub class=3D"EBsub">1</sub>) 1300=C2=B0C and (T=
<sub class=3D"EBsub">3</sub>) 115=C2=B0C The first slab has a thickness of =
500 mm (L<sub class=3D"EBsub">1</sub>) and thermal conductivity (K<sub clas=
s=3D"EBsub">1</sub>) of 1.4 W/mK and the thickness and the thermal conducti=
vity (K<sub class=3D"EBsub">2</sub>) of the second slab are 161 mm (L<sub c=
lass=3D"EBsub">2</sub>) and 0.35 W/mK respectively. Calculate the conductio=
n heat transfer through this composite wall per square metre and the temper=
ature of the surfaces in contact</em>.</p>
<p id=3D"p0454" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0144" class=3D"imagewrap">
<img id=3D"img0441" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg42_img01.png" alt=3D"image" width=3D"293" he=
ight=3D"182" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg42_img01.png">
</div>
<p id=3D"p0455" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0456" class=3D"EB27SmallTextExtraIndent">Also</p>
<p id=3D"p0457" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0145" class=3D"imagewrap">
<img id=3D"img0442" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg42_img01d.png" alt=3D"image" width=3D"65" he=
ight=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg42_img01d.png">
</div>
<p id=3D"p0458" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0146" class=3D"imagewrap">Therefore, <em>T</em><sub class=3D"=
EBsub">2</sub> =3D 782.1 =C2=B0C.</div>
<p id=3D"p0459" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0460" class=3D"EB26SmallTextHangingIndent">2.2. <em>A furnace wal=
l slab is constructed with fire clay of thickness 90 mm <em>(L<sub class=3D=
"EBsub">1</sub>)</em> inside and red brick of thickness 450 mm</em> <em>(L<=
sub class=3D"EBsub">2</sub>)</em> <em>outside. The temperatures inside and =
outside the furnace wall are 1100=C2=B0C</em> <em>(T<sub class=3D"EBsub">1<=
/sub>)</em> <em>and 30=C2=B0C</em> <em>(T<sub class=3D"EBsub">3</sub>)</em>=
, <em>respectively. The thermal conductivity of the red brick</em> <em>(K<s=
ub class=3D"EBsub">2</sub>)</em> <em>is 0.8 W/mK and that of the fire clay<=
/em> <em>(K<sub class=3D"EBsub">1</sub>)</em>, <em>is 0.3(1 + 0.001T)</em> =
<em>W/mK where T is the temperature of the clay in degrees Celsius. Assumin=
g unit surface area, find the conductive heat loss through the furnace wall=
 and the temperature at the interface of the fire clay and red brick.</em><=
/p>
<p id=3D"p0461" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0462" class=3D"EB27SmallTextExtraIndent">We know that</p>
<p id=3D"p0463" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0147" class=3D"imagewrap">
<img id=3D"img0443" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg42_img02.png" alt=3D"image" width=3D"401" he=
ight=3D"47" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg42_img02.png">
</div>
<p id=3D"p0464" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0465" class=3D"EB27SmallTextExtraIndent">Here</p>
<p id=3D"p0466" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0148" class=3D"imagewrap">
<img id=3D"img0444" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg42_img04a.png" alt=3D"image" width=3D"53" he=
ight=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg42_img04a.png">
</div>
<p id=3D"p0467" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0468" class=3D"EB27SmallTextExtraIndent">where</p>
<p id=3D"p0469" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0149" class=3D"imagewrap">
<img id=3D"img0445" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg42_img04.png" alt=3D"image" width=3D"171" he=
ight=3D"139" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg42_img04.png">
</div>
<p id=3D"p0470" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0150" class=3D"imagewrap"><a id=3D"page_43"></a>
<img id=3D"img0446" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg43_img01.png" alt=3D"image" width=3D"265" he=
ight=3D"77" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg43_img01.png">
</div>
<p id=3D"p0471" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0472" class=3D"EB27SmallTextExtraIndent">Therefore,</p>
<p id=3D"p0473" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0151" class=3D"imagewrap">
<img id=3D"img0447" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg43_img01b.png" alt=3D"image" width=3D"210" h=
eight=3D"52" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg43_img01b.png">
</div>
<p id=3D"p0474" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0475" class=3D"EB27SmallTextExtraIndent">i.e.</p>
<p id=3D"p0476" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0152" class=3D"imagewrap">(1100 =E2=80=93 <em>T</em><sub clas=
s=3D"EBsub">2</sub>)[0.3  + 0.00015(1100 + <em>T</em><sub class=3D"EBsub">2=
</sub>)] =C3=97 0.5625 =3D (<em>T</em><sub class=3D"EBsub">2</sub> =E2=80=
=93 30)(0.09) =3D 0.09<em>T</em><sub class=3D"EBsub">2</sub> =E2=80=93 2.7<=
/div>
<div id=3D"div0153" class=3D"imagewrap">(1100 =E2=80=93 <em>T</em><sub clas=
s=3D"EBsub">2</sub>)[0.169 + 0.093 + 8.44 =C3=97 10<sup class=3D"EBsup">=E2=
=80=935</sup> <em>T</em><sub class=3D"EBsub">2</sub>] =3D 0.09 <em>T</em><s=
ub class=3D"EBsub">2</sub> =E2=80=93 2.7</div> =20
<p id=3D"p0477" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0154" class=3D"imagewrap">
<img id=3D"img0448" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg43_img02.png" alt=3D"image" width=3D"505" he=
ight=3D"74" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg43_img02.png">
</div>
<p id=3D"p0478" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0479" class=3D"EB27SmallTextExtraIndent">Solving the equation we =
can get <em>T</em><sub class=3D"EBsub">2</sub> =3D 873.15=C2=B0 C.</p>
<p id=3D"p0480" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0481" class=3D"EB26SmallTextHangingIndent">2.3. <em>A hollow cyli=
nder of length 2 m (L) has inner and outer radii of 50 mm</em> <em>(r<sub c=
lass=3D"EBsub">1</sub>)</em> <em>and 100 mm</em> <em>(r<sub class=3D"EBsub"=
>2</sub>)</em>. <em>The inner and outer surface temperatures of this cylind=
er are 300=C2=B0C</em> <em>(T<sub class=3D"EBsub">1</sub>)</em><em> and 200=
=C2=B0C </em><em>(T<sub class=3D"EBsub">2</sub>)</em>, <em>respectively. De=
termine the conduction heat transfer rate through this cylinder. Assume tha=
t the thermal conductivity (K) of the cylinder is 70 W/mK.</em></p>
<p id=3D"p0482" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0483" class=3D"EB27SmallTextExtraIndent">The heat transfer rate</=
p>
<p id=3D"p0484" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0155" class=3D"imagewrap">
<img id=3D"img0449" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg43_img03.png" alt=3D"image" width=3D"427" he=
ight=3D"248" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg43_img03.png">
</div>
<p id=3D"p0485" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0486" class=3D"EB26SmallTextHangingIndent">2.4. <em>The inner and=
 outer radii of a hollow cylinder are 15 mm (r</em><sub class=3D"EBsub">1</=
sub><em>) and 25 mm (r</em><sub class=3D"EBsub">2</sub><em>)</em>, <em>resp=
ectively. The temperatures of the inner and outer walls are 400=C2=B0C (T</=
em><sub class=3D"EBsub">1</sub><em>) and 350=C2=B0C (T</em><sub class=3D"EB=
sub">2</sub><em>)</em>, <em>respectively. The thermal conductivity of the c=
ylinder material obeys the relationship K =3D (400=E2=80=930.05T) W/mK wher=
e T is in degrees Celsius. Find the heat transferred from the hollow cylind=
er per unit length. The thermal conductivity</em>,</p>
<p id=3D"p0487" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0156" class=3D"imagewrap"><a id=3D"page_44"></a>
<img id=3D"img0450" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg44_img01.png" alt=3D"image" width=3D"155" he=
ight=3D"95" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg44_img01.png">
</div>
<p id=3D"p0488" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0489" class=3D"EB27SmallTextExtraIndent">The heat transfer per un=
it length, <em>Q =3D T/R</em>.</p>
<p id=3D"p0490" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0157" class=3D"imagewrap">
<img id=3D"img0451" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg44_img02.png" alt=3D"image" width=3D"356" he=
ight=3D"186" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg44_img02.png">
</div>
<p id=3D"p0491" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0492" class=3D"EB26SmallTextHangingIndent">2.5. <em>Steam is carr=
ied in a steel pipe having inner radius 5 cm (r<sub class=3D"EBsub">1</sub>=
) and outer radius 5.5 cm (r<sub class=3D"EBsub">2</sub>). This pipe is cov=
ered with two layers of insulation each 5 cm thick (t). The thermal conduct=
ivity of the steel pipe and the first and second layers of insulation are 0=
.12 W/mK (K<sub class=3D"EBsub">3</sub>)</em>, <em>50 (K</em><sub class=3D"=
EBsub">1</sub><em>) and 0.06 (K<sub class=3D"EBsub">2</sub>)</em>, <em>resp=
ectively. The temperature of steam is 225=C2=B0C (T<sub class=3D"EBsub">1</=
sub>) and the temperature of the outermost surface is 25=C2=B0C (T<sub clas=
s=3D"EBsub">4</sub>) Calculate the conduction transfer rate per unit length=
 of pipe and the intermediate temperatures.</em></p>
<ol id=3D"ol0010" class=3D"LowerAlpha">
<li id=3D"li0034" class=3D"EB23ListFirst">
<p id=3D"p0493" class=3D"EB02BodyTextFullOut">Conduction transfer rate</p>
<p id=3D"p0494" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0158" class=3D"imagewrap">
<img id=3D"img0452" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg44_img03.png" alt=3D"image" width=3D"413" he=
ight=3D"423" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg44_img03.png">
</div>
<p id=3D"p0495" class=3D"EB02BodyTextFullOut">&nbsp;</p>
</li>
<li id=3D"li0035" class=3D"EB25ListLast"><a id=3D"page_45"></a>
<p id=3D"p0496" class=3D"EB02BodyTextFullOut">Intermediate temperatures</p>
<p id=3D"p0497" class=3D"EB02BodyTextFullOut">We know that</p>
<p id=3D"p0498" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0159" class=3D"imagewrap">
<img id=3D"img0453" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg45_img01.png" alt=3D"image" width=3D"254" he=
ight=3D"82" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg45_img01.png">
</div>
<p id=3D"p0499" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0500" class=3D"EB02BodyTextFullOut">Also</p>
<p id=3D"p0501" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0160" class=3D"imagewrap"><em>T</em><sub class=3D"EBsub">3</s=
ub> =3D <em>T</em><sub class=3D"EBsub">2</sub> =E2=80=93 <em>QR</em><sub cl=
ass=3D"EBsub">2</sub> =3D 224.97 =E2=80=93 89.61 =C3=97 1.715 =3D 71.29=C2=
=B0C.</div>
<p id=3D"p0502" class=3D"EB02BodyTextFullOut">&nbsp;</p>
</li></ol>
<p id=3D"p0503" class=3D"EB26SmallTextHangingIndent">2.6. <em>Determine the=
 surface temperature of an insulated cable of radius 10 mm. When the cable =
was exposed to air</em>, <em>its surface temperature (T) was 80=C2=B0C. The=
 convective heat transfer coefficient (h) with and without insulation was 5=
 W/m<sup class=3D"EBsup">2</sup>K. The temperature (T<sub class=3D"EBsub">a=
</sub>) of air surrounding the cable was 30=C2=B0C Also find the optimum th=
ickness of the insulation. Assume that the intensity of current remains unc=
hanged and that the thermal conductivity (K) of the insulation material is =
0.2 W/mK.</em></p>
<p id=3D"p0504" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0161" class=3D"imagewrap">
<img id=3D"img0454" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg45_img02.png" alt=3D"image" width=3D"250" he=
ight=3D"47" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg45_img02.png">
</div>
<ol id=3D"ol0011" class=3D"LowerAlpha">
<li id=3D"li0036" class=3D"EB23ListFirst">
<p id=3D"p0505" class=3D"EB02BodyTextFullOut">The heat transfer rate withou=
t the insulation</p>
<p id=3D"p0506" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0162" class=3D"imagewrap"> =3D <em>Q</em><sub class=3D"EBsub"=
>1</sub> =3D <em>hA</em>(<em>T</em> =E2=80=93 <em>T<sub class=3D"EBsub">a</=
sub></em>)</div>
<div id=3D"div0163" class=3D"imagewrap">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=3D 5 =C3=97(2 =C3=97 =
=CF=80 =C3=97 0.01 =C3=97 1) =C3=97 (80 =E2=80=93 30)
<div id=3D"div0164" class=3D"imagewrap">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=3D 1=
5.71W (=E2=88=B5 <em>L</em> =3D 1m)</div>
</div>
<p id=3D"p0507" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0508" class=3D"EB02BodyTextFullOut">Optimum radius of the insulat=
ion,</p>
<p id=3D"p0509" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0165" class=3D"imagewrap">
<img id=3D"img0455" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg45_img04.png" alt=3D"image" width=3D"148" he=
ight=3D"31" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg45_img04.png">
</div>
<p id=3D"p0510" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0511" class=3D"EB02BodyTextFullOut">The heat transfer rate with t=
he insulation is</p>
<p id=3D"p0512" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0166" class=3D"imagewrap">
<img id=3D"img0456" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg45_img05.png" alt=3D"image" width=3D"257" he=
ight=3D"148" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg45_img05.png">
</div>
<p id=3D"p0513" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0514" class=3D"EB02BodyTextFullOut">Therefore</p>
<p id=3D"p0515" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0167" class=3D"imagewrap">
<img id=3D"img0457" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg45_img05c.png" alt=3D"image" width=3D"74" he=
ight=3D"30" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg45_img05c.png">
</div>
<p id=3D"p0516" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0517" class=3D"EB02BodyTextFullOut">As the intensity of current r=
emains uncharged, that is <em>Q</em><sub class=3D"EBsub">1</sub> =3D <em>Q<=
/em><sub class=3D"EBsub">2</sub></p>
<p id=3D"p0518" class=3D"EB02BodyTextFullOut">Therefore</p>
<p id=3D"p0519" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0168" class=3D"imagewrap">
<img id=3D"img0458" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg45_img05d.png" alt=3D"image" width=3D"78" he=
ight=3D"30" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg45_img05d.png">
</div>
<p id=3D"p0520" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0169" class=3D"imagewrap"><em>T</em><sub class=3D"EBsub">1</s=
ub> =3D 59.83=C2=B0 C</div>
<p id=3D"p0521" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0522" class=3D"EB02BodyTextFullOut">Therefore, the surface temper=
ature of the cable, <em>T</em><sub class=3D"EBsub">1</sub> =3D 59.83=C2=B0C=
 (after adding the insulation).</p></li>
</ol>
<ol id=3D"ol0012" class=3D"LowerAlpha">
<li id=3D"li0037" class=3D"EB23ListFirst">
<p id=3D"p0523" class=3D"EB02BodyTextFullOut">With optimum thickness of ins=
ulation, the outer radius is</p>
<p id=3D"p0524" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0170" class=3D"imagewrap"><a id=3D"page_46"></a>
<img id=3D"img0459" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg46_img01.png" alt=3D"image" width=3D"177" he=
ight=3D"30" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg46_img01.png">
</div>
<p id=3D"p0525" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0526" class=3D"EB02BodyTextFullOut">Therefore thickness of the in=
sulation =3D <em>r</em><sub class=3D"EBsub">2</sub>  =E2=88=92 <em>r</em><s=
ub class=3D"EBsub">1</sub> =3D <em>r<sub class=3D"EBsub">c</sub></em> =E2=
=88=92 <em>r</em><sub class=3D"EBsub">1</sub> =3D 40 =E2=88=92 10 =3D 30 mm=
.</p></li>
</ol>
<p id=3D"p0527" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0528" class=3D"EB26SmallTextHangingIndent">2.7. <em>Plastic mater=
ial of thermal conductivity (K<sub class=3D"EBsub">1</sub></em><em>) 0.9 kJ=
 / mhrK is used to insulate a copper wire of radius (r<sub class=3D"EBsub">=
1</sub></em><em>) 10 mm</em>, <em>to a thickness of up to 5 mm. The convect=
ive heat transfer coefficient h<sub class=3D"EBsub">0</sub> on the surface =
of the wire is 50 kJ / m<sup class=3D"EBsup">2</sup>hrK. What is the effect=
 of the insulation on the heat transfer rate? What should be the outer radi=
us of insulation such that the surface temperature is kept at the same valu=
e as that without insulation?</em></p>
<p id=3D"p0529" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0530" class=3D"EB27SmallTextExtraIndent">The critical radius of t=
he insulation is</p>
<p id=3D"p0531" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0171" class=3D"imagewrap">
<img id=3D"img0460" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg46_img02.png" alt=3D"image" width=3D"132" he=
ight=3D"56" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg46_img02.png">
</div>
<p id=3D"p0532" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0533" class=3D"EB27SmallTextExtraIndent">As the critical radius i=
s greater than the outer radius of the insulated wire, this insulation help=
s to dissipate more heat and therefore cools the wire.</p>
<p id=3D"p0534" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0535" class=3D"EB27SmallTextExtraIndent">The heat transfer withou=
t insulation,</p>
<p id=3D"p0536" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0172" class=3D"imagewrap">
<img id=3D"img0461" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg46_img03.png" alt=3D"image" width=3D"97" hei=
ght=3D"54" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg46_img03.png">
</div>
<p id=3D"p0537" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0538" class=3D"EB27SmallTextExtraIndent">The heat transfer throug=
h the insulated wire,</p>
<p id=3D"p0539" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0173" class=3D"imagewrap">
<img id=3D"img0462" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg46_img04.png" alt=3D"image" width=3D"168" he=
ight=3D"56" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg46_img04.png">
</div>
<p id=3D"p0540" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0541" class=3D"EB27SmallTextExtraIndent">In order to obtain the s=
ame wire temperature with and without insulation, the conditions is</p>
<p id=3D"p0542" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0174" class=3D"imagewrap">
<img id=3D"img0463" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg46_img05.png" alt=3D"image" width=3D"189" he=
ight=3D"162" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg46_img05.png">
</div>
<p id=3D"p0543" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0544" class=3D"EB27SmallTextExtraIndent">Solving, the outer radiu=
s of insulation =3D 0.037 m =3D 37 mm.</p>
<p id=3D"p0545" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0546" class=3D"EB26SmallTextHangingIndent">2.8. <em>The electrica=
l resistance of a copper rod is 15 =C3=97 10<sup class=3D"EBsup">=E2=88=926=
</sup> ohmm<sup class=3D"EBsup">=E2=88=921</sup>. It conducts a current of =
900 A and has a radius of 1 cm <em>(r<sub class=3D"EBsub">1</sub>)</em> It =
is insulated to a thickness of 5 mm <em>(t<sub class=3D"EBsub">1</sub>)</em=
> using a material having a thermal conductivity of 0.05 W/mK <em>(K<sub cl=
ass=3D"EBsub">1</sub>)</em> and then further covered to a thickness of (t<s=
ub class=3D"EBsub">2</sub>) 1.8 cm with plastic material of thermal conduct=
ivity (K<sub class=3D"EBsub">2</sub>) 0.5 W/mK. This plastic outer layer is=
 exposed to air at 30=C2=B0C (T<sub class=3D"EBsub">0</sub>) and the convec=
tive heat transfer coefficient is 15 W/m<sup class=3D"EBsup">2</sup>K (h). =
Determine the outer surface temperature of the plastic insulation.</em></p>
<p id=3D"p0547" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0548" class=3D"EB27SmallTextExtraIndent">The heat generated in th=
e copper rod due to the flow of current,</p>
<p id=3D"p0549" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0175" class=3D"imagewrap"><em>Q<sub class=3D"EBsub">g</sub></=
em> =3D <em>I</em><sup class=3D"EBsup">2</sup><em>R</em></div>
<div id=3D"div0176" class=3D"imagewrap"><a id=3D"page_47"></a>&nbsp;&nbsp;&=
nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=3D (900)<sup class=3D"E=
Bsup">2</sup>(15=C3=9710<sup class=3D"EBsup">=E2=88=926</sup>)</div>
<div id=3D"div0177" class=3D"imagewrap">&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;=3D 12.15 W/m</di=
v>
<p id=3D"p0550" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0551" class=3D"EB27SmallTextExtraIndent">For a steady-state condi=
tion, the heat generated in the copper rod should be convected to the air, =
such that</p>
<p id=3D"p0552" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0178" class=3D"imagewrap">
<img id=3D"img0464" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg47_img01.png" alt=3D"image" width=3D"122" he=
ight=3D"146" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg47_img01.png">
</div>
<p id=3D"p0553" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0554" class=3D"EB27SmallTextExtraIndent">Therefore,</p>
<p id=3D"p0555" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0179" class=3D"imagewrap">
<img id=3D"img0465" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg47_img01a.png" alt=3D"image" width=3D"86" he=
ight=3D"31" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg47_img01a.png">
</div>
<p id=3D"p0556" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0557" class=3D"EB27SmallTextExtraIndent">which means</p>
<p id=3D"p0558" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0180" class=3D"imagewrap"><em>T<sub class=3D"EBsub">s</sub></=
em> =3D 33.91=C2=B0 C.</div>
<p id=3D"p0559" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0560" class=3D"EB26SmallTextHangingIndent">2.9. <em>A hollow sphe=
re is made up of two layers. The inner radius (r<sub class=3D"EBsub">1</sub=
></em><em>) is 5 cm. The radius (r<sub class=3D"EBsub">2</sub></em><em>) of=
 the interface between the two layers is 15 cm. The outer layer thickness (=
t<sub class=3D"EBsub">2</sub>) is 5 cm. The thermal conductivity of the inn=
er and outer layers are (K<sub class=3D"EBsub">1</sub></em><em>) 70 and (K<=
sub class=3D"EBsub">2</sub></em><em>) 15 W/mK</em>, <em>respectively. The i=
nner- and outer-most surface temperatures are (T<sub class=3D"EBsub">1</sub=
></em><em>) 290 and (T<sub class=3D"EBsub">2</sub></em><em>) 20 K</em>, <em=
>respectively. Calculate the conduction heat transfer rate through this hol=
low sphere and the interface temperature between the layers.</em></p>
<p id=3D"p0561" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0562" class=3D"EB27SmallTextExtraIndent">Heat transfer rate,</p>
<p id=3D"p0563" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0181" class=3D"imagewrap">
<img id=3D"img0466" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg47_img02.png" alt=3D"image" width=3D"73" hei=
ght=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg47_img02.png">
</div>
<p id=3D"p0564" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0565" class=3D"EB27SmallTextExtraIndent">Therefore</p>
<p id=3D"p0566" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0182" class=3D"imagewrap">
<img id=3D"img0467" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg47_img02a.png" alt=3D"image" width=3D"143" h=
eight=3D"30" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg47_img02a.png">
</div>
<p id=3D"p0567" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0568" class=3D"EB27SmallTextExtraIndent">Also</p>
<p id=3D"p0569" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0183" class=3D"imagewrap">
<img id=3D"img0468" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg47_img02b.png" alt=3D"image" width=3D"64" he=
ight=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg47_img02b.png">
</div>
<p id=3D"p0570" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0571" class=3D"EB27SmallTextExtraIndent">Therefore</p>
<p id=3D"p0572" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0184" class=3D"imagewrap"><em>T</em><sub class=3D"EBsub">2</s=
ub> =3D <em>T</em><sub class=3D"EBsub">1</sub> =E2=80=93 <em>QR</em><sub cl=
ass=3D"EBsub">1</sub> =3D 290 =E2=80=93 11230 =C3=97 0.0152</div>
<div id=3D"div0185" class=3D"imagewrap">=3D 119.3K</div>
<p id=3D"p0573" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0574" class=3D"EB27SmallTextExtraIndent">where</p>
<p id=3D"p0575" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0186" class=3D"imagewrap">
<img id=3D"img0469" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg47_img02d.png" alt=3D"image" width=3D"130" h=
eight=3D"103" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/ima=
ges/pg47_img02d.png">
</div>
<p id=3D"p0576" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0577" class=3D"EB27SmallTextExtraIndent"><a id=3D"page_48"></a>an=
d</p>
<p id=3D"p0578" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0187" class=3D"imagewrap">
<img id=3D"img0470" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg48_img01.png" alt=3D"image" width=3D"138" he=
ight=3D"101" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg48_img01.png">
</div>
<p id=3D"p0579" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0580" class=3D"EB26SmallTextHangingIndent">2.10. <em>A long steel=
 rod of diameter (d) 3 cm is attached to a wall. The wall temperature (T<su=
b class=3D"EBsub">b</sub>) is 190=C2=B0C and the temperature (T<sub class=
=3D"EBsub">a</sub>) of air surrounding the rod is 30=C2=B0C. The thermal co=
nductivity (K) of the rod is 45 W/mK and the convective heat transfer coeff=
icient (h) is 19 W/m<sup class=3D"EBsup">2</sup>K. Calculate the heat loss =
from the fin.</em></p>
<p id=3D"p0581" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0582" class=3D"EB27SmallTextExtraIndent">The long rod is assumed =
to have infinite length.</p>
<p id=3D"p0583" class=3D"EB27SmallTextExtraIndent">Therefore the heat trans=
fer,</p>
<p id=3D"p0584" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0188" class=3D"imagewrap">
<img id=3D"img0471" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg48_img02.png" alt=3D"image" width=3D"124" he=
ight=3D"19" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg48_img02.png">
</div>
<p id=3D"p0585" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0586" class=3D"EB27SmallTextExtraIndent">where the circumference =
of the rod,</p>
<p id=3D"p0587" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0189" class=3D"imagewrap">
<img id=3D"img0472" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg48_img02a.png" alt=3D"image" width=3D"378" h=
eight=3D"97" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg48_img02a.png">
</div>
<p id=3D"p0588" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0589" class=3D"EB26SmallTextHangingIndent">2.11. <em>A steel rod =
of length (L) 20 cm with a diameter (d) of 2 cm is attached to a surface ma=
intained at 300=C2=B0C (T<sub class=3D"EBsub">b</sub>) The end of the rod i=
s insulated. The fluid (air) surrounding the rod is at 30=C2=B0C (T<sub cla=
ss=3D"EBsub">a</sub></em>)<em>Determine the heat transferred to the fluid f=
rom the rod if K =3D 45 W/mK and h =3D 30 W/m<sup class=3D"EBsup">2</sup>K.=
</em></p>
<p id=3D"p0590" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0591" class=3D"EB27SmallTextExtraIndent">The heat transfer at the=
 insulated end, <img class=3D"Eq1" id=3D"img0183" src=3D"https://learning.o=
reilly.com/library/view/heat-and-mass/9789332515680/images/pg48_img03.png" =
alt=3D"image" width=3D"167" height=3D"19" data-mfp-src=3D"/library/view/hea=
t-and-mass/9789332515680/images/pg48_img03.png"></p>
<p id=3D"p0592" class=3D"EB27SmallTextExtraIndent">The circumference,</p>
<p id=3D"p0593" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0190" class=3D"imagewrap"><em>P</em> =3D =CF=80<em>d</em> =3D=
 (=CF=80 =C3=97 0.02) =3D 0.0628 m</div>
<p id=3D"p0594" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0595" class=3D"EB27SmallTextExtraIndent">The area of cross-sectio=
n,</p>
<p id=3D"p0596" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0191" class=3D"imagewrap">
<img id=3D"img0473" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg48_img03b.png" alt=3D"image" width=3D"252" h=
eight=3D"84" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg48_img03b.png">
</div>
<p id=3D"p0597" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0192" class=3D"imagewrap">
Therefore, <img class=3D"Eq1" id=3D"img0186" src=3D"https://learning.oreill=
y.com/library/view/heat-and-mass/9789332515680/images/pg48_img03c.png" alt=
=3D"image" width=3D"356" height=3D"39" data-mfp-src=3D"/library/view/heat-a=
nd-mass/9789332515680/images/pg48_img03c.png">
</div>
<p id=3D"p0598" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0599" class=3D"EB26SmallTextHangingIndent">2.12. <em>A linear tri=
angular fin of length (L) 5 cm</em>, <em>base thickness (t) 1 cm and width =
25 cm is attached to a surface. If the thermal conductivity (K) of the fin =
material is 175 W/mK and its surface convection coefficient (h) is 45 W/m<s=
up class=3D"EBsup">2</sup>K determine the fin efficiency.</em></p>
<p id=3D"p0600" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0601" class=3D"EB27SmallTextExtraIndent">The critical length,</p>
<p id=3D"p0602" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0193" class=3D"imagewrap"><a id=3D"page_49"></a>
<img id=3D"img0474" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg48_img04.png" alt=3D"image" width=3D"288" he=
ight=3D"141" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg48_img04.png">
</div>
<p id=3D"p0603" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0604" class=3D"EB27SmallTextExtraIndent">From the graph, fin effi=
ciency =3D 95%.</p>
<p id=3D"p0605" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0606" class=3D"EB26SmallTextHangingIndent">2.13. <em>A circumfere=
ntial fin having outer and inner radii of 10 cm (r<sub class=3D"EBsub">i</s=
ub>) and 7 cm (r<sub class=3D"EBsub">0</sub>)</em>, <em>respectively with t=
hickness (t) 3 mm is attached to a cylinder. If the cylinder surface is mai=
ntained at 400=C2=B0C T<sub class=3D"EBsub">b</sub> and the surrounding air=
 temperature is 30=C2=B0C T<sub class=3D"EBsub">a</sub></em>, <em>determine=
 the heat transfer from the fin. Assume the convective heat transfer coeffi=
cient (h) as 40 W/m<sup class=3D"EBsup">2</sup>K and the thermal conductivi=
ty (K) of the fin as 175 W/mK.</em></p>
<p id=3D"p0607" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0194" class=3D"imagewrap">The heat transfer, <em>Q</em> =3D <=
em>=CE=B7A<sub class=3D"EBsub">s</sub>h</em>(<em>T<sub class=3D"EBsub">b</s=
ub></em> =E2=80=93 <em>T<sub class=3D"EBsub">a</sub></em>)</div>
<p id=3D"p0608" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0195" class=3D"imagewrap">
<img id=3D"img0475" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg49_img02.png" alt=3D"image" width=3D"154" he=
ight=3D"95" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg49_img02.png">
</div>
<p id=3D"p0609" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0610" class=3D"EB27SmallTextExtraIndent">and</p>
<p id=3D"p0611" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0196" class=3D"imagewrap"><em>r</em><sub class=3D"EBsub">2</s=
ub><em><sub class=3D"EBsub">c</sub></em> =3D <em>r<sub class=3D"EBsub">i</s=
ub></em> + <em>L<sub class=3D"EBsub">c</sub></em> =3D 0.1 + 0.0315 =3D 0.13=
15m</div>
<p id=3D"p0612" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0613" class=3D"EB27SmallTextExtraIndent">Therefore,</p>
<p id=3D"p0614" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0197" class=3D"imagewrap">
<img id=3D"img0476" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg49_img03.png" alt=3D"image" width=3D"300" he=
ight=3D"118" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg49_img03.png">
</div>
<p id=3D"p0615" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0616" class=3D"EB27SmallTextExtraIndent">From the graph, fin effi=
ciency =3D 90%</p>
<p id=3D"p0617" class=3D"EB27SmallTextExtraIndent">Fin surface area,</p>
<p id=3D"p0618" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0198" class=3D"imagewrap">
<img id=3D"img0477" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg49_img04.png" alt=3D"image" width=3D"152" he=
ight=3D"17" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg49_img04.png">
</div>
<p id=3D"p0619" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0199" class=3D"imagewrap">=3D 2 =C3=97 =CF=80[(100 =E2=88=92 =
49) + (0.3 =C3=97 10)] =C3=97 10<sup class=3D"EBsup">=E2=88=924</sup> m<sup=
 class=3D"EBsup">2</sup></div>
<div id=3D"div0200" class=3D"imagewrap">=3D 0.034m<sup class=3D"EBsup">2</s=
up></div>
<p id=3D"p0620" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0201" class=3D"imagewrap">Therefore, <em>Q</em> =3D 0.9 =C3=
=97 0.034 =C3=97 40(400 =E2=88=92 30)</div> =20
<div id=3D"div0202" class=3D"imagewrap">=3D 452.9W.</div>
<p id=3D"p0621" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0622" class=3D"EB26SmallTextHangingIndent">2.14. <em>Heat is gene=
rated in a long chromium steel bar of thickness 3 cm (t) and width 30 cm (w=
) at the rate of 3000 kW/m<sup class=3D"EBsup">3</sup>. If the surface temp=
erature of the steel bar is (T<sub class=3D"EBsub">w</sub>) 450=C2=B0C</em>=
, <em>find the maximum temperature within the steel bar. The thermal conduc=
tivity of the chromium steel is 24 W/mK (K).</em></p>
<p id=3D"p0623" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0203" class=3D"imagewrap">
<img id=3D"img0478" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg49_img05.png" alt=3D"image" width=3D"197" he=
ight=3D"106" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg49_img05.png">
</div>
<p id=3D"p0624" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0625" class=3D"EB26SmallTextHangingIndent"><a id=3D"page_50"></a>=
2.15. <em>In a nuclear reactor</em>, <em>a uranium fuel rod of diameter (d)=
 3 cm is used to heat the water. The rate of heat generation (q<sub class=
=3D"EBsub">g</sub>) in the rod is 50</em>, <em>000 kW/m<sup class=3D"EBsup"=
>3</sup> and the thermal conductivity (K) is 30 W/mK. If the surface temper=
ature of the rod is maintained at 120=C2=B0C (T<sub class=3D"EBsub">w</sub>=
)</em>, <em>what is the maximum temperature inside the rod?</em></p>
<p id=3D"p0626" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0204" class=3D"imagewrap">
<img id=3D"img0479" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg50_img01.png" alt=3D"image" width=3D"196" he=
ight=3D"113" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg50_img01.png">
</div>
<p id=3D"p0627" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0628" class=3D"EB26SmallTextHangingIndent">2.16. <em>A hollow sph=
ere of inner radius</em>, <em>r<sub class=3D"EBsub">1</sub> =3D 4 cm and ou=
ter radius</em>, <em>r<sub class=3D"EBsub">2</sub> =3D 6 cm is heated at th=
e inner surface at the rate of 10<sup class=3D"EBsup">5</sup> W/m<sup class=
=3D"EBsup">2</sup> (q). The outer surface is exposed to a fluid at temperat=
ure (T<sub class=3D"EBsub">a</sub>) of 100=C2=B0C with heat transfer coeffi=
cient (h) of 450 W/m<sup class=3D"EBsup">2</sup>=C2=B0C. Find the surface t=
emperatures of the sphere. The thermal conductivity (K) is 20 W/m<sup class=
=3D"EBsup">2</sup>=C2=B0C.</em></p>
<p id=3D"p0629" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0630" class=3D"EB27SmallTextExtraIndent">Here</p>
<p id=3D"p0631" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0205" class=3D"imagewrap">
<img id=3D"img0480" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg50_img02.png" alt=3D"image" width=3D"70" hei=
ght=3D"62" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg50_img02.png">
</div>
<p id=3D"p0632" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0633" class=3D"EB27SmallTextExtraIndent">where <em>T</em><sub cla=
ss=3D"EBsub">1</sub> is the inner surface temperature</p>
<p id=3D"p0634" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0206" class=3D"imagewrap">
<img id=3D"img0481" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg50_img02a.png" alt=3D"image" width=3D"146" h=
eight=3D"102" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/ima=
ges/pg50_img02a.png">
</div>
<p id=3D"p0635" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0636" class=3D"EB27SmallTextExtraIndent">and</p>
<p id=3D"p0637" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0207" class=3D"imagewrap">
<img id=3D"img0482" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg50_img03.png" alt=3D"image" width=3D"202" he=
ight=3D"85" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg50_img03.png">
</div>
<p id=3D"p0638" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0639" class=3D"EB27SmallTextExtraIndent">Therefore,</p>
<p id=3D"p0640" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0208" class=3D"imagewrap">
<img id=3D"img0483" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg50_img03a.png" alt=3D"image" width=3D"232" h=
eight=3D"30" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg50_img03a.png">
</div>
<p id=3D"p0641" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0642" class=3D"EB27SmallTextExtraIndent">Then</p>
<p id=3D"p0643" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0209" class=3D"imagewrap">
<img class=3D"Eq1" id=3D"img0197" src=3D"https://learning.oreilly.com/libra=
ry/view/heat-and-mass/9789332515680/images/pg50_img04.png" alt=3D"image" wi=
dth=3D"213" height=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/97893=
32515680/images/pg50_img04.png"> (outside surface temperature).
</div>
<p id=3D"p0644" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0645" class=3D"EB26SmallTextHangingIndent">2.17. <em>A hollow sph=
ere with an outer diameter (d<sub class=3D"EBsub">1</sub>) of 4 cm and oute=
r diameter of 12 cm is kept at an inner surface temperature (T</em><sub cla=
ss=3D"EBsub">1</sub><em>) of 383 K and outer surface temperature (T<sub cla=
ss=3D"EBsub">2</sub>) of 323 K. Calculate the heat transfer and temperature=
 at d =3D 8 cm. The thermal conductivity of the sphere is 150 W/m=C2=B0C.</=
em></p>
<p id=3D"p0646" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0647" class=3D"EB27SmallTextExtraIndent">Heat transfer,</p>
<p id=3D"p0648" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0210" class=3D"imagewrap">
<img id=3D"img0484" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg50_img05.png" alt=3D"image" width=3D"64" hei=
ght=3D"30" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg50_img05.png">
</div>
<p id=3D"p0649" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0650" class=3D"EB27SmallTextExtraIndent"><a id=3D"page_51"></a>wh=
ere</p>
<p id=3D"p0651" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0211" class=3D"imagewrap">
<img id=3D"img0485" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg51_img01.png" alt=3D"image" width=3D"205" he=
ight=3D"55" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg51_img01.png">
</div>
<p id=3D"p0652" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0212" class=3D"imagewrap">
Therefore, <img class=3D"Eq1" id=3D"img0200" src=3D"https://learning.oreill=
y.com/library/view/heat-and-mass/9789332515680/images/pg51_img01a.png" alt=
=3D"image" width=3D"82" height=3D"51" data-mfp-src=3D"/library/view/heat-an=
d-mass/9789332515680/images/pg51_img01a.png">
</div>
<p id=3D"p0653" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0213" class=3D"imagewrap">
Also, <img class=3D"Eq1" id=3D"img0201" src=3D"https://learning.oreilly.com=
/library/view/heat-and-mass/9789332515680/images/pg51_img02.png" alt=3D"ima=
ge" width=3D"61" height=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/=
9789332515680/images/pg51_img02.png">
</div>
<p id=3D"p0654" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0214" class=3D"imagewrap">
<img id=3D"img0486" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg51_img02a.png" alt=3D"image" width=3D"289" h=
eight=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg51_img02a.png">
</div>
<p id=3D"p0655" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0215" class=3D"imagewrap">
<img class=3D"Eq1" id=3D"img0202" src=3D"https://learning.oreilly.com/libra=
ry/view/heat-and-mass/9789332515680/images/pg51_img02aa.png" alt=3D"image" =
width=3D"176" height=3D"31" data-mfp-src=3D"/library/view/heat-and-mass/978=
9332515680/images/pg51_img02aa.png"> (Temperature at <em>d</em> =3D 0.08m).
</div>
<p id=3D"p0656" class=3D"EB02BodyTextFullOut">&nbsp;</p>

<p id=3D"p0657" class=3D"EB26SmallTextHangingIndent">2.18. <em>A spherical<=
/em>, <em>thin-walled metallic container is used to store liquid nitrogen a=
t a temperature (T<sub class=3D"EBsub">1</sub>) of 193=C2=B0C. The containe=
r diameter (r<sub class=3D"EBsub">1</sub>) is 0.5 m and it is covered with =
two insulating materials each of thickness 25 mm and the outer surface is e=
xposed to ambient air at 303 K (T<sub class=3D"EBsub">a</sub>). The thermal=
 conductivities of the first and second insulating layers are 0.042 W/mK (K=
<sub class=3D"EBsub">1</sub>) and 0.0017 W/mK</em>, <em>respectively. If ou=
ter heat transfer coefficient is 20 W/m<sup class=3D"EBsup">2</sup>K and th=
e latent heat of vaporization (h<sub class=3D"EBsub">fg</sub>) of liquid ni=
trogen is 2</em> =C3=97 <em>10<sup class=3D"EBsup">2</sup> kJ/kg=C2=B0C. De=
termine the rate of vaporization of liquid nitrogen per hour.</em></p>
<p id=3D"p0658" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0659" class=3D"EB27SmallTextExtraIndent">Heat transfer rate,</p>
<p id=3D"p0660" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0216" class=3D"imagewrap">
<img id=3D"img0487" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg51_img03.png" alt=3D"image" width=3D"344" he=
ight=3D"276" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg51_img03.png">
</div>
<p id=3D"p0661" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0217" class=3D"imagewrap">{Heat flows from the ambient air to=
 nitrogen}</div>
<p id=3D"p0662" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0218" class=3D"imagewrap">Also <em>mh<sub class=3D"EBsub">fg<=
/sub> =3D Q</em></div>
<p id=3D"p0663" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0219" class=3D"imagewrap">
Therefore, <img class=3D"Eq1" id=3D"img0204" src=3D"https://learning.oreill=
y.com/library/view/heat-and-mass/9789332515680/images/pg51_img03e.png" alt=
=3D"image" width=3D"234" height=3D"56" data-mfp-src=3D"/library/view/heat-a=
nd-mass/9789332515680/images/pg51_img03e.png">
</div>
<p id=3D"p0664" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0665" class=3D"EB26SmallTextHangingIndent"><a id=3D"page_52"></a>=
2.19. <em>A composite wall consisting of four different materials is shown =
in the figure. Determine the heat flow rate and the interface temperatures =
also.</em></p>
<p id=3D"p0666" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0667" class=3D"EB27SmallTextExtraIndent">Let the width of the wal=
l be 1 m</p>
<p id=3D"p0668" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0220" class=3D"imagewrap">
<img id=3D"img0488" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg52_img01.png" alt=3D"image" width=3D"395" he=
ight=3D"136" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg52_img01.png">
</div>
<p id=3D"p0669" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0670" class=3D"EB27SmallTextExtraIndent">Heat transfer through th=
e wall, <em>Q</em> =3D <em>T</em><sub class=3D"EBsub">1</sub> =E2=80=93 <em=
>T</em><sub class=3D"EBsub">4</sub>/<em>R</em><sub class=3D"EBsub">total</s=
ub></p>
<p id=3D"p0671" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0221" class=3D"imagewrap">
<img id=3D"img0489" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg52_img02.png" alt=3D"image" width=3D"443" he=
ight=3D"128" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg52_img02.png">
</div>
<p id=3D"p0672" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0673" class=3D"EB27SmallTextExtraIndent">Here, <em>R</em><sub cla=
ss=3D"EBsub">total</sub> =3D <em>R<sub class=3D"EBsub">A</sub></em> + <em>R=
</em> + <em>R<sub class=3D"EBsub">B</sub></em></p>
<p id=3D"p0674" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0222" class=3D"imagewrap">
<img id=3D"img0490" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg52_img03.png" alt=3D"image" width=3D"326" he=
ight=3D"48" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg52_img03.png">
</div>
<p id=3D"p0675" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0223" class=3D"imagewrap">
<img id=3D"img0491" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg52_img04a.png" alt=3D"image" width=3D"226" h=
eight=3D"187" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/ima=
ges/pg52_img04a.png">
</div>
<p id=3D"p0676" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0224" class=3D"imagewrap">Therefore, <em>R</em> =3D 1.11 =C3=
=97 10<sup class=3D"EBsup">=E2=88=923=C2=B0</sup> C/W</div>
<p id=3D"p0677" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0225" class=3D"imagewrap">
<img id=3D"img0492" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg52_img04b.png" alt=3D"image" width=3D"270" h=
eight=3D"35" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg52_img04b.png">
</div>
<p id=3D"p0678" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0226" class=3D"imagewrap">Therefore, <em>R</em><sub class=3D"=
EBsub">total</sub> =3D 1.667 =C3=97 10<sup class=3D"EBsup">=E2=80=9330</sup=
> C/W</div>
<p id=3D"p0679" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0227" class=3D"imagewrap">
<img id=3D"img0493" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg52_img04.png" alt=3D"image" width=3D"207" he=
ight=3D"30" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg52_img04.png">
</div>
<p id=3D"p0680" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0681" class=3D"EB27SmallTextExtraIndent">Also we can write</p>
<p id=3D"p0682" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0228" class=3D"imagewrap"><a id=3D"page_53"></a>
<img id=3D"img0494" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg52_img04e.png" alt=3D"image" width=3D"212" h=
eight=3D"196" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/ima=
ges/pg52_img04e.png">
</div>
<p id=3D"p0683" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0684" class=3D"EB26SmallTextHangingIndent">2.20. <em>Consider a p=
ipe with an inner radius (r<sub class=3D"EBsub">1</sub>) of 5 cm and an out=
er radius (r<sub class=3D"EBsub">2</sub>) of 7 cm. The inner surface is kep=
t at 100=C2=B0C (T</em><sub class=3D"EBsub">1</sub><em>) and the outer surf=
ace at 80=C2=B0C (T<sub class=3D"EBsub">2</sub>). Determine the heat loss p=
er metre length of the pipe if the pipe is made up of pure copper (K<sub cl=
ass=3D"EBsub">c</sub> =3D 387 W/m=C2=B0C)</em>, <em>pure aluminium (K<sub c=
lass=3D"EBsub">a</sub> =3D 200 W/m=C2=B0C) and pure iron (K<sub class=3D"EB=
sub">i</sub>. =3D 62 W/m=C2=B0C).</em></p>
<p id=3D"p0685" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0686" class=3D"EB27SmallTextExtraIndent">Heat loss per metre leng=
th of copper pipe (<em>Q<sub class=3D"EBsub">c</sub></em>) =3D (<em>T</em><=
sub class=3D"EBsub">1</sub> =E2=88=92 <em>T</em><sub class=3D"EBsub">2</sub=
>)/<em>R</em></p>
<p id=3D"p0687" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0229" class=3D"imagewrap">
<img id=3D"img0495" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg53_img02a.png" alt=3D"image" width=3D"142" h=
eight=3D"29" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg53_img02a.png">
</div>
<p id=3D"p0688" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0230" class=3D"imagewrap">
<img id=3D"img0496" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg53_img02.png" alt=3D"image" width=3D"293" he=
ight=3D"96" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg53_img02.png">
</div>
<p id=3D"p0689" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0690" class=3D"EB27SmallTextExtraIndent">For a pure aluminium pip=
e</p>
<p id=3D"p0691" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0231" class=3D"imagewrap">
<img id=3D"img0497" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg53_img03b.png" alt=3D"image" width=3D"229" h=
eight=3D"93" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg53_img03b.png">
</div>
<p id=3D"p0692" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0232" class=3D"imagewrap">For a pure iron pipe, <em>R</em> =
=3D 8.637 =C3=97 10<sup class=3D"EBsup">=E2=88=924=C2=B0</sup> C/W.</div>
<p id=3D"p0693" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0233" class=3D"imagewrap">
<img id=3D"img0498" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg53_img03bb.png" alt=3D"image" width=3D"256" =
height=3D"30" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/ima=
ges/pg53_img03bb.png">
</div>
<p id=3D"p0694" class=3D"EB02BodyTextFullOut">&nbsp;</p>


<p id=3D"p0695" class=3D"EB26SmallTextHangingIndent">2.21. <em>A pipe of ou=
ter diameter 5 cm and thickness (t) 0.5 cm and thermal conductivity</em>, <=
em>K =3D 386 W/mK has hot gas flowing inside at a temperature of T<sub clas=
s=3D"EBsub">g</sub> of 200=C2=B0C with h<sub class=3D"EBsub">i</sub> =3D 30=
 W/m<sup class=3D"EBsup">2</sup>K. The outer surface dissipates heat by con=
vection into the ambient air at 20=C2=B0C (T<sub class=3D"EBsub">a</sub>) w=
ith h<sub class=3D"EBsub">0</sub> =3D 15 W/mK. Determine the heat loss from=
 the pipe per metre length of the pipe.</em></p>
<p id=3D"p0696" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0697" class=3D"EB27SmallTextExtraIndent">Heat loss per metre leng=
th of the pipe,</p>
<p id=3D"p0698" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0234" class=3D"imagewrap">
<img id=3D"img0499" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg53_img04.png" alt=3D"image" width=3D"98" hei=
ght=3D"36" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg53_img04.png">
</div>
<p id=3D"p0699" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0700" class=3D"EB27SmallTextExtraIndent">where</p>
<p id=3D"p0701" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0235" class=3D"imagewrap">
<img id=3D"img0500" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg53_img04a.png" alt=3D"image" width=3D"282" h=
eight=3D"97" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg53_img04a.png">
</div>
<p id=3D"p0702" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0236" class=3D"imagewrap">
<img id=3D"img0501" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg54_img01.png" alt=3D"image" width=3D"250" he=
ight=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg54_img01.png">
</div>
<div id=3D"div0237" class=3D"imagewrap"><a id=3D"page_54"></a>
Therefore, <img class=3D"Eq1" id=3D"img0215" src=3D"https://learning.oreill=
y.com/library/view/heat-and-mass/9789332515680/images/pg54_img01a.png" alt=
=3D"image" width=3D"202" height=3D"30" data-mfp-src=3D"/library/view/heat-a=
nd-mass/9789332515680/images/pg54_img01a.png">
</div>
<p id=3D"p0703" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0704" class=3D"EB26SmallTextHangingIndent">2.22. <em>Consider a s=
teel pipe (K<sub class=3D"EBsub">1</sub> =3D 10 W/m=C2=B0C) with an inner r=
adius (r<sub class=3D"EBsub">1</sub>) of 5 cm and outer radius (r<sub class=
=3D"EBsub">2</sub>) of 10 cm. The outer surface is to be insulated with a f=
ibreglass insulation (K<sub class=3D"EBsub">2</sub> =3D 0.05 W/m=C2=B0C) to=
 reduce the heat flow rate through the pipe wall by 50%. Determine the thic=
kness of the fibreglass insulation.</em></p>
<p id=3D"p0705" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0706" class=3D"EB27SmallTextExtraIndent">The heat transfer withou=
t the insulation, <em>Q</em><sub class=3D"EBsub">1</sub> =3D (<em>T</em><su=
b class=3D"EBsub">1</sub> =E2=80=93 <em>T</em><sub class=3D"EBsub">2</sub>)=
/R<sub class=3D"EBsub">l</sub></p>
<p id=3D"p0707" class=3D"EB27SmallTextExtraIndent">The heat transfer with t=
he insulation, <em>Q</em><sub class=3D"EBsub">2</sub> =3D <em>T</em><sub cl=
ass=3D"EBsub">1</sub> =E2=80=93 <em>T</em><sub class=3D"EBsub">2</sub>/<em>=
R</em><sub class=3D"EBsub">1</sub> + <em>R</em><sub class=3D"EBsub">2</sub>=
</p>
<p id=3D"p0708" class=3D"EB27SmallTextExtraIndent">But <em>Q</em><sub class=
=3D"EBsub">2</sub> =3D 0.5<em>Q</em><sub class=3D"EBsub">1</sub>for the sam=
e temperature difference</p>
<p id=3D"p0709" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0710" class=3D"EB27SmallTextExtraIndent">Therefore,</p>
<p id=3D"p0711" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0238" class=3D"imagewrap"><em>R</em><sub class=3D"EBsub">1</s=
ub> + <em>R</em><sub class=3D"EBsub">2</sub> =3D 2<em>R</em><sub class=3D"E=
Bsub">1</sub> =E2=87=92 <em>R</em><sub class=3D"EBsub">2</sub> =3D <em>R</e=
m><sub class=3D"EBsub">1</sub></div>
<p id=3D"p0712" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0713" class=3D"EB27SmallTextExtraIndent">That is,</p>
<p id=3D"p0714" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0239" class=3D"imagewrap">
<img id=3D"img0502" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg54_img02.png" alt=3D"image" width=3D"269" he=
ight=3D"199" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg54_img02.png">
</div>
<p id=3D"p0715" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0716" class=3D"EB27SmallTextExtraIndent">The thickness of the ins=
ulation is <em>r</em><sub class=3D"EBsub">3</sub> =E2=88=92 <em>r</em><sub =
class=3D"EBsub">2</sub> =3D 0.0347 cm.</p>
<p id=3D"p0717" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0718" class=3D"EB26SmallTextHangingIndent">2.23. <em>A pipe havin=
g an outer diameter (r<sub class=3D"EBsub">1</sub>) of 40 mm is to be insul=
ated with two layers of insulation</em>, <em>each having a thickness of 30 =
mm. The thermal conductivities of the inner and outer insulation materials =
are (K<sub class=3D"EBsub">1</sub>) 0.8 W/m<sup class=3D"EBsup">2</sup>=C2=
=B0C and (K<sub class=3D"EBsub">2</sub>) 0.4 W/m<sup class=3D"EBsup">2</sup=
>=C2=B0C</em>, <em>respectively. Calculate the change in heat transfer rate=
 if the two insulators are interchanged</em>, <em>if the pipe temperature (=
T<sub class=3D"EBsub">1</sub>) is 200=C2=B0C and the temperature of the out=
er insulation is 50=C2=B0C (T<sub class=3D"EBsub">3</sub>).</em></p>
<ol id=3D"ol0013" class=3D"LowerAlpha">
<li id=3D"li0038" class=3D"EB23ListFirst">The better insulator is outside
<p id=3D"p0719" class=3D"EB02BodyTextFullOut">The heat transfer,</p>
<p id=3D"p0720" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0240" class=3D"imagewrap">
<img id=3D"img0503" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg54_img03.png" alt=3D"image" width=3D"73" hei=
ght=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg54_img03.png">
</div>
<p id=3D"p0721" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0722" class=3D"EB02BodyTextFullOut">where</p>
<p id=3D"p0723" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0241" class=3D"imagewrap">
<img id=3D"img0504" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg54_img03a.png" alt=3D"image" width=3D"261" h=
eight=3D"125" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/ima=
ges/pg54_img03a.png">
</div>
<p id=3D"p0724" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0242" class=3D"imagewrap"><a id=3D"page_55"></a>
<img class=3D"Eq1" id=3D"img0219" src=3D"https://learning.oreilly.com/libra=
ry/view/heat-and-mass/9789332515680/images/pg54_img03b.png" alt=3D"image" w=
idth=3D"204" height=3D"30" data-mfp-src=3D"/library/view/heat-and-mass/9789=
332515680/images/pg54_img03b.png"> W/m length of the pipe
</div>
<p id=3D"p0725" class=3D"EB02BodyTextFullOut">&nbsp;</p></li>
<li id=3D"li0039" class=3D"EB25ListLast">The better insulation is inside
<p id=3D"p0726" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0243" class=3D"imagewrap">
<img id=3D"img0505" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg55_img02.png" alt=3D"image" width=3D"227" he=
ight=3D"163" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg55_img02.png">
</div>
<p id=3D"p0727" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0728" class=3D"EB02BodyTextFullOut">Drop in heat transfer rate =
=3D <em>Q</em><sub class=3D"EBsub">1</sub> =E2=80=93 <em>Q</em><sub class=
=3D"EBsub">2</sub> =3D 82.88 W/m.</p>
</li></ol>
<p id=3D"p0729" class=3D"EB26SmallTextHangingIndent">2.24. <em>Two stainles=
s steel blocks each having K =3D 20 W/m=C2=B0C thickness (t) of 1 cm</em>, =
<em>length (b) of 8 cm and width of 6 cm are pressed together. The contact =
conductance becomes h =3D 10</em>, <em>000 W/m<sup class=3D"EBsup">2</sup>=
=C2=B0C. The outer surfaces of the blocks are at 120=C2=B0 and 70=C2=B0 Cal=
culate the heat flow rate and temperature drop at the interface.</em></p>
<p id=3D"p0730" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0244" class=3D"imagewrap">
<img id=3D"img0506" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg55_img03.png" alt=3D"image" width=3D"342" he=
ight=3D"207" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg55_img03.png">
</div>
<p id=3D"p0731" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0732" class=3D"EB27SmallTextExtraIndent">The heat transfer,</p>
<p id=3D"p0733" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0245" class=3D"imagewrap">
<img id=3D"img0507" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg55_img04.png" alt=3D"image" width=3D"98" hei=
ght=3D"35" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg55_img04.png">
</div>
<p id=3D"p0734" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0735" class=3D"EB27SmallTextExtraIndent">where</p>
<p id=3D"p0736" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0246" class=3D"imagewrap">
<img id=3D"img0508" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg55_img04b.png" alt=3D"image" width=3D"241" h=
eight=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg55_img04b.png">
</div>
<p id=3D"p0737" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0738" class=3D"EB27SmallTextExtraIndent">The contact resistance, =
<em>R</em><sub class=3D"EBsub">2</sub> =3D 1/<em>hA</em> =3D 110,000 =C3=97=
 0.08 =C3=97 0.06 =3D 0.021=C2=B0C/W</p>
<p id=3D"p0739" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0740" class=3D"EB27SmallTextExtraIndent">and</p>
<p id=3D"p0741" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0247" class=3D"imagewrap"><em>R</em><sub class=3D"EBsub">3</s=
ub> =3D <em>R</em><sub class=3D"EBsub">1</sub> =3D 0.1042=C2=B0C/W</div>
<p id=3D"p0742" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0743" class=3D"EB27SmallTextExtraIndent">Therefore,</p>
<p id=3D"p0744" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0248" class=3D"imagewrap">
<img id=3D"img0509" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg55_img04c.png" alt=3D"image" width=3D"143" h=
eight=3D"31" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg55_img04c.png">
</div>
<p id=3D"p0745" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0746" class=3D"EB27SmallTextExtraIndent">Also</p>
<p id=3D"p0747" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0249" class=3D"imagewrap">
<img id=3D"img0510" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg55_img04d.png" alt=3D"image" width=3D"65" he=
ight=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg55_img04d.png">
</div>
<p id=3D"p0748" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0749" class=3D"EB27SmallTextExtraIndent"><a id=3D"page_56"></a>Th=
at is, temperature drop across the contact,</p>
<p id=3D"p0750" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0250" class=3D"imagewrap"><em>T</em><sub class=3D"EBsub">2</s=
ub> =E2=80=93 <em>T</em><sub class=3D"EBsub">3</sub> =3D <em>QR</em><sub cl=
ass=3D"EBsub">2</sub></div>
<div id=3D"div0251" class=3D"imagewrap">=3D 217.96 =C3=97 0.021</div>
<div id=3D"div0252" class=3D"imagewrap">=3D 4.58=C2=B0C.</div>
<p id=3D"p0751" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0752" class=3D"EB26SmallTextHangingIndent">2.25. <em>Determine th=
e interface temperature T<sub class=3D"EBsub">2</sub> and the surface tempe=
rature T<sub class=3D"EBsub">4</sub> of the composite wall shown in the fig=
ure.</em></p>
<p id=3D"p0753" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0253" class=3D"imagewrap">
<img id=3D"img0511" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg56_img01.png" alt=3D"image" width=3D"308" he=
ight=3D"326" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg56_img01.png">
</div>
<p id=3D"p0754" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0755" class=3D"EB27SmallTextExtraIndent">Let <em>A</em> =3D 1 m<s=
up class=3D"EBsup">2</sup></p>
<p id=3D"p0756" class=3D"EB27SmallTextExtraIndent">The heat transfer rate,<=
/p>
<p id=3D"p0757" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0254" class=3D"imagewrap">
<img id=3D"img0512" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg56_img02.png" alt=3D"image" width=3D"176" he=
ight=3D"79" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg56_img02.png">
</div>
<p id=3D"p0758" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0759" class=3D"EB27SmallTextExtraIndent">here</p>
<p id=3D"p0760" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0255" class=3D"imagewrap">
<img id=3D"img0513" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg56_img02a.png" alt=3D"image" width=3D"165" h=
eight=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg56_img02a.png">
</div>
<p id=3D"p0761" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0256" class=3D"imagewrap">
<img id=3D"img0514" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg56_img02b.png" alt=3D"image" width=3D"166" h=
eight=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg56_img02b.png">
</div>
<p id=3D"p0762" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0763" class=3D"EB27SmallTextExtraIndent">and</p>
<p id=3D"p0764" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0257" class=3D"imagewrap">
<img id=3D"img0515" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg56_img02c.png" alt=3D"image" width=3D"173" h=
eight=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg56_img02c.png">
</div>
<p id=3D"p0765" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0766" class=3D"EB27SmallTextExtraIndent">Therefore,</p>
<p id=3D"p0767" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0258" class=3D"imagewrap">
<img id=3D"img0516" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg56_img02d.png" alt=3D"image" width=3D"179" h=
eight=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg56_img02d.png">
</div>
<p id=3D"p0768" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0769" class=3D"EB27SmallTextExtraIndent"><a id=3D"page_57"></a>Al=
so</p>
<p id=3D"p0770" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0259" class=3D"imagewrap">
<img id=3D"img0517" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg57_img01.png" alt=3D"image" width=3D"273" he=
ight=3D"57" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg57_img01.png">
</div>
<p id=3D"p0771" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0772" class=3D"EB27SmallTextExtraIndent">Similarly,</p>
<p id=3D"p0773" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0260" class=3D"imagewrap"><em>T</em><sub class=3D"EBsub">2</s=
ub> =3D <em>T</em><sub class=3D"EBsub">1</sub> =E2=80=93 <em>QR</em><sub cl=
ass=3D"EBsub">1</sub> =3D 150 =E2=80=93 416.7 =C3=97 0.2 =3D 66.7=C2=B0C.</=
div>
<p id=3D"p0774" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0775" class=3D"EB26SmallTextHangingIndent">2.26. <em>The surface =
of a slab of thickness 20 cm (L) is kept at 30=C2=B0C (T<sub class=3D"EBsub=
">a</sub>) and the other surface is at 110=C2=B0C (T<sub class=3D"EBsub">b<=
/sub>) Compare the heat flux across the slab if the slab were made of pure =
copper (K<sub class=3D"EBsub">c</sub> =3D 390 W/s=C2=B0C)</em>, <em>pure al=
uminium (K<sub class=3D"EBsub">a</sub> =3D 200 W/m=C2=B0C) and steel (K<sub=
 class=3D"EBsub">s</sub> =3D 50 W/m=C2=B0C).</em></p>
<p id=3D"p0776" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0777" class=3D"EB27SmallTextExtraIndent">Heat transfer across a c=
opper slab,</p>
<p id=3D"p0778" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0261" class=3D"imagewrap">
<img id=3D"img0518" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg57_img02.png" alt=3D"image" width=3D"215" he=
ight=3D"72" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg57_img02.png">
</div>
<p id=3D"p0779" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0780" class=3D"EB27SmallTextExtraIndent">Heat transfer across an =
aluminium slab,</p>
<p id=3D"p0781" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0262" class=3D"imagewrap">
<img id=3D"img0519" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg57_img02a.png" alt=3D"image" width=3D"199" h=
eight=3D"73" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg57_img02a.png">
</div>
<p id=3D"p0782" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0783" class=3D"EB27SmallTextExtraIndent">Heat transfer across a s=
teel slab,</p>
<p id=3D"p0784" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0263" class=3D"imagewrap">
<img id=3D"img0520" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg57_img02b.png" alt=3D"image" width=3D"219" h=
eight=3D"73" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg57_img02b.png">
</div>
<p id=3D"p0785" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0786" class=3D"EB26SmallTextHangingIndent">2.27. <em>A wall of a =
building is made up of 8 cm of brick (K<sub class=3D"EBsub">1</sub> =3D 0.6=
9 W/m =C2=B0C)</em>, <em>2 cm of celotex (K<sub class=3D"EBsub">2</sub> =3D=
 0.048 W/m=C2=B0C) and 2 cm of an asbestos cemented board (K<sub class=3D"E=
Bsub">3</sub> =3D 0.74 W/m=C2=B0C). Glass wool (K<sub class=3D"EBsub">4</su=
b> =3D 0.038 W/m=C2=B0C) is to be added between the celotex and asbestos in=
 order to reduce the heat flow rate through the wall by 50%. Determine the =
thickness of the glass wool.</em></p>
<p id=3D"p0787" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0788" class=3D"EB27SmallTextExtraIndent">Let the area of the wall=
 considered be 1 m<sup class=3D"EBsup">2</sup></p>
<p id=3D"p0789" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0264" class=3D"imagewrap">
<img id=3D"img0521" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg57_img03.png" alt=3D"image" width=3D"333" he=
ight=3D"45" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg57_img03.png">
</div>
<p id=3D"p0790" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0791" class=3D"EB27SmallTextExtraIndent">Heat transfer across the=
 three layers,</p>
<p id=3D"p0792" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0265" class=3D"imagewrap">
<img id=3D"img0522" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg57_img04a.png" alt=3D"image" width=3D"98" he=
ight=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg57_img04a.png">
</div>
<p id=3D"p0793" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0794" class=3D"EB27SmallTextExtraIndent">where</p>
<p id=3D"p0795" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0266" class=3D"imagewrap">
<img id=3D"img0523" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg57_img04.png" alt=3D"image" width=3D"197" he=
ight=3D"77" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg57_img04.png">
</div>
<p id=3D"p0796" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0267" class=3D"imagewrap"><a id=3D"page_58"></a>
and  <img class=3D"Eq1" id=3D"img0239" src=3D"https://learning.oreilly.com/=
library/view/heat-and-mass/9789332515680/images/pg58_img01.png" alt=3D"imag=
e" width=3D"189" height=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/=
9789332515680/images/pg58_img01.png">
</div>
<p id=3D"p0797" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0798" class=3D"EB27SmallTextExtraIndent">Addition of glass wool r=
educes the heat transfer by 50% due to an increase in the thermal resistanc=
e for the same temperature difference.</p>
<p id=3D"p0799" class=3D"EB27SmallTextExtraIndent">That is,</p>
<p id=3D"p0800" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0268" class=3D"imagewrap">
<img id=3D"img0524" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg58_img02.png" alt=3D"image" width=3D"234" he=
ight=3D"39" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg58_img02.png">
</div>
<p id=3D"p0801" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0802" class=3D"EB27SmallTextExtraIndent">where</p>
<p id=3D"p0803" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0269" class=3D"imagewrap"><em>T</em><sub class=3D"EBsub">5</s=
ub>  =3D <em>T</em><sub class=3D"EBsub">4</sub> <em>and R</em><sub class=3D=
"EBsub">4</sub> =3D <em>L</em><sub class=3D"EBsub">4</sub>/<em>K</em><sub c=
lass=3D"EBsub">4</sub> =C3=97 <em>A</em> for the glass wool layer</div>
<p id=3D"p0804" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0805" class=3D"EB27SmallTextExtraIndent">Therefore,</p>
<p id=3D"p0806" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0270" class=3D"imagewrap">2(<em>R</em><sub class=3D"EBsub">1<=
/sub> + <em>R</em><sub class=3D"EBsub">2</sub><em>+ R</em><sub class=3D"EBs=
ub">3</sub>) =3D <em>R</em><sub class=3D"EBsub">1</sub><em>+ R</em><sub cla=
ss=3D"EBsub">2</sub><em>+ R</em><sub class=3D"EBsub">3</sub> + <em>R</em><s=
ub class=3D"EBsub">4</sub></div>
<div id=3D"div0271" class=3D"imagewrap"><em>R</em><sub class=3D"EBsub">4</s=
ub> =3D <em>R</em><sub class=3D"EBsub">1</sub> + <em>R</em><sub class=3D"EB=
sub">2</sub> + <em>R</em><sub class=3D"EBsub">3</sub></div>
<p id=3D"p0807" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0272" class=3D"imagewrap">
<img id=3D"img0525" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg58_img02a.png" alt=3D"image" width=3D"164" h=
eight=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg58_img02a.png">
</div>
<p id=3D"p0808" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0809" class=3D"EB27SmallTextExtraIndent">Therefore, <em>L</em><su=
b class=3D"EBsub">4</sub> =3D 2.13 cm thickness of glass wool.</p>
<p id=3D"p0810" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0811" class=3D"EB02BodyTextFullOut"><em>2.28. A container wall ma=
de of a 2-cm-thick (L) iron plate (K =3D 62 W/m=C2=B0C) is exposed to hot g=
as at 530=C2=B0C (T<sub class=3D"EBsub">g</sub>) with heat transfer coeffic=
ient of 100 W/m<sup class=3D"EBsup">2</sup>=C2=B0C (h<sub class=3D"EBsub">g=
</sub>) and the other side is in contact with cool air at 30=C2=B0C (T<sub =
class=3D"EBsub">a</sub>) with a heat transfer coefficient of 20 W/m<sup cla=
ss=3D"EBsup">2</sup>=C2=B0C (h</em><sub class=3D"EBsub">a</sub> <em>)</em>.=
 <em>Calculate the heat flowing through the wall per unit surface area and =
the wall temperature.</em></p>
<p id=3D"p0812" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0813" class=3D"EB27SmallTextExtraIndent">Heat transfer per unit a=
rea, <em>q</em> =3D (<em>T<sub class=3D"EBsub">g</sub></em> =E2=88=92 <em>T=
<sub class=3D"EBsub">a</sub></em>)/(<em>R</em><sub class=3D"EBsub">1</sub> =
+ <em>R</em><sub class=3D"EBsub">2</sub> + <em>R</em><sub class=3D"EBsub">3=
</sub>)</p>
<p id=3D"p0814" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0273" class=3D"imagewrap">
<img id=3D"img0526" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg58_img03.png" alt=3D"image" width=3D"333" he=
ight=3D"56" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg58_img03.png">
</div>
<p id=3D"p0815" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0816" class=3D"EB27SmallTextExtraIndent">where</p>
<p id=3D"p0817" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0274" class=3D"imagewrap">
<img id=3D"img0527" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg58_img04.png" alt=3D"image" width=3D"223" he=
ight=3D"161" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg58_img04.png">
</div>
<p id=3D"p0818" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0819" class=3D"EB27SmallTextExtraIndent">If the wall temperatures=
 are <em>T</em><sub class=3D"EBsub">1</sub> and <em>T</em><sub class=3D"EBs=
ub">2</sub>, then</p>
<p id=3D"p0820" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0275" class=3D"imagewrap">
<img id=3D"img0528" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg58_img05.png" alt=3D"image" width=3D"211" he=
ight=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg58_img05.png">
</div>
<p id=3D"p0821" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0822" class=3D"EB27SmallTextExtraIndent">Also</p>
<p id=3D"p0823" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0276" class=3D"imagewrap">
<img id=3D"img0529" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg58_img05a.png" alt=3D"image" width=3D"213" h=
eight=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg58_img05a.png">
</div>
<p id=3D"p0824" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0825" class=3D"EB26SmallTextHangingIndent">2.29. <em>A styrofoam =
ice box (K =3D 0.033 W/m=C2=B0C) has inner dimensions 25 cm</em> =C3=97 <em=
>40 cm</em> =C3=97 <em>100 cm. The thickness of the wall is 5 cm. The outsi=
de of the box is exposed to air at 25=C2=B0C with h =3D 10 W/m<sup class=3D=
"EBsup">2</sup>=C2=B0C. If the box is <a id=3D"page_59"></a>completely fill=
ed with ice</em>, <em>calculate the time required for the ice to completely=
 melt. State your assumptions. The heat of fusion for water is 330 kJ/kg. L=
et the heat be transferred to the air through the walls only and assume tha=
t density of ice is 1000 kg/m<sup class=3D"EBsup">3</sup>.</em></p>
<p id=3D"p0826" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0277" class=3D"imagewrap">Mass of the ice, <em>m =3D</em> vol=
ume of the box =C3=97 the density of ice</div>
<div id=3D"div0278" class=3D"imagewrap">=3D 0.25 =C3=97 0.40 =C3=97 1 =C3=
=97 1000 =3D 100kg</div>
<p id=3D"p0827" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0279" class=3D"imagewrap">The heat that has to be supplied</d=
iv>
<div id=3D"div0280" class=3D"imagewrap">to melt the ice completely</div>
<div id=3D"div0281" class=3D"imagewrap">=3D <em>m</em> =C3=97 heat of fusio=
n</div>
<div id=3D"div0282" class=3D"imagewrap">=3D 100 =C3=97 330 =3D 33000 kJ</di=
v>
<p id=3D"p0828" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0283" class=3D"imagewrap">Total heat transfer area =3D LH + B=
H + LB=C3=972</div>
<div id=3D"div0284" class=3D"imagewrap">=3D 2[0.25 =C3=97 1 + 0.4 =C3=97 1 =
+ 0.25 =C3=97 0.4]</div>
<div id=3D"div0285" class=3D"imagewrap">=3D 1.5m<sup class=3D"EBsup">2</sup=
></div>
<p id=3D"p0829" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0830" class=3D"EB27SmallTextExtraIndent">Therefore the heat trans=
fer rate, <em>Q</em> =3D (<em>T</em><sub class=3D"EBsub">a</sub> =E2=88=92 =
<em>T</em>)/(<em>R</em><sub class=3D"EBsub">1</sub> + <em>R</em><sub class=
=3D"EBsub">2</sub>), where <em>T</em> =3D temperature of ice</p>
<p id=3D"p0831" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0286" class=3D"imagewrap">
where <img class=3D"Eq1" id=3D"img0246" src=3D"https://learning.oreilly.com=
/library/view/heat-and-mass/9789332515680/images/pg59_img01.png" alt=3D"ima=
ge" width=3D"192" height=3D"30" data-mfp-src=3D"/library/view/heat-and-mass=
/9789332515680/images/pg59_img01.png">
</div>
<p id=3D"p0832" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0287" class=3D"imagewrap">
<img id=3D"img0530" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg59_img01a.png" alt=3D"image" width=3D"182" h=
eight=3D"29" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg59_img01a.png">
</div>
<p id=3D"p0833" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0288" class=3D"imagewrap">
Therefore, <img class=3D"Eq1" id=3D"img0248" src=3D"https://learning.oreill=
y.com/library/view/heat-and-mass/9789332515680/images/pg59_img01b.png" alt=
=3D"image" width=3D"126" height=3D"30" data-mfp-src=3D"/library/view/heat-a=
nd-mass/9789332515680/images/pg59_img01b.png">
</div>
<p id=3D"p0834" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0835" class=3D"EB27SmallTextExtraIndent">and the time taken for m=
elting =3D 395.1 h.</p>
<p id=3D"p0836" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0837" class=3D"EB26SmallTextHangingIndent">2.30. <em>A long hollo=
w cylinder of inner radius (r<sub class=3D"EBsub">1</sub>) 5 cm and outer r=
adius (r<sub class=3D"EBsub">2</sub>) 15 cm is considered. The inner surfac=
e is heated uniformly at a constant rate of (q) =3D 10<sup class=3D"EBsup">=
5</sup> W/m<sup class=3D"EBsup">2</sup>. If the inner surface is maintained=
 at 0=C2=B0C</em>, <em>T<sub class=3D"EBsub">1</sub></em>, <em>calculate th=
e temperature of the outer surface for K =3D 75 W/m=C2=B0C.</em></p>
<p id=3D"p0838" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0839" class=3D"EB27SmallTextExtraIndent">Total heat transfer,</p>
<p id=3D"p0840" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0289" class=3D"imagewrap">
<img id=3D"img0531" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg59_img02.png" alt=3D"image" width=3D"244" he=
ight=3D"204" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg59_img02.png">
</div>
<p id=3D"p0841" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0842" class=3D"EB27SmallTextExtraIndent">Outer surface temperatur=
e, <em>T</em><sub class=3D"EBsub">2</sub>=3D 1073=C2=B0 C.</p>
<p id=3D"p0843" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0844" class=3D"EB26SmallTextHangingIndent">2.31. <em>A hollow sph=
ere of inner radius (r<sub class=3D"EBsub">1</sub>) 10 cm and outer radius =
(r<sub class=3D"EBsub">2</sub>) 20 cm is considered. The inner surface is u=
niformly heated at a constant rate q =3D 1.6</em> =C3=97 <em>10<sup class=
=3D"EBsup">5</sup> W/m<sup class=3D"EBsup">2</sup> with an electric heater,=
 while the outer surface is maintained at zero temperature</em>, <em>calcul=
ate the inner surface temperature for K =3D 40 W/m=C2=B0C.</em></p>
<p id=3D"p0845" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0846" class=3D"EB27SmallTextExtraIndent">Total heat transfer,</p>
<p id=3D"p0847" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0290" class=3D"imagewrap"><a id=3D"page_60"></a>
<img id=3D"img0532" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg60_img01.png" alt=3D"image" width=3D"269" he=
ight=3D"153" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg60_img01.png">
</div>
<p id=3D"p0848" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0849" class=3D"EB27SmallTextExtraIndent">Therefore the inner surf=
ace temperature, <em>T</em><sub class=3D"EBsub">1</sub> =3D 200=C2=B0C.</p>
<p id=3D"p0850" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0851" class=3D"EB26SmallTextHangingIndent">2.32. <em>A long cylin=
drical rod of radius R =3D 5 cm; K =3D 10 W/m=C2=B0C contains radioactive m=
aterial which generates heat uniformly within the cylinder at a constant ra=
te of q<sub class=3D"EBsub">g</sub> =3D 3</em> =C3=97 <em>10<sup class=3D"E=
Bsup">5</sup> W/m<sup class=3D"EBsup">3</sup> The rod is cooled by convecti=
on taking place from its cylindrical surface into the ambient air at T<sub =
class=3D"EBsub">a</sub> =3D 50=C2=B0C with a heat transfer coefficient h =
=3D 60 W/m<sup class=3D"EBsup">2</sup>=C2=B0C. Determine the temperature at=
 the centre and the outer surface of this cylindrical rod.</em></p>
<p id=3D"p0852" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0853" class=3D"EB27SmallTextExtraIndent">Temperature at the centr=
e,</p>
<p id=3D"p0854" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0291" class=3D"imagewrap">
<img id=3D"img0533" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg60_img02b.png" alt=3D"image" width=3D"94" he=
ight=3D"32" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg60_img02b.png">
</div>
<p id=3D"p0855" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0856" class=3D"EB27SmallTextExtraIndent">where</p>
<p id=3D"p0857" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0292" class=3D"imagewrap">
<img id=3D"img0534" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg60_img02c.png" alt=3D"image" width=3D"129" h=
eight=3D"75" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg60_img02c.png">
<div id=3D"div0293" class=3D"imagewrap">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;=3D 175=C2=B0C, the outer surface temperature</div=
>
</div>
<p id=3D"p0858" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0859" class=3D"EB27SmallTextExtraIndent">Therefore</p>
<p id=3D"p0860" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0294" class=3D"imagewrap">
<img id=3D"img0535" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg60_img02a.png" alt=3D"image" width=3D"230" h=
eight=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg60_img02a.png">
</div>
<p id=3D"p0861" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0862" class=3D"EB26SmallTextHangingIndent">2.33. <em>An electric =
resistance wire of radius R =3D 1 mm</em>, <em>with K =3D 25 W/m=C2=B0C is =
heated by the passage of electric current which generates heat within the w=
ire at a constant rate of q<sub class=3D"EBsub">g</sub> =3D 2</em> =C3=97 <=
em>10<sup class=3D"EBsup">9</sup> W/m<sup class=3D"EBsup">3</sup>. Determin=
e the increase in centre-line temperature above the surface temperature of =
the wire if the surface is maintained at a constant temperature.</em></p>
<p id=3D"p0863" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0295" class=3D"imagewrap">
The centre-line temperature increase <img class=3D"Eq1" id=3D"img0254" src=
=3D"https://learning.oreilly.com/library/view/heat-and-mass/9789332515680/i=
mages/pg60_img03.png" alt=3D"image" width=3D"107" height=3D"34" data-mfp-sr=
c=3D"/library/view/heat-and-mass/9789332515680/images/pg60_img03.png">
</div>
<p id=3D"p0864" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0296" class=3D"imagewrap">
<img id=3D"img0536" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg60_img03a.png" alt=3D"image" width=3D"155" h=
eight=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg60_img03a.png">
</div>
<p id=3D"p0865" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0866" class=3D"EB02BodyTextFullOut"><em>2.34. A solid sphere of r=
adius R =3D 5 cm and K =3D 20 W/m=C2=B0C is heated uniformly at a rate of 2=
0000 W/m<sup class=3D"EBsup">3</sup> and convection heat transfer takes pla=
ce into the ambient air at T<sub class=3D"EBsub">a</sub> =3D 25=C2=B0C. The=
 heat transfer coefficient h is 20 W/m<sup class=3D"EBsup">2</sup>=C2=B0C. =
Determine temperature at the centre and the outer surface of the sphere at =
steady-state conditions.</em></p>
<p id=3D"p0867" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0297" class=3D"imagewrap">
The outer surface temperature <img class=3D"Eq1" id=3D"img0255" src=3D"http=
s://learning.oreilly.com/library/view/heat-and-mass/9789332515680/images/pg=
60_img04.png" alt=3D"image" width=3D"79" height=3D"32" data-mfp-src=3D"/lib=
rary/view/heat-and-mass/9789332515680/images/pg60_img04.png">
</div>
<p id=3D"p0868" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0298" class=3D"imagewrap">
<img id=3D"img0537" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg60_img04b.png" alt=3D"image" width=3D"173" h=
eight=3D"31" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg60_img04b.png">
</div>
<div id=3D"div0299" class=3D"imagewrap">
The temperature at the centre, <img class=3D"Eq1" id=3D"img0256" src=3D"htt=
ps://learning.oreilly.com/library/view/heat-and-mass/9789332515680/images/p=
g60_img04a.png" alt=3D"image" width=3D"94" height=3D"35" data-mfp-src=3D"/l=
ibrary/view/heat-and-mass/9789332515680/images/pg60_img04a.png">
</div>
<p id=3D"p0869" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0300" class=3D"imagewrap"><a id=3D"page_61"></a>
<img id=3D"img0538" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg61_img01.png" alt=3D"image" width=3D"203" he=
ight=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg61_img01.png">
</div>
<p id=3D"p0870" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0871" class=3D"EB26SmallTextHangingIndent">2.35. <em>An iron rod =
is attached horizontally to a large tank at temperature T<sub class=3D"EBsu=
b">b</sub> =3D 200=C2=B0C. The diameter of the rod (d) is 1 cm</em>, <em>le=
ngth (<strong>L</strong>) is 30 cm and thermal conductivity (<strong>K</str=
ong>) is 65 W/m=C2=B0C. The rod dissipates heat by convection into the ambi=
ent air at T<sub class=3D"EBsub">a</sub> =3D 20=C2=B0C</em>, <em>with h =3D=
 15 W/m<sup class=3D"EBsup">2</sup>=C2=B0C. What is the temperature of the =
rod at 10 cm and 20 cm from the tank? Calculate the heat transfer rate</em>=
, <em>the fin efficiency and effectiveness. Since the length to diameter ra=
tio is high</em>, <em>it is assumed to be a long fin.</em></p>
<p id=3D"p0872" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0301" class=3D"imagewrap">
<img id=3D"img0539" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg61_img02.png" alt=3D"image" width=3D"250" he=
ight=3D"39" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg61_img02.png">
</div>
<div id=3D"div0302" class=3D"imagewrap"><em>=CE=B8</em><sub class=3D"EBsub"=
>b</sub> =3D <em>T</em><sub class=3D"EBsub"><em>b</em></sub> =E2=88=92 <em>=
T</em><sub class=3D"EBsub"><em>a</em></sub> =3D 200 =E2=88=92 20 =3D 180=C2=
=B0C</div>
<p id=3D"p0873" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0874" class=3D"EB27SmallTextExtraIndent">Therefore</p>
<p id=3D"p0875" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0303" class=3D"imagewrap"><em>=CE=B8</em><sub class=3D"EBsub"=
><em>x</em> =3D 10</sub> =3D <em>=CE=B8</em><sub class=3D"EBsub"><em>b</em>=
</sub><em>e</em><sup class=3D"EBsup">=E2=88=92<em>mx</em></sup> =3D  180 =
=C3=97 <em>e</em><sup class=3D"EBsup">=E2=88=929.61</sup><sup class=3D"EBsu=
p">=C3=970.1</sup></div>
<div id=3D"div0304" class=3D"imagewrap">=3D 68.85=C2=B0C</div>
<p id=3D"p0876" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0877" class=3D"EB27SmallTextExtraIndent">That is</p>
<p id=3D"p0878" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0305" class=3D"imagewrap"><em>T</em><sub class=3D"EBsub"><em>=
x</em> =3D 10</sub> =3D 68.85 + 20 =3D 88.85=C2=B0C</div>
<p id=3D"p0879" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0880" class=3D"EB27SmallTextExtraIndent">Similarly</p>
<p id=3D"p0881" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0306" class=3D"imagewrap"><em>=CE=B8</em><sub class=3D"EBsub"=
><em>x</em> =3D 20</sub> =3D 180 =C3=97 <em>e</em><sup class=3D"EBsup">=E2=
=88=929.61=C3=970.2</sup> =3D 26.34=C2=B0C</div>
<p id=3D"p0882" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0883" class=3D"EB27SmallTextExtraIndent">That is</p>
<p id=3D"p0884" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0307" class=3D"imagewrap"><em>T</em><sub class=3D"EBsub"><em>=
x</em> =3D 20</sub> =3D 46.34=C2=B0C</div>
<p id=3D"p0885" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0886" class=3D"EB27SmallTextExtraIndent">The heat transfer rate,<=
/p>
<p id=3D"p0887" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0308" class=3D"imagewrap">
<img id=3D"img0540" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg61_img03.png" alt=3D"image" width=3D"251" he=
ight=3D"86" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg61_img03.png">
</div>
<p id=3D"p0888" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0889" class=3D"EB27SmallTextExtraIndent">The maximum heat transfe=
r,</p>
<p id=3D"p0890" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0309" class=3D"imagewrap"><em>Q</em><sub class=3D"EBsub">max<=
/sub> =3D <em>A<sub class=3D"EBsub">s</sub>h=CE=B8</em><sub class=3D"EBsub"=
>b</sub></div>
<div id=3D"div0310" class=3D"imagewrap">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=3D (<em=
>=CF=80</em> =C3=97 0.01 =C3=97 0.3) =C3=97 15 =C3=97 180</div>
<div id=3D"div0311" class=3D"imagewrap">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=3D 25.45W</div>
<p id=3D"p0891" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0312" class=3D"imagewrap">
<img id=3D"img0541" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg61_img04.png" alt=3D"image" width=3D"244" he=
ight=3D"137" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg61_img04.png">
</div>
<p id=3D"p0892" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0893" class=3D"EB26SmallTextHangingIndent">2.36. <em>Copper-plate=
 fins of rectangular cross-section having thickness t =3D 1 mm</em>, <em>he=
ight L =3D 10 mm and thermal conductivity K =3D 380 W/m=C2=B0C are attached=
 to a plane wall maintained at a temperature T<sub class=3D"EBsub">b</sub> =
=3D 230=C2=B0C. Fins dissipate heat by convection into ambient air at T<sub=
 class=3D"EBsub">a</sub> =3D 30=C2=B0C with h =3D 40 W/m<sup class=3D"EBsup=
">2</sup>=C2=B0C. Fins are spaced <a id=3D"page_62"></a>at 8 mm (that is</e=
m>, <em>125 fins/m). Assume heat loss from the fin tip to be negligible. De=
termine the fin efficiency</em>, <em>heat transfer per square metre of wall=
 surface and heat transfer without fins.</em></p>
<p id=3D"p0894" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0313" class=3D"imagewrap">
<img id=3D"img0542" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg62_img01.png" alt=3D"image" width=3D"254" he=
ight=3D"36" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg62_img01.png">
</div>
<div id=3D"div0314" class=3D"imagewrap"><em>=CE=B8</em><sub class=3D"EBsub"=
>b</sub> =3D <em>T</em><sub class=3D"EBsub"><em>b</em></sub> =E2=88=92 <em>=
T</em><sub class=3D"EBsub"><em>a</em></sub> =3D 230 =E2=88=92 30 =3D 200=C2=
=B0C</div>
<p id=3D"p0895" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0896" class=3D"EB27SmallTextExtraIndent">Total heat transfer =3D =
<em>Q<sub class=3D"EBsub">f</sub> + Q</em><sub class=3D"EBsub">unfinned</su=
b></p>
<p id=3D"p0897" class=3D"EB27SmallTextExtraIndent">Heat transfer through fi=
n,</p>
<p id=3D"p0898" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0315" class=3D"imagewrap">
<img class=3D"Eq1" id=3D"img0261" src=3D"https://learning.oreilly.com/libra=
ry/view/heat-and-mass/9789332515680/images/pg62_img02.png" alt=3D"image" wi=
dth=3D"161" height=3D"45" data-mfp-src=3D"/library/view/heat-and-mass/97893=
32515680/images/pg62_img02.png"> (assume the width of fin to be 1m)
</div>
<div id=3D"div0316" class=3D"imagewrap"><em>Q<sub class=3D"EBsub">f</sub> =
=3D</em> 125 =C3=97 200 =C3=97 380 =C3=97 (1 =C3=97 0.001) =C3=97 14.51 =C3=
=97 tanh(14.51 =C3=97 0.01)</div>
<div id=3D"div0317" class=3D"imagewrap">=3D 19862.1 W</div>
<p id=3D"p0899" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0900" class=3D"EB27SmallTextExtraIndent">Heat transfer through th=
e unfinned area =3D unfinned area =C3=97 <em>h</em> =C3=97 <em>=CE=B8<sub c=
lass=3D"EBsub">b</sub></em></p>
<p id=3D"p0901" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0318" class=3D"imagewrap"><em>Q</em><sub class=3D"EBsub">unfi=
nned</sub> =3D (1 =E2=88=92 125 =C3=97 0.001) =C3=97 40 =C3=97 200 =3D 7000=
 W</div>
<p id=3D"p0902" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0903" class=3D"EB27SmallTextExtraIndent">Therefore total heat tra=
nsfer =3D 26.86 kW</p>
<p id=3D"p0904" class=3D"EB27SmallTextExtraIndent">Maximum possible heat tr=
ansfer through the fin,</p>
<p id=3D"p0905" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0319" class=3D"imagewrap"><em>Q</em><sub class=3D"EBsub">max<=
/sub> =3D <em>nA<sub class=3D"EBsub">s</sub>h</em>, b</div>
<div id=3D"div0320" class=3D"imagewrap">=3D 125 =C3=97 (l =C3=97 0.0l =C3=
=97 2)40 =C3=97 200</div>
<div id=3D"div0321" class=3D"imagewrap">=3D 20, 000 W</div>
<p id=3D"p0906" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0322" class=3D"imagewrap">
<img id=3D"img0543" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg62_img03.png" alt=3D"image" width=3D"263" he=
ight=3D"35" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg62_img03.png">
</div>
<p id=3D"p0907" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0908" class=3D"EB27SmallTextExtraIndent">That is,</p>
<p id=3D"p0909" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0323" class=3D"imagewrap">
<img id=3D"img0544" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg62_img03a.png" alt=3D"image" width=3D"119" h=
eight=3D"30" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg62_img03a.png">
</div>
<p id=3D"p0910" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0911" class=3D"EB27SmallTextExtraIndent">The heat transfer withou=
t fins,</p>
<p id=3D"p0912" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0324" class=3D"imagewrap"><em>Q =3D Ah=CE=B8<sub class=3D"EBs=
ub">b</sub></em></div>
<div id=3D"div0325" class=3D"imagewrap">=3D l =C3=97 l =C3=97 40 =C3=97 200=
</div>
<div id=3D"div0326" class=3D"imagewrap">=3D 8000 W</div>
<p id=3D"p0913" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0914" class=3D"EB26SmallTextHangingIndent">2.37. <em>Consider two=
 very long rods of equal diameters; one is of aluminium and has a thermal c=
onductivity K<sub class=3D"EBsub">a</sub> =3D 200 W/m=C2=B0C but the therma=
l conductivity of the other rod is not known. One end of each rod is insert=
ed into the furnace that is maintained at a temperature T<sub class=3D"EBsu=
b">b</sub>. Both rods lose heat by convection</em>, <em>with a heat transfe=
r coefficient h</em>, <em>into the ambient air at T<sub class=3D"EBsub">a</=
sub>. The surface temperature of each rod is measured at various distances =
from the hot base surface. The temperature of the aluminium rod at a distan=
ce (x<sub class=3D"EBsub">a</sub>) 40 cm from its base is the same as that =
of the rod of unknown K at a distance (x) 20 cm from its base. Determine th=
e thermal conductivity of the latter rod.</em></p>
<p id=3D"p0915" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0916" class=3D"EB27SmallTextExtraIndent">The temperature ratio fo=
r the aluminium rod <img id=3D"img0545" class=3D"Eq1" src=3D"https://learni=
ng.oreilly.com/library/view/heat-and-mass/9789332515680/images/pg62_img05.p=
ng" alt=3D"image" width=3D"87" height=3D"17" data-mfp-src=3D"/library/view/=
heat-and-mass/9789332515680/images/pg62_img05.png"></p>
<p id=3D"p0917" class=3D"EB27SmallTextExtraIndent">The reason for this is t=
hat the rod is infinitely long.</p>
<p id=3D"p0918" class=3D"EB27SmallTextExtraIndent">Therefore, (<em>T</em> =
=E2=88=92 <em>T<sub class=3D"EBsub">a</sub></em>)/(<em>T<sub class=3D"EBsub=
">b</sub></em> =E2=88=92 <em>T<sub class=3D"EBsub">a</sub></em>) <em>e<sup =
class=3D"EBsup">=E2=88=92m<sub class=3D"EBsub">a</sub>x<sub class=3D"EBsub"=
>a</sub></sup></em></p>
<p id=3D"p0919" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0327" class=3D"imagewrap"><em>T</em> =3D <em>T<sub class=3D"E=
Bsub">a</sub></em> + (<em>T<sub class=3D"EBsub">b</sub></em> =E2=88=92 <em>=
T<sub class=3D"EBsub">a</sub></em>) <em>e<sup class=3D"EBsup">=E2=88=92m<su=
b class=3D"EBsub">a</sub>x<sub class=3D"EBsub">a</sub></sup></em></div>
<p id=3D"p0920" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0921" class=3D"EB27SmallTextExtraIndent"><a id=3D"page_63"></a>Fo=
r the other rod, we can write <em>T</em> =3D <em>T<sub class=3D"EBsub">a</s=
ub></em> + (<em>T<sub class=3D"EBsub">b</sub></em> =E2=88=92 <em>T<sub clas=
s=3D"EBsub">a</sub></em>) <em>e<sup class=3D"EBsup">=E2=88=92mx</sup></em>,=
 for the same <em>T<sub class=3D"EBsub">a</sub></em> and <em>T<sub class=3D=
"EBsub">b</sub></em>.</p>
<p id=3D"p0922" class=3D"EB27SmallTextExtraIndent">Equating the two express=
ions for <em>T</em>,</p>
<p id=3D"p0923" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0328" class=3D"imagewrap">
<img id=3D"img0546" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg63_img01.png" alt=3D"image" width=3D"72" hei=
ght=3D"13" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images=
/pg63_img01.png">
</div>
<p id=3D"p0924" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0925" class=3D"EB27SmallTextExtraIndent">Because</p>
<p id=3D"p0926" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0329" class=3D"imagewrap">
<img id=3D"img0547" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg63_img01a.png" alt=3D"image" width=3D"186" h=
eight=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg63_img01a.png">
</div>
<p id=3D"p0927" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0928" class=3D"EB27SmallTextExtraIndent">But</p>
<p id=3D"p0929" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0330" class=3D"imagewrap">
<img id=3D"img0548" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg63_img01b.png" alt=3D"image" width=3D"187" h=
eight=3D"41" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg63_img01b.png">
</div>
<p id=3D"p0930" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0931" class=3D"EB27SmallTextExtraIndent">The thermal conductivity=
 of the other rod is given by</p>
<p id=3D"p0932" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0331" class=3D"imagewrap"><em>K =3D K<sub class=3D"EBsub">a</=
sub></em>(0.5)<sup class=3D"EBsup">2</sup> =3D 50 W/m=C2=B0 C.</div>
<p id=3D"p0933" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0934" class=3D"EB26SmallTextHangingIndent">2.38. <em>A mercury th=
ermometer is placed in an oil well to measure the temperature of the air fl=
owing in a pipe. The wall material has K of 60 W/m=C2=B0C</em>, <em>length =
L of 15 cm and thickness</em>, <em>t</em>, <em>of 1 mm. The heat transfer c=
oefficient between the air and the well wall is</em>, <em>h =3D 25 W/m<sup =
class=3D"EBsup">2</sup>=C2=B0C. The temperature reading in the thermometer =
is T<sub class=3D"EBsub">h</sub> =3D 100=C2=B0C and pipe wall temperature i=
s T<sub class=3D"EBsub">b</sub> =3D 50=C2=B0C. Calculate the temperature of=
 the air and the percentage of error.</em></p>
<p id=3D"p0935" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0936" class=3D"EB27SmallTextExtraIndent">Assuming that the well t=
ip is insulated, we obtain the following expression for the temperature pro=
file.</p>
<p id=3D"p0937" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0332" class=3D"imagewrap">
<img id=3D"img0549" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg63_img02.png" alt=3D"image" width=3D"196" he=
ight=3D"37" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg63_img02.png">
</div>
<p id=3D"p0938" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0939" class=3D"EB27SmallTextExtraIndent">(because <em>L</em> =3D =
<em>x</em>),</p>
<p id=3D"p0940" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0333" class=3D"imagewrap">
where <img id=3D"img0550" src=3D"https://learning.oreilly.com/library/view/=
heat-and-mass/9789332515680/images/pg63_img02a.png" alt=3D"image" width=3D"=
56" height=3D"36" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680=
/images/pg63_img02a.png">
</div>
<p id=3D"p0941" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0942" class=3D"EB27SmallTextExtraIndent">That is,</p>
<p id=3D"p0943" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0334" class=3D"imagewrap"><em>P =3D</em> =CF=80 (<em>d +</em>=
 2<em>t</em>) =3D <em>=CF=80d</em></div>
<p id=3D"p0944" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0945" class=3D"EB27SmallTextExtraIndent">(as 2<em>t</em> is small=
)</p>
<p id=3D"p0946" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0335" class=3D"imagewrap"><em>A =3D =CF=80dt</em></div>
<p id=3D"p0947" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0948" class=3D"EB27SmallTextExtraIndent">Therefore,</p>
<p id=3D"p0949" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0336" class=3D"imagewrap">
<img id=3D"img0551" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg63_img02b.png" alt=3D"image" width=3D"203" h=
eight=3D"35" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg63_img02b.png">
</div>
<p id=3D"p0950" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0951" class=3D"EB27SmallTextExtraIndent">Therefore <em>mL =3D</em=
> 20.41 =C3=97 0.15 =3D 3.062</p>
<p id=3D"p0952" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0337" class=3D"imagewrap">
<img id=3D"img0552" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg63_img03.png" alt=3D"image" width=3D"177" he=
ight=3D"37" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg63_img03.png">
</div>
<p id=3D"p0953" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0954" class=3D"EB27SmallTextExtraIndent">Therefore the temperatur=
e for air, <em>T<sub class=3D"EBsub">f</sub></em> =3D 105.1=C2=B0 C.</p>
<p id=3D"p0955" class=3D"EB27SmallTextExtraIndent">Error in the reading is =
5.1=C2=B0 C.</p>
<p id=3D"p0956" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0338" class=3D"imagewrap">Therefore percentage of error =3D 5=
.1/105.1 =3D 4.85%.</div>
<p id=3D"p0957" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0958" class=3D"EB26SmallTextHangingIndent"><a id=3D"page_64"></a>=
2.39. <em>Pin-fins are provided to increase the heat transfer rate from a h=
ot surface. The following data give the details of the insulated-end condit=
ion. Thermal conductivity of the fin (K) =3D 250 W/mK.</em></p>
<p id=3D"p0959" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0960" class=3D"EB27SmallTextExtraIndent">Heat transfer coefficien=
t between the fin surface and the surrounding air, <em>h</em> =3D 30 W/m<su=
p class=3D"EBsup">2</sup>K</p>
<p id=3D"p0961" class=3D"EB27SmallTextExtraIndent">Diameter of the fin, <em=
>d</em> =3D 1.5 cm</p>
<p id=3D"p0962" class=3D"EB27SmallTextExtraIndent">Base temperature of the =
fin, <em>T<sub class=3D"EBsub">b</sub></em> =3D 250=C2=B0 C</p>
<p id=3D"p0963" class=3D"EB27SmallTextExtraIndent">Surrounding air temperat=
ure, <em>T<sub class=3D"EBsub">c</sub> =3D</em> 25=C2=B0 C</p>
<p id=3D"p0964" class=3D"EB27SmallTextExtraIndent">Find the heat transfer r=
ate and effectiveness of the fins for</p>
<ol id=3D"ol0014" class=3D"LowerAlpha">
<li id=3D"li0040" class=3D"EB23ListFirst">6 fins of length <em>(L)</em> 15 =
<em>cm</em></li>
<li id=3D"li0041" class=3D"EB24List">12 fins of length <em>(L)</em> 7.5 cm<=
/li>
<li id=3D"li0042" class=3D"EB25ListLast">3 fins of length 30 cm.</li>
</ol>
<p id=3D"p0965" class=3D"EB27SmallTextExtraIndent">Here</p>
<p id=3D"p0966" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0339" class=3D"imagewrap">
<img id=3D"img0553" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg64_img01.png" alt=3D"image" width=3D"189" he=
ight=3D"25" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg64_img01.png">
</div>
<div id=3D"div0340" class=3D"imagewrap"><em>P =3D d =3D</em> =C3=97 0.015 =
=3D 0.0471m</div>
<p id=3D"p0967" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0968" class=3D"EB27SmallTextExtraIndent">Therefore,</p>
<p id=3D"p0969" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0341" class=3D"imagewrap">
<img id=3D"img0554" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg64_img01a.png" alt=3D"image" width=3D"255" h=
eight=3D"35" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg64_img01a.png">
</div>
<p id=3D"p0970" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<ol id=3D"ol0015" class=3D"LowerAlpha">
<li id=3D"li0043" class=3D"EB23ListFirst">
<p id=3D"p0971" class=3D"EB02BodyTextFullOut">6 fins of length <em>(L)</em>=
 15 <em>cm</em></p>
<p id=3D"p0972" class=3D"EB02BodyTextFullOut">Heat transfer, <em>Q</em> =3D=
 <em>n</em>[<em>K Am</em>(<em>T<sub class=3D"EBsub">b</sub> =E2=88=92 T<sub=
 class=3D"EBsub">a</sub></em>)tanh <em>mL</em>]</p>
<p id=3D"p0973" class=3D"EB02BodyTextFullOut">(as the tip is insulated)</p>
<p id=3D"p0974" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0342" class=3D"imagewrap">
<img id=3D"img0555" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg64_img02.png" alt=3D"image" width=3D"344" he=
ight=3D"56" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg64_img02.png">
</div>
<p id=3D"p0975" class=3D"EB02BodyTextFullOut">&nbsp;</p></li>
<li id=3D"li0044" class=3D"EB24List">
<p id=3D"p0976" class=3D"EB02BodyTextFullOut">12 fins of length <em>(L)</em=
> 7.5 cm</p>
<p id=3D"p0977" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0343" class=3D"imagewrap">
<img id=3D"img0556" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg64_img03.png" alt=3D"image" width=3D"355" he=
ight=3D"42" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg64_img03.png">
</div>
<p id=3D"p0978" class=3D"EB02BodyTextFullOut">&nbsp;</p>
</li>
<li id=3D"li0045" class=3D"EB25ListLast">
<p id=3D"p0979" class=3D"EB02BodyTextFullOut">3 fins of length <em>(L)</em>=
 30 cm</p>
<p id=3D"p0980" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0344" class=3D"imagewrap">
<img id=3D"img0557" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg64_img04.png" alt=3D"image" width=3D"336" he=
ight=3D"57" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg64_img04.png">
</div>
<p id=3D"p0981" class=3D"EB02BodyTextFullOut">&nbsp;</p></li>
</ol>
<p id=3D"p0982" class=3D"EB27SmallTextExtraIndent">Effectiveness of the fin=
s</p>
<ol id=3D"ol0016" class=3D"LowerRoman">
<li id=3D"li0046" class=3D"EB23ListFirst"><img id=3D"img0558" class=3D"Eq1"=
 src=3D"https://learning.oreilly.com/library/view/heat-and-mass/97893325156=
80/images/pg64_img05.png" alt=3D"image" width=3D"267" height=3D"47" data-mf=
p-src=3D"/library/view/heat-and-mass/9789332515680/images/pg64_img05.png"><=
/li>
<li id=3D"li0047" class=3D"EB24List"><em>=CE=B5 =3D</em> 20.0</li>
<li id=3D"li0048" class=3D"EB25ListLast"><em>=CE=B5</em> =3D 44.1.</li>
</ol>
<p id=3D"p0983" class=3D"EB02BodyTextFullOut"><a id=3D"page_65"></a><em>2.4=
0. To determine the thermal conductivity of a long solid rod of diameter (d=
) 2.5 cm</em>, <em>one half is inserted into a furnace while the other half=
 projects into the air at 27=C2=B0C (T<sub class=3D"EBsub">a</sub>). After =
a steady-state had been reached</em>, <em>the temperature at two points 7.6=
 cm apart were measured as 126=C2=B0C (T<sub class=3D"EBsub">1</sub>) and 9=
1=C2=B0C (T<sub class=3D"EBsub">2</sub></em>), <em>respectively. The heat t=
ransfer coefficient between the air and the surface of the rod was estimate=
d as 22.7 W/m<sup class=3D"EBsup">2</sup>K. What is the thermal conductivit=
y of the rod?</em></p>
<p id=3D"p0984" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0985" class=3D"EB27SmallTextExtraIndent">Since it is a long fin, =
the equation for the temperature is</p>
<p id=3D"p0986" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0345" class=3D"imagewrap"><em>=CE=B8</em> =3D <em>=CE=B8<sub =
class=3D"EBsub">b</sub> e</em> <sup class=3D"EBsup">=E2=88=92<em>mx</em></s=
up></div>
<p id=3D"p0987" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0988" class=3D"EB27SmallTextExtraIndent">But <img id=3D"img0559" =
src=3D"https://learning.oreilly.com/library/view/heat-and-mass/978933251568=
0/images/pg65_img02a.png" alt=3D"image" width=3D"67" height=3D"17" data-mfp=
-src=3D"/library/view/heat-and-mass/9789332515680/images/pg65_img02a.png"> =
at distance <em>x</em><sub class=3D"EBsub">1</sub> from the furnace</p>
<p id=3D"p0989" class=3D"EB27SmallTextExtraIndent">and <img id=3D"img0560" =
src=3D"https://learning.oreilly.com/library/view/heat-and-mass/978933251568=
0/images/pg65_img02b.png" alt=3D"image" width=3D"70" height=3D"16" data-mfp=
-src=3D"/library/view/heat-and-mass/9789332515680/images/pg65_img02b.png"> =
at distance <em>x</em><sub class=3D"EBsub">2</sub> from the furnace</p>
<p id=3D"p0990" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0991" class=3D"EB27SmallTextExtraIndent">Therefore,</p>
<p id=3D"p0992" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0346" class=3D"imagewrap">
<img id=3D"img0561" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg65_img03.png" alt=3D"image" width=3D"201" he=
ight=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg65_img03.png">
</div>
<p id=3D"p0993" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0347" class=3D"imagewrap">{Since <em>=CE=B8</em><sub class=3D=
"EBsub">1</sub> =3D <em>T</em><sub class=3D"EBsub">1</sub> =E2=88=92 <em>T<=
sub class=3D"EBsub">a</sub></em> and <em>=CE=B8</em><sub class=3D"EBsub">2<=
/sub> =3D <em>Td</em><sub class=3D"EBsub">2</sub> =E2=88=92 <em>T</em><sub =
class=3D"EBsub"><em>a</em></sub>}</div>
<p id=3D"p0994" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0995" class=3D"EB27SmallTextExtraIndent">Therefore,</p>
<p id=3D"p0996" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0348" class=3D"imagewrap">
<img id=3D"img0562" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg65_img03a.png" alt=3D"image" width=3D"193" h=
eight=3D"30" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg65_img03a.png">
</div>
<p id=3D"p0997" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p0998" class=3D"EB27SmallTextExtraIndent">Therefore,</p>
<p id=3D"p0999" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0349" class=3D"imagewrap">
<img id=3D"img0563" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg65_img03b.png" alt=3D"image" width=3D"262" h=
eight=3D"60" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg65_img03b.png">
</div>
<p id=3D"p1000" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1001" class=3D"EB26SmallTextHangingIndent">2.41. <em>A metal rod =
is cooled by inserting it in a sleeve having 12 (N) longitudinal fins on it=
s outer surface. Thermal conductivity (k) of sleeve material is 210 W/mK an=
d thickness (b) of the sleeve base is 1 mm. The contact resistance (R<sub c=
lass=3D"EBsub">c</sub>) of the sleeve-rod interface is 0.002 m<sup class=3D=
"EBsup">2</sup>k/W. The rod radius (r<sub class=3D"EBsub">1</sub>) and leng=
th (L) are 0.0025 m and 0.008 m</em>, <em>respectively. The fins are 0.015 =
m height (H) and 0.8 mm thickness (t). Air at a temperature (T<sub class=3D=
"EBsub">a</sub>) of 30=C2=B0C flows over the fin surface with a heat transf=
er coefficient (h) of 30 W/m<sup class=3D"EBsup">2</sup>K. If the surface t=
emperature (T<sub class=3D"EBsub">s</sub>) of the rod is maintained at 100=
=C2=B0C</em>, <em>compare the heat transfer rates with sleeve and without s=
leeve.</em></p>
<p id=3D"p1002" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1003" class=3D"EB27SmallTextExtraIndent">Heat transfer rate from =
the rod without fin (<em>Q</em>) =3D <em>Ah</em>(<em>T<sub class=3D"EBsub">=
s</sub> =E2=80=93 T<sub class=3D"EBsub">a</sub></em>), where <em>A =3D 2=CF=
=80r</em><sub class=3D"EBsub">1</sub><em>L</em></p>
<p id=3D"p1004" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0350" class=3D"imagewrap"><em>Q =3D</em> (2 =C3=97 0.0025 =C3=
=97 0.008) =C3=97 30 =C3=97 [100 =E2=88=92 30]</div>
<div id=3D"div0351" class=3D"imagewrap">=3D 0.264 W</div>
<p id=3D"p1005" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1006" class=3D"EB27SmallTextExtraIndent">Heat transfer from the f=
in surface (<em>Q<sub class=3D"EBsub">f</sub></em>) for convection heat tra=
nsfer tip</p>
<p id=3D"p1007" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0352" class=3D"imagewrap">
<img id=3D"img0564" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg65_img05.png" alt=3D"image" width=3D"235" he=
ight=3D"71" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg65_img05.png">
</div>
<p id=3D"p1008" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0353" class=3D"imagewrap">where <em>P =3D </em> 2(<em>L + t</=
em>) =3D 2(0.008 + 0.0008) =3D 0.0176 m</div>
<div id=3D"div0354" class=3D"imagewrap">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;<em>A<sub class=3D"EBsub">c</sub> =3D L =C3=97 t =3D</em> 0.008 =C3=97 0.0=
008 =3D 6.4 =C3=97 10<sup class=3D"EBsup">=E2=88=926</sup>m<sup class=3D"EB=
sup">2</sup></div>
<p id=3D"p1009" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0355" class=3D"imagewrap">
<img id=3D"img0565" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg65_img05a.png" alt=3D"image" width=3D"265" h=
eight=3D"38" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg65_img05a.png">
</div>
<p id=3D"p1010" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0356" class=3D"imagewrap"><a id=3D"page_66"></a>
<img id=3D"img0566" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg66_img01a.png" alt=3D"image" width=3D"265" h=
eight=3D"117" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/ima=
ges/pg66_img01a.png">
</div>
<p id=3D"p1011" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1012" class=3D"EB27SmallTextExtraIndent">and</p>
<p id=3D"p1013" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0357" class=3D"imagewrap">
<img id=3D"img0567" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg66_img02.png" alt=3D"image" width=3D"377" he=
ight=3D"78" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg66_img02.png">
</div>
<p id=3D"p1014" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1015" class=3D"EB27SmallTextExtraIndent">But fin resistance for a=
 single <img id=3D"img0568" class=3D"Eq1" src=3D"https://learning.oreilly.c=
om/library/view/heat-and-mass/9789332515680/images/pg66_img03.png" alt=3D"i=
mage" width=3D"55" height=3D"35" data-mfp-src=3D"/library/view/heat-and-mas=
s/9789332515680/images/pg66_img03.png"></p>
<p id=3D"p1016" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0358" class=3D"imagewrap">
<img id=3D"img0569" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg66_img04.png" alt=3D"image" width=3D"147" he=
ight=3D"30" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg66_img04.png">
</div>
<p id=3D"p1017" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1018" class=3D"EB27SmallTextExtraIndent">=E2=88=B4 Fin resistance=
 for 12 fins =3D <img id=3D"img0570" class=3D"Eq1" src=3D"https://learning.=
oreilly.com/library/view/heat-and-mass/9789332515680/images/pg66_img04a.png=
" alt=3D"image" width=3D"49" height=3D"30" data-mfp-src=3D"/library/view/he=
at-and-mass/9789332515680/images/pg66_img04a.png"></p>
<p id=3D"p1019" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0359" class=3D"imagewrap">
<img id=3D"img0571" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg66_img04b.png" alt=3D"image" width=3D"130" h=
eight=3D"30" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg66_img04b.png">
</div>
<p id=3D"p1020" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1021" class=3D"EB27SmallTextExtraIndent">Contact resistance,</p>
<p id=3D"p1022" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0360" class=3D"imagewrap">
<img id=3D"img0572" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg66_img04c.png" alt=3D"image" width=3D"257" h=
eight=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg66_img04c.png">
</div>
<p id=3D"p1023" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1024" class=3D"EB27SmallTextExtraIndent">Sleeve resistance,</p>
<p id=3D"p1025" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0361" class=3D"imagewrap">
<img id=3D"img0573" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg66_img04d.png" alt=3D"image" width=3D"187" h=
eight=3D"83" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg66_img04d.png">
</div>
<p id=3D"p1026" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1027" class=3D"EB27SmallTextExtraIndent">Resistance from the expo=
sed base,</p>
<p id=3D"p1028" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0362" class=3D"imagewrap">
<img id=3D"img0574" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg66_img04e.png" alt=3D"image" width=3D"292" h=
eight=3D"69" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg66_img04e.png">
</div>
<p id=3D"p1029" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1030" class=3D"EB27SmallTextExtraIndent">Fin resistance and resis=
tance from the exposed base are parallel.</p>
<p id=3D"p1031" class=3D"EB27SmallTextExtraIndent">=E2=88=B4 Equivalent res=
istance <img class=3D"Eq1" id=3D"img0295" src=3D"https://learning.oreilly.c=
om/library/view/heat-and-mass/9789332515680/images/pg66_img05.png" alt=3D"i=
mage" width=3D"267" height=3D"40" data-mfp-src=3D"/library/view/heat-and-ma=
ss/9789332515680/images/pg66_img05.png"></p>

<p id=3D"p1032" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1033" class=3D"EB27SmallTextExtraIndent">=E2=88=B4 Total resistan=
ce,</p>
<p id=3D"p1034" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0363" class=3D"imagewrap"><em>R</em><sub class=3D"EBsub">tot<=
/sub> =3D <em>R<sub class=3D"EBsub">e</sub> + R<sub class=3D"EBsub">c</sub>=
</em> + <em>R<sub class=3D"EBsub">s</sub></em></div>
<div id=3D"div0364" class=3D"imagewrap">=3D 10.51 + 15.92 + 0.032</div>
<div id=3D"div0365" class=3D"imagewrap">=3D 26.46 k/W</div>
<p id=3D"p1035" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1036" class=3D"EB27SmallTextExtraIndent"><a id=3D"page_67"></a>He=
at transfer with sleeve,</p>
<p id=3D"p1037" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0366" class=3D"imagewrap">
<img id=3D"img0575" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg67_img01.png" alt=3D"image" width=3D"121" he=
ight=3D"77" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg67_img01.png">
</div>
<p id=3D"p1038" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1039" class=3D"EB26SmallTextHangingIndent">2.42. <em>Engine oil i=
s filled in between two plates kept at a distance of (L) 5 mm. The top plat=
e is moving with a velocity (U) of 15 m/s and maintained at a temperature (=
T<sub class=3D"EBsub">L</sub>) of 40=C2=B0C. The bottom plate is stationary=
 and its temperature (T<sub class=3D"EBsub">o</sub>) is 20=C2=B0C. Find the=
 heat flux to each of the plates and determine the maximum temperature of t=
he oil.</em></p>
<p id=3D"p1040" class=3D"EB27SmallTextExtraIndent">Oil properties at <img i=
d=3D"img0576" class=3D"Eq1" src=3D"https://learning.oreilly.com/library/vie=
w/heat-and-mass/9789332515680/images/pg67_img02.png" alt=3D"image" width=3D=
"56" height=3D"34" data-mfp-src=3D"/library/view/heat-and-mass/978933251568=
0/images/pg67_img02.png"> 30=C2=B0C are:</p>
<p id=3D"p1041" class=3D"EB27SmallTextExtraIndent"><em>=CF=81 =3D</em> 882.=
0 kg/m<sup class=3D"EBsup">3</sup>; =CE=B3 <em>=3D</em> 571 =C3=97 10<sup c=
lass=3D"EBsup">=E2=88=926</sup> m<sup class=3D"EBsup">2</sup>/s; <em>k =3D<=
/em> 0.145 W/mK; <em>=CE=BC =3D</em> 0.504 N-s/m<sup class=3D"EBsup">2</sup=
></p>
<p id=3D"p1042" class=3D"EB27SmallTextExtraIndent">The continuity equation =
becomes <img id=3D"img0577" class=3D"Eq1" src=3D"https://learning.oreilly.c=
om/library/view/heat-and-mass/9789332515680/images/pg67_img04.png" alt=3D"i=
mage" width=3D"47" height=3D"30" data-mfp-src=3D"/library/view/heat-and-mas=
s/9789332515680/images/pg67_img04.png"> momentum equation in <em>x</em> dir=
ection is</p>
<p id=3D"p1043" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0367" class=3D"imagewrap">
<img id=3D"img0578" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg67_img05.png" alt=3D"image" width=3D"437" he=
ight=3D"93" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg67_img05.png">
</div>
<p id=3D"p1044" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1045" class=3D"EB27SmallTextExtraIndent">The above equation is re=
duced to <img id=3D"img0579" class=3D"Eq1" src=3D"https://learning.oreilly.=
com/library/view/heat-and-mass/9789332515680/images/pg67_img06.png" alt=3D"=
image" width=3D"49" height=3D"35" data-mfp-src=3D"/library/view/heat-and-ma=
ss/9789332515680/images/pg67_img06.png"> =3D 0,</p>
<p id=3D"p1046" class=3D"EB27SmallTextExtraIndent">By integration, <em>u</e=
m> =3D <em>C</em><sub class=3D"EBsub">1</sub><em>y</em> + <em>C</em><strong=
><sub class=3D"EBsub">2</sub></strong></p>
<p id=3D"p1047" class=3D"EB27SmallTextExtraIndent">Applying the boundary co=
nditions <em>u</em> =3D 0; at <em>y</em> =3D 0; <em>u</em> =3D <em>U</em> a=
t <em>y</em> =3D <em>C</em></p>
<p id=3D"p1048" class=3D"EB27SmallTextExtraIndent">We get <img id=3D"img058=
0" class=3D"Eq1" src=3D"https://learning.oreilly.com/library/view/heat-and-=
mass/9789332515680/images/pg67_img07.png" alt=3D"image" width=3D"56" height=
=3D"36" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/images/pg=
67_img07.png"></p>
<p id=3D"p1049" class=3D"EB27SmallTextExtraIndent">Energy equation becomes,=
 when <img id=3D"img0581" class=3D"Eq1" src=3D"https://learning.oreilly.com=
/library/view/heat-and-mass/9789332515680/images/pg67_img07a.png" alt=3D"im=
age" width=3D"88" height=3D"31" data-mfp-src=3D"/library/view/heat-and-mass=
/9789332515680/images/pg67_img07a.png"> (heat generated) <em>q</em> =3D 0</=
p>
<p id=3D"p1050" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0368" class=3D"imagewrap">
<img id=3D"img0582" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg67_img08.png" alt=3D"image" width=3D"163" he=
ight=3D"40" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg67_img08.png">
</div>
<p id=3D"p1051" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1052" class=3D"EB27SmallTextExtraIndent">By integration,</p>
<p id=3D"p1053" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0369" class=3D"imagewrap">
<img id=3D"img0583" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg67_img08a.png" alt=3D"image" width=3D"149" h=
eight=3D"38" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg67_img08a.png">
</div>
<p id=3D"p1054" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1055" class=3D"EB27SmallTextExtraIndent">Using boundary condition=
, <em>y =3D</em> 0, <em>T =3D T<sub class=3D"EBsub">o</sub></em> &nbsp;&nbs=
p;&amp;  &nbsp;&nbsp;&nbsp; <em>y =3D L; T =3D T<sub class=3D"EBsub">L</sub=
></em></p>
<p id=3D"p1056" class=3D"EB27SmallTextExtraIndent">The temperature distribu=
tion</p>
<p id=3D"p1057" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0370" class=3D"imagewrap">
<img id=3D"img0584" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg67_img08b.png" alt=3D"image" width=3D"232" h=
eight=3D"42" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg67_img08b.png">
</div>
<p id=3D"p1058" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1059" class=3D"EB27SmallTextExtraIndent">Heat flux to stationary =
plate,</p>
<p id=3D"p1060" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0371" class=3D"imagewrap">
<img id=3D"img0585" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg67_img08c.png" alt=3D"image" width=3D"241" h=
eight=3D"40" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg67_img08c.png">
</div>
<p id=3D"p1061" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1062" class=3D"EB27SmallTextExtraIndent"><a id=3D"page_68"></a>&a=
mp; Heat flux to moving plate,</p>
<p id=3D"p1063" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0372" class=3D"imagewrap">
<img id=3D"img0586" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg68_img01.png" alt=3D"image" width=3D"236" he=
ight=3D"164" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg68_img01.png">
</div>
<p id=3D"p1064" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1065" class=3D"EB27SmallTextExtraIndent">The temperature gradient=
</p>
<p id=3D"p1066" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0373" class=3D"imagewrap">
<img id=3D"img0587" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg68_img02.png" alt=3D"image" width=3D"175" he=
ight=3D"35" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg68_img02.png">
</div>
<p id=3D"p1067" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1068" class=3D"EB27SmallTextExtraIndent">For maximum temperature =
<img id=3D"img0588" class=3D"Eq1" src=3D"https://learning.oreilly.com/libra=
ry/view/heat-and-mass/9789332515680/images/pg68_img03.png" alt=3D"image" wi=
dth=3D"44" height=3D"33" data-mfp-src=3D"/library/view/heat-and-mass/978933=
2515680/images/pg68_img03.png"></p>
<p id=3D"p1069" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0374" class=3D"imagewrap">
<img id=3D"img0589" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg68_img04.png" alt=3D"image" width=3D"273" he=
ight=3D"117" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg68_img04.png">
</div>
<p id=3D"p1070" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1071" class=3D"EB27SmallTextExtraIndent">Hence <em>T</em><sub cla=
ss=3D"EBsub">max</sub></p>
<p id=3D"p1072" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0375" class=3D"imagewrap">
<img id=3D"img0590" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg68_img05.png" alt=3D"image" width=3D"304" he=
ight=3D"109" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg68_img05.png">
</div>
<p id=3D"p1073" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1074" class=3D"EB26SmallTextHangingIndent">2.43. <em>A wall is ma=
de up of two layers</em> =E2=80=98<em>A</em>=E2=80=99 <em>and</em> =E2=80=
=98<em>B</em>=E2=80=99 <em>and the layer</em> =E2=80=98<em>A</em>=E2=80=99 =
<em>has uniform heat generation (q<sub class=3D"EBsub">A</sub>) of 2 =C3=97=
 10<sup class=3D"EBsup">6</sup> W/m<sup class=3D"EBsup">3</sup></em>, <em>t=
hermal conductivity (k<sub class=3D"EBsub">c</sub>) of 80 W/m=C2=B0C and th=
ickness (L<sub class=3D"EBsub">A</sub>) of 6 cm. The outer surfaces of laye=
r A and B are well insulated and cooled by water respectively. The layer</e=
m> =E2=80=98<em>B</em>=E2=80=99 <em>has no heat generation and thermal cond=
uctivity (k<sub class=3D"EBsub">B</sub>) is 160 W/m=C2=B0C. The temperature=
 (T<sub class=3D"EBsub">a</sub>) of water is 25=C2=B0C and heat transfer co=
efficient (h) between layer</em> =E2=80=98<em>B</em>=E2=80=99 <em>and water=
 is 1100 W/m<sup class=3D"EBsup">2</sup>K. Determine the outer surface and =
interface temperatures if thickness of layer</em> =E2=80=98(<em>L<sub class=
=3D"EBsub">D</sub>)=E2=80=99 is 3 cm.</em></p>
<p id=3D"p1075" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1076" class=3D"EB27SmallTextExtraIndent">Heat balance:</p>
<p id=3D"p1077" class=3D"EB27SmallTextExtraIndent">Here heat transfer to wa=
ter =3D heat transferred through the layer =E2=80=98<em>B</em>=E2=80=99 =3D=
 heat generated in the layer =E2=80=98<em>A</em>=E2=80=99</p>
<p id=3D"p1078" class=3D"EB27SmallTextExtraIndent">For a unit surface area,=
</p>
<p id=3D"p1079" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0376" class=3D"imagewrap"><a id=3D"page_69"></a>
<img id=3D"img0591" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg68_img06.png" alt=3D"image" width=3D"268" he=
ight=3D"242" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg68_img06.png">
</div>
<p id=3D"p1080" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0377" class=3D"imagewrap">&nbsp;=E2=88=B4 <em>T</em><sub clas=
s=3D"EBsub">2</sub> =3D <em>T</em><sub class=3D"EBsub">=CE=B1</sub> + <em>q=
</em>(<em>R<sub class=3D"EBsub">B</sub></em> + <em>R<sub class=3D"EBsub">A<=
/sub></em>)</div>
<div id=3D"div0378" class=3D"imagewrap">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;=E2=88=B4 <em>T</em><sub class=3D"EBsub">2</sub> =
=3D <em>T</em><sub class=3D"EBsub">=CE=B1</sub> + <em>q</em>(<em>L<sub clas=
s=3D"EBsub">A</sub></em>) (<em>R<sub class=3D"EBsub">A</sub></em> + <em>R<s=
ub class=3D"EBsub">B</sub></em>)</div>
<div id=3D"div0379" class=3D"imagewrap">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=3D 25 + 2 =C3=97 106 (0.06) [(1.88 + 9.0=
9) =C3=97 10<sup class=3D"EBsup">=E2=80=934 </sup></div>
<div id=3D"div0380" class=3D"imagewrap">=3D 156.6=C2=B0C</div>
<p id=3D"p1081" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1082" class=3D"EB27SmallTextExtraIndent">Temperature of insulated=
 surface</p>
<p id=3D"p1083" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0381" class=3D"imagewrap">
<img id=3D"img0592" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg69_img02.png" alt=3D"image" width=3D"305" he=
ight=3D"36" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg69_img02.png">
</div>
<p id=3D"p1084" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1085" class=3D"EB26SmallTextHangingIndent">2.44. <em>A water pipe=
 line is placed below the earth surface to avoid freezing for a period (t) =
of 50 days. The soil temperature (T<sub class=3D"EBsub">i</sub>) is 30=C2=
=B0C initially and surface temperature (T<sub class=3D"EBsub">s</sub>) is =
=E2=88=9220=C2=B0C. Determine the minimum distance between pipe and earth s=
urfaces to avoid the freezing of water. (Assume =CE=B1 =3D 0.14 =C3=97 10<s=
up class=3D"EBsup">=E2=88=926</sup> m<sup class=3D"EBsup">2</sup>/s).</em><=
/p>
<p id=3D"p1086" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1087" class=3D"EB27SmallTextExtraIndent">The temperature ratio fo=
r one-dimensional and semi infinite medium</p>
<p id=3D"p1088" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0382" class=3D"imagewrap">
<img id=3D"img0593" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg69_img03.png" alt=3D"image" width=3D"113" he=
ight=3D"32" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg69_img03.png">
</div>
<p id=3D"p1089" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1090" class=3D"EB27SmallTextExtraIndent">For, <em>T<sub class=3D"=
EBsub">(x, t)</sub> =3D</em> 0=C2=B0C</p>
<p id=3D"p1091" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0383" class=3D"imagewrap">
<img id=3D"img0594" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg69_img03a.png" alt=3D"image" width=3D"132" h=
eight=3D"29" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg69_img03a.png">
</div>
<p id=3D"p1092" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1093" class=3D"EB27SmallTextExtraIndent">From the table,</p>
<p id=3D"p1094" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0384" class=3D"imagewrap">
<img id=3D"img0595" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg69_img03b.png" alt=3D"image" width=3D"380" h=
eight=3D"105" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/ima=
ges/pg69_img03b.png">
</div>
<p id=3D"p1095" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1096" class=3D"EB26SmallTextHangingIndent">2.45. <em>A journal be=
aring has a radius of 5 cm (r) runs at 60 rps (N) and is lubricated using o=
il with viscosity (=CE=BC) of 0.52 kg/ms and thermal conductivity (k) of 0.=
25 W/mK. The inner moving and outer stationary temperatures are 52=C2=B0C (=
T<sub class=3D"EBsub">1</sub>) and 32=C2=B0C (T<sub class=3D"EBsub">2</sub>=
) respectively. The radial clearance (t) between them is 0.15 mm. Determine=
 the maximum temperature in lubricating oil and surface heat flux.</em></p>
<p id=3D"p1097" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1098" class=3D"EB27SmallTextExtraIndent">The temperature distribu=
tion in the oil</p>
<p id=3D"p1099" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0385" class=3D"imagewrap">
<img id=3D"img0596" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg69_img04.png" alt=3D"image" width=3D"203" he=
ight=3D"43" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg69_img04.png">
</div>
<p id=3D"p1100" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1101" class=3D"EB27SmallTextExtraIndent">where</p>
<p id=3D"p1102" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0386" class=3D"imagewrap"><em>U</em> =3D 2<em>=CF=80</em> =CF=
=81<em>N</em></div>
<div id=3D"div0387" class=3D"imagewrap">=3D 2<em>=CF=80</em> =C3=97 0.05 =
=C3=97 60</div>
<div id=3D"div0388" class=3D"imagewrap">=3D 18.85 m/s</div>
<p id=3D"p1103" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0389" class=3D"imagewrap"><a id=3D"page_70"></a>
<img id=3D"img0597" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg70_img01.png" alt=3D"image" width=3D"422" he=
ight=3D"85" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg70_img01.png">
</div>
<p id=3D"p1104" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1105" class=3D"EB27SmallTextExtraIndent">For maximum temperature =
<img id=3D"img0598" class=3D"Eq1" src=3D"https://learning.oreilly.com/libra=
ry/view/heat-and-mass/9789332515680/images/pg70_img01a.png" alt=3D"image" w=
idth=3D"49" height=3D"32" data-mfp-src=3D"/library/view/heat-and-mass/97893=
32515680/images/pg70_img01a.png"> =3D 0;</p>
<p id=3D"p1106" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0390" class=3D"imagewrap">
<img id=3D"img0599" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg70_img01b.png" alt=3D"image" width=3D"222" h=
eight=3D"53" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg70_img01b.png">
</div>
<p id=3D"p1107" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0391" class=3D"imagewrap">=E2=88=B4 <em>T</em><sub class=3D"E=
Bsub">max</sub> =3D 32 + 259.7 =C3=97 10<sup class=3D"EBsup">4</sup> =C3=97=
 0.079 =C3=97 10<sup class=3D"EBsup">=E2=88=923</sup> =E2=88=92 164.2 =C3=
=97 10<sup class=3D"EBsup">8</sup> =C3=97 (0.079 =C3=97 10<sup class=3D"EBs=
up">=E2=88=923</sup>)<sup class=3D"EBsup">2</sup>|<em>y</em> =3D <em>y</em>=
<sub class=3D"EBsub">max</sub></div>
<div id=3D"div0392" class=3D"imagewrap">=3D 134.7=C2=B0C</div>
<p id=3D"p1108" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1109" class=3D"EB27SmallTextExtraIndent">At the outer surface, (<=
em>y</em> =3D 0)</p>
<p id=3D"p1110" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0393" class=3D"imagewrap">
<img id=3D"img0600" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg70_img02.png" alt=3D"image" width=3D"258" he=
ight=3D"92" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/image=
s/pg70_img02.png">
</div>
<p id=3D"p1111" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<p id=3D"p1112" class=3D"EB27SmallTextExtraIndent">Heat transfer to inner s=
urface:</p>
<p id=3D"p1113" class=3D"EB02BodyTextFullOut">&nbsp;</p>
<div id=3D"div0394" class=3D"imagewrap">
<img id=3D"img0601" src=3D"https://learning.oreilly.com/library/view/heat-a=
nd-mass/9789332515680/images/pg70_img02a.png" alt=3D"image" width=3D"358" h=
eight=3D"72" data-mfp-src=3D"/library/view/heat-and-mass/9789332515680/imag=
es/pg70_img02a.png">
</div>
<h5 id=3D"h50012" class=3D"EB07SmallCapsMediumHead"><a id=3D"ch02lev1sec10"=
></a>REVIEW QUESTIONS</h5>
<ol id=3D"ol0017">
<li id=3D"li0049" class=3D"EB23ListFirst">Define Fourier's law.</li>
<li id=3D"li0050" class=3D"EB24List">Derive the general energy equation.</l=
i>
<li id=3D"li0051" class=3D"EB24List">Discuss the heat transfer in a plane w=
all with constant surface temperature without heat generation.</li>
<li id=3D"li0052" class=3D"EB24List">Discuss the concept of an electrical a=
nalogy.</li>
<li id=3D"li0053" class=3D"EB24List">Derive an expression for heat transfer=
 in a slab with convection boundaries.</li>
<li id=3D"li0054" class=3D"EB24List">Derive an expression for the temperatu=
re distribution for one-dimensional steady-state conduction through a compo=
site slab.</li>
<li id=3D"li0055" class=3D"EB24List">State the equation for the temperature=
 distribution in a slab with heat generation, if the slab has uniform therm=
al conductivity.</li>
<li id=3D"li0056" class=3D"EB24List">Derive an expression for the temperatu=
re distribution for one-dimensional steady-state heat conduction in a slab =
with variable thermal conductivity.</li>
<li id=3D"li0057" class=3D"EB24List">Derive an expression for the temperatu=
re distribution in a hollow cylinder without heat generation.</li>
<li id=3D"li0058" class=3D"EB24List">Derive an expression for temperature d=
istribution in a hollow cylinder with convection boundaries.</li>
<li id=3D"li0059" class=3D"EB24List">Derive an expression for heat transfer=
 in a solid cylinder with heat generation.</li>
<li id=3D"li0060" class=3D"EB24List">Derive an expression for heat transfer=
 in a hollow sphere without heat generation.</li>
<li id=3D"li0061" class=3D"EB24List"><a id=3D"page_71"></a>Derive an expres=
sion for heat transfer in a hollow sphere in the case of convection heat tr=
ansfer and without heat generation.</li>
<li id=3D"li0062" class=3D"EB24List">Derive an expression for heat transfer=
 in a hollow composite sphere without heat generation.</li>
<li id=3D"li0063" class=3D"EB24List">Derive an expression for heat transfer=
 in a solid sphere with heat generation.</li>
<li id=3D"li0064" class=3D"EB24List">What is the logarithmic mean area for =
a hollow cylinder and sphere?</li>
<li id=3D"li0065" class=3D"EB24List">What is meant by thermal contact resis=
tance?</li>
<li id=3D"li0066" class=3D"EB24List">Define critical thickness of an insula=
tion.</li>
<li id=3D"li0067" class=3D"EB24List">Classify fins.</li>
<li id=3D"li0068" class=3D"EB24List">Derive an expression for heat transfer=
 through a rectangular fin.</li>
<li id=3D"li0069" class=3D"EB24List">Derive an expression for heat transfer=
 if the end of the fin is insulated (negligible heat loss at the tip).</li>
<li id=3D"li0070" class=3D"EB24List">Derive an expression for heat transfer=
 through a fin with convection heat transfer at the end.</li>
<li id=3D"li0071" class=3D"EB24List">Derive an expression for heat transfer=
 when the fin tip is at a specific temperature.</li>
<li id=3D"li0072" class=3D"EB24List">Derive an expression for heat transfer=
 with the fin tip at fluid temperature (infinitely long fin).</li>
<li id=3D"li0073" class=3D"EB24List">Derive an expression for heat transfer=
 in a triangular fin.</li>
<li id=3D"li0074" class=3D"EB24List">Define efficiency of a fin.</li>
<li id=3D"li0075" class=3D"EB25ListLast">Define effectiveness of a fin.</li=
>
</ol>
<h5 id=3D"h50013" class=3D"EB07SmallCapsMediumHead"><a id=3D"ch02lev1sec11"=
></a>OBJECTIVE QUESTIONS</h5>
<ol id=3D"ol0018">
<li id=3D"li0076" class=3D"EB23ListFirst">Fourier's law states that the rat=
e of heat transfer per unit surface area is proportional to the gradient no=
rmal to the surface
<ol id=3D"ol0019" class=3D"LowerAlpha">
<li id=3D"li0077" class=3D"EB23ListFirst">Viscosity</li>
<li id=3D"li0078" class=3D"EB24List">Temperature</li>
<li id=3D"li0079" class=3D"EB24List">Pressure</li>
<li id=3D"li0080" class=3D"EB25ListLast">Velocity</li>
</ol></li>
<li id=3D"li0081" class=3D"EB24List">The thermal diffusivity is defined as =
<em>K =CF=81K</em>
<ol id=3D"ol0020" class=3D"LowerAlpha">
<li id=3D"li0082" class=3D"EB23ListFirst"><img id=3D"img0602" class=3D"Eq1"=
 src=3D"https://learning.oreilly.com/library/view/heat-and-mass/97893325156=
80/images/pg71_img01.png" alt=3D"image" width=3D"15" height=3D"31" data-mfp=
-src=3D"/library/view/heat-and-mass/9789332515680/images/pg71_img01.png"></=
li>
<li id=3D"li0083" class=3D"EB24List"><img id=3D"img0603" class=3D"Eq1" src=
=3D"https://learning.oreilly.com/library/view/heat-and-mass/9789332515680/i=
mages/pg71_img01a.png" alt=3D"image" width=3D"21" height=3D"31" data-mfp-sr=
c=3D"/library/view/heat-and-mass/9789332515680/images/pg71_img01a.png"></li=
>
<li id=3D"li0084" class=3D"EB24List"><img id=3D"img0604" class=3D"Eq1" src=
=3D"https://learning.oreilly.com/library/view/heat-and-mass/9789332515680/i=
mages/pg71_img01b.png" alt=3D"image" width=3D"21" height=3D"30" data-mfp-sr=
c=3D"/library/view/heat-and-mass/9789332515680/images/pg71_img01b.png"></li=
>
<li id=3D"li0085" class=3D"EB25ListLast"><img id=3D"img0605" class=3D"Eq1" =
src=3D"https://learning.oreilly.com/library/view/heat-and-mass/978933251568=
0/images/pg71_img01c.png" alt=3D"image" width=3D"19" height=3D"33" data-mfp=
-src=3D"/library/view/heat-and-mass/9789332515680/images/pg71_img01c.png"><=
/li>
</ol></li>
<li id=3D"li0086" class=3D"EB24List">The critical radius for a cylindrical =
insulation is <em>K h</em>
<ol id=3D"ol0021" class=3D"LowerAlpha">
<li id=3D"li0087" class=3D"EB23ListFirst"><img id=3D"img0606" class=3D"Eq1"=
 src=3D"https://learning.oreilly.com/library/view/heat-and-mass/97893325156=
80/images/pg71_img02.png" alt=3D"image" width=3D"43" height=3D"30" data-mfp=
-src=3D"/library/view/heat-and-mass/9789332515680/images/pg71_img02.png"></=
li>
<li id=3D"li0088" class=3D"EB24List"><img id=3D"img0607" class=3D"Eq1" src=
=3D"https://learning.oreilly.com/library/view/heat-and-mass/9789332515680/i=
mages/pg71_img02a.png" alt=3D"image" width=3D"43" height=3D"29" data-mfp-sr=
c=3D"/library/view/heat-and-mass/9789332515680/images/pg71_img02a.png"></li=
>
<li id=3D"li0089" class=3D"EB24List"><img id=3D"img0608" class=3D"Eq1" src=
=3D"https://learning.oreilly.com/library/view/heat-and-mass/9789332515680/i=
mages/pg71_img02b.png" alt=3D"image" width=3D"50" height=3D"30" data-mfp-sr=
c=3D"/library/view/heat-and-mass/9789332515680/images/pg71_img02b.png"></li=
>
<li id=3D"li0090" class=3D"EB25ListLast"><img id=3D"img0609" class=3D"Eq1" =
src=3D"https://learning.oreilly.com/library/view/heat-and-mass/978933251568=
0/images/pg71_img02c.png" alt=3D"image" width=3D"46" height=3D"30" data-mfp=
-src=3D"/library/view/heat-and-mass/9789332515680/images/pg71_img02c.png"><=
/li>
</ol></li>
<li id=3D"li0091" class=3D"EB24List">The maximum possible heat transfer occ=
urs if the surface temperature of the fin is the base temperature
<ol id=3D"ol0022" class=3D"LowerAlpha">
<li id=3D"li0092" class=3D"EB23ListFirst">half</li>
<li id=3D"li0093" class=3D"EB24List">twice</li>
<li id=3D"li0094" class=3D"EB24List">equal to</li>
<li id=3D"li0095" class=3D"EB25ListLast">less than</li>
</ol></li>
<li id=3D"li0096" class=3D"EB24List">Effectiveness of a fin is defined as t=
he ratio of heat transfer with the fin to the heat transfer at the base wit=
hout
<ol id=3D"ol0023" class=3D"LowerAlpha">
<li id=3D"li0097" class=3D"EB23ListFirst">the insulation</li>
<li id=3D"li0098" class=3D"EB24List">convection</li>
<li id=3D"li0099" class=3D"EB24List">conduction</li>
<li id=3D"li0100" class=3D"EB25ListLast">the fin</li>
</ol></li>
<li id=3D"li0101" class=3D"EB24List">The heat flux (in W/m<sup class=3D"EBs=
up">2</sup>) across a 10-cm-thick plate (<em>K</em> =3D 20 W/mK) having a t=
emperature gradient of 500=C2=B0Cis
<ol id=3D"ol0024" class=3D"LowerAlpha">
<li id=3D"li0102" class=3D"EB23ListFirst">100</li>
<li id=3D"li0103" class=3D"EB24List">10</li>
<li id=3D"li0104" class=3D"EB24List">1</li>
<li id=3D"li0105" class=3D"EB25ListLast">1000</li>
</ol></li>
<li id=3D"li0106" class=3D"EB24List">The thermal resistance of a hollow cyl=
inder (<em>L</em> =3D 1 m, <em>K</em> =3D 381.25 W/mK) of inner diameter 15=
 mm and outer diameter 25 mm is
<ol id=3D"ol0025" class=3D"LowerAlpha">
<li id=3D"li0107" class=3D"EB23ListFirst">2.13 =C3=97 10<sup class=3D"EBsup=
">=E2=88=92</sup><sup class=3D"EBsup">3</sup>=C2=B0C/W</li>
<li id=3D"li0108" class=3D"EB24List">2.13 =C3=97 10<sup class=3D"EBsup">=E2=
=88=92</sup><sup class=3D"EBsup">4</sup>=C2=B0C/W</li>
<li id=3D"li0109" class=3D"EB24List">21.3 =C3=97 10<sup class=3D"EBsup">=E2=
=88=92</sup><sup class=3D"EBsup">4</sup>=C2=B0C/W</li>
<li id=3D"li0110" class=3D"EB25ListLast">0.213=C2=B0C/W</li>
</ol></li>
<li id=3D"li0111" class=3D"EB24List">An insulated cable (<em>K</em> =3D 0.2=
W/mK) is exposed to an environment with <em>h</em> =3D 5W/m<sup class=3D"EB=
sup">2</sup> K. The optimum thickness of the insulation is
<ol id=3D"ol0026" class=3D"LowerAlpha">
<li id=3D"li0112" class=3D"EB23ListFirst">0.4 m</li>
<li id=3D"li0113" class=3D"EB24List">4 m</li>
<li id=3D"li0114" class=3D"EB24List">0.04 m</li>
<li id=3D"li0115" class=3D"EB25ListLast">0.02 m</li>
</ol></li>
<li id=3D"li0116" class=3D"EB24List">The three-dimensional steady-state con=
duction equation with internal heat generation is known as equation
<ol id=3D"ol0027" class=3D"LowerAlpha">
<li id=3D"li0117" class=3D"EB23ListFirst">Laplace</li>
<li id=3D"li0118" class=3D"EB24List">Fourier</li>
<li id=3D"li0119" class=3D"EB24List">momentum</li>
<li id=3D"li0120" class=3D"EB25ListLast">Poisson</li>
</ol></li>
<li id=3D"li0121" class=3D"EB25ListLast">The three-dimensional unsteady-sta=
te conduction equation without internal heat generation is known as equatio=
n
<ol id=3D"ol0028" class=3D"LowerAlpha">
<li id=3D"li0122" class=3D"EB23ListFirst">Laplace</li>
<li id=3D"li0123" class=3D"EB24List">Fourier</li>
<li id=3D"li0124" class=3D"EB24List">Poisson</li>
<li id=3D"li0125" class=3D"EB25ListLast">momentum</li>
</ol></li>
</ol>
<h4 id=3D"h40016" class=3D"EB10SmallHead4"><strong>Answers:</strong></h4>
<ol id=3D"ol0029">
<li id=3D"li0126" class=3D"EB23ListFirst">(b)</li>
<li id=3D"li0127" class=3D"EB24List">(a)</li>
<li id=3D"li0128" class=3D"EB24List">(a)</li>
<li id=3D"li0129" class=3D"EB24List">(c)</li>
<li id=3D"li0130" class=3D"EB24List">(d)</li>
<li id=3D"li0131" class=3D"EB24List">(a)</li>
<li id=3D"li0132" class=3D"EB24List">(b)</li>
<li id=3D"li0133" class=3D"EB24List">(c)</li>
<li id=3D"li0134" class=3D"EB24List">(d)</li>
<li id=3D"li0135" class=3D"EB25ListLast">(b)</li>
</ol>
<h5 id=3D"h50014" class=3D"EB07SmallCapsMediumHead"><a id=3D"ch02lev1sec12"=
></a>EXERCISE PROBLEMS</h5>
<ol id=3D"ol0030">
<li id=3D"li0136" class=3D"EB23ListFirst"><a id=3D"page_72"></a>A pipe with=
 inner diameter of 16.83 cm and thickness 10 cm is insulated with a materia=
l having thermal conductivity 0.0847 W/mK. The temperatures on the outer su=
rface of the pipe and on the outside of the insulation are 450=C2=B0C and 5=
0=C2=B0C, respectively. Find the heat loss per metre length of the pipe. <s=
trong>(Ans.</strong> 270 W)</li>
<li id=3D"li0137" class=3D"EB24List">A wall of thickness 50 mm is subjected=
 to differential temperature on both sides at made of 373 K and 363 K. Find=
 the heat flux if the wall is made of
<ol id=3D"ol0031" class=3D"LowerAlpha">
<li id=3D"li0138" class=3D"EB23ListFirst">Steel, <em>K =3D</em> 40 W/mK</li=
>
<li id=3D"li0139" class=3D"EB25ListLast">Concrete, <em>K =3D</em> 1.1 W/mK =
<strong>(Ans.</strong> 8kW/m, 0.22 kW/m<sup class=3D"EBsup">2</sup>)</li>
</ol></li>
<li id=3D"li0140" class=3D"EB24List">The heat flux across a plane wall of t=
hickness 0.05 m is 10 kW/m<sup class=3D"EBsup">2</sup>. If it is made from =
(a) Brass (<em>K</em> =3D 70 W/mK) (b) Red brick (<em>K</em> =3D 0.7W/mK), =
find the difference in temperature across the wall for this heat flux. <str=
ong>(Ans.</strong> 7.14, 714.3)</li>
<li id=3D"li0141" class=3D"EB24List">The heat from a surface will not excee=
d 450 W/m<sup class=3D"EBsup">2</sup>. The temperature of this surface bene=
ath the layer of insulation is 723 <em>K</em> and the temperature of the ex=
ternal surface of the insulating layer is 323 K. Determine the thickness of=
 the insulation if its thermal conductivity <em>K</em> =3D 0.09 + 0.0000877=
 W/mK. <strong>(Ans.</strong> 99.4 mm)</li>
<li id=3D"li0142" class=3D"EB24List">A plane wall is made up of fine clay b=
rick to a thickness of 0.25 m. The temperatures of the wall surfaces are 16=
23 K and 323 K. The thermal conductivity of fire clay brick is a function o=
f temperature, <em>K</em> =3D 0.838(1 + 0.00077). Find the temperature dist=
ribution and the temperature at a point 5 cm from the hot end. <strong>(Ans=
.</strong> 1143=C2=B0C, 1193 K)</li>
<li id=3D"li0143" class=3D"EB24List">A furnace is built out of layers of fi=
re clay and red brick with the space between them being filled with crushed=
 brick. The thickness of the fire clay layer is 0.12 m, that of the filling=
 is 0.05 m and the red brick is 0.25 m. The conductivities are 0.93, 0.13, =
0.7 W/mK, respectively. Find the thickness of the red-brick layer if the br=
icks are laid without filling and the heat transfer rate remains the same? =
<strong>(Ans.</strong> 0.5 m)</li>
<li id=3D"li0144" class=3D"EB24List">A furnace is made of a layer of foamed=
 fire clay of thickness 0.125 m and a layer of red brick of thickness 0.5 m=
. The wall temperature inside is 1373 K and the wall temperature outside is=
 323 K. The thermal conductivity of the fire clay varies as <em>K =3D </em>=
 0.28 + 0.000237 and that of the red brick is <em>K</em>  =3D 0.7 W/mK. Fin=
d the amount of heat lost and the interfacial temperature. <strong>(Ans.</s=
trong> 1090 kW/m<sup class=3D"EBsup">2</sup>, 1102 K)</li>
<li id=3D"li0145" class=3D"EB24List">Find the rate of heat flow through 1 m=
<sup class=3D"EBsup">2</sup> of the heating surface of the boiler if the fl=
ue gas temperature is 1273 K. The boiling water temperature is 473 K. The c=
oefficient of heat transfer 2 from the flue gases to the walls is 0.1 kW/m<=
sup class=3D"EBsup">2</sup> and that from the walls to the water is 5 kW/m.=
 The thermal conductivity of the material is 0.05 kW/mK. Wall thickness is =
1.2 cm.</li>
<li id=3D"li0146" class=3D"EB24List">The loops of a boiler are made from tu=
bes of steel with internal and external diameters 3.2 cm and 4.2 cm, respec=
tively and the thermal conductivity is 0.014 kW/mK. The temperature outside=
 is 853 K and inside is 723 K. Find the heat loss per metre length. <strong=
>(Ans.</strong> 42.05 kW/m)</li>
<li id=3D"li0147" class=3D"EB24List">A pipe with inner and outer diameters =
equal to 15 and 16 cm, respectively, is covered by a layer of insulating ma=
terial of thickness 10 cm. The thermal conductivity of the tube material is=
 0.05 kW/mK and conductivity of the insulating material is 8 =C3=97 10<sup =
class=3D"EBsup">=E2=88=925</sup> kW/mK. The temperature inside the pipe is =
673 K and that outside is 323 K. Find the heat loss and the interfacial tem=
perature. <strong>(Ans.</strong> 216 W; 673 K)</li>
<li id=3D"li0148" class=3D"EB24List">A pipeline of inner and outer diameter=
s equal to 10 and 11 cm, respectively, with a thermal conductivity 0.05 kW/=
mK is covered with two layers of insulation of thickness 5 cm each. The tem=
perature of the tube's inner surface is 523 K and temperature on the outsid=
e of insulation is 323 K. Find the loss of heat if the corresponding therma=
l conductivities are 0.06 and 0.12 W/mK for the insulations. <strong>(Ans.<=
/strong> 369.3)</li>
<li id=3D"li0149" class=3D"EB24List">Take a pipe of outer diameter 0.1 m an=
d inner diameter 0.08 m whose conductivity varies as <em>K</em> =3D 5 + 0.0=
17 W/m=C2=B0C, where <em>T</em> is expressed in =C2=B0C. The temperatures i=
nside and outside are 373 K and 293 K, respectively. Find the heat loss if =
the pipe is of length 2 m? <strong>(Ans.</strong> 25.23 kW)</li>
<li id=3D"li0150" class=3D"EB24List">A pipeline with inner and outer diamet=
ers equal to 16 and 17 cm is covered with a layer of insulation of thicknes=
s 10 cm with its thermal conductivity depending on temperature as <em>K</em=
> =3D 0.062(1 + 0.000363T)W/m=C2=B0C. Find the <a id=3D"page_73"></a>heat l=
oss per metre length of the pipe if the temperature of the outer pipeline s=
urface is 573 K and the temperature of outer insulation is 323K. <strong>(A=
ns.</strong> 0.205 kW)</li>
<li id=3D"li0151" class=3D"EB24List">A pipe was insulated and exposed to fl=
uid at 313 K with a convection heat transfer coefficient of 45 =C3=97 10<su=
p class=3D"EBsup">=E2=88=924</sup> kW/m<sup class=3D"EBsup">2</sup> K. Find=
 the critical radius of the insulation. Also find the heat loss from a 7-cm=
-diameter pipe at 673 K, covered with an insulator at critical radius and w=
ithout an insulation. The length of the pipe is 2 m. <strong>(Ans.</strong>=
 0.038 m, 7.3 kW, 7.125 kW)</li>
<li id=3D"li0152" class=3D"EB25ListLast">A rod 25 mm in diameter and 0.15 m=
 long protrudes from a wall which is maintained at 533 K. The rod is expose=
d to an environment at 333 K. The convection heat transfer coefficient is 0=
.015 kW/m<sup class=3D"EBsup">2</sup> K. Find the heat loss from the rod. <=
strong>(Ans.</strong> 0.046 kW)<a id=3D"page_74"></a></li>
</ol>
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g-bottom, #ad_primaryAd, #ad_slot_livesky, #SE_ADLINK_LAY_gd, .bodyads2, #a=
dsense-2, .slideshowadvert, .ad_sonar, .footerAdverts, .home_ad, .shunno-si=
debar-advert, #mapAdvert, #adv_box_a, #adslot-4-container, div[id^=3D"dfp-s=
lot-"], .content-advertisment, .omnitureAdImpression, .partnersTextLinks, #=
toppannonse, #nbcAd300x250, .js-advert--vc, #rside_ad, a[href^=3D"http://en=
gine.newsmaxfeednetwork.com/"], .home_ad_300x100, #js-outbrain-rightrail-ad=
s-module, #news_article_ad_mrec, .td_footer_ads, #aboveNodeAds, #pageads_to=
p, .FeaturedAdIndexAd, .mslo-ad-300x250, .BigBoxAdLabel, #ad_rotator-2, #ad=
_rotator-3, #ad-megaban2, #js-react-video-player-ad-right, .box_ad_horizont=
al, #urban_contentad_article, #pg-ad-item-160x600, #ad-flex-top, #adsense03=
, #adsense04, #adsense05, #ConversationDivAd, .top_advert, #site_content_ad=
_div, #Ad_Premier, .taboola-widget, object[width=3D"360"][height=3D"120"], =
.Ad160x600right, .box_ad, .add_728x90_teckpage, #adInstoryTwoWrap, .sidebar=
ad, #cph_cph_tlda_pnlAd, .wsSponsoredLinksRight, .ads-module, .adsenseblock=
_bottom, .rt-ad, .sponsor_label, #imageadsbox, .publicity-box, .jobkeyworda=
ds, .postbit_adbit_register, .mod-ad-box, #adPopover, #tf_page_ad_content_b=
ottom, .advert-footer, .banner728x90, #top_span_ad, #ads_box_top, #ad-right=
, .adInfo, .adlinkdiv, .SponsoredLinkItemTD, .openx_frame, #ads_container, =
.ads-left, .tb-ad, .top-side-advertisement, .interstitial-ad, .pageGoogleAd=
s, .text-ad-300, .container-advMoreAbout, #textad_block, .tm-ad, .dfp-ads-a=
d-article-middle, div[class^=3D"lifeOnwerAd"], .page-header-ad, #sway-banne=
r-ad1, .idc-adWrapper, .homeAdBox, .adholder-300, #adv-container, .sponsors=
_spacer, a[href^=3D"https://medleyads.com/"], #ad-mpu600-right-container, .=
sponsorheader, .medium_ad, #adv_overlay, #advx3_banner, #adheadhubs, #secti=
on-blog-ad, .adBox230X96, .article_adbox, #adpos1-leaderboard, .divAdsBanne=
r, .adsright, #footer-ad-unit, #headerNewAdsContainer, .square_banner_ad, o=
bject[height=3D"200"][width=3D"100%"], .UpperAdsContainer, #AdBoxMoreGames,=
 .AD728x90L, #BBCPH_MCPH_MCPH_SponsoredLinks1, .blockrightsmallads, #ad_isl=
and, #ad-gutter-left, .editorial-adsense, #adv-ext-ext-1, #adv-ext-ext-2, #=
col3_advertising, #rh_tower_ad, #article-island-ad, .NGOLocalFooterAd, .rev=
iewpage_ad2, .dfp_ad_block, .ezoic-ad, .g_ad336, #dfp_ad_Entry_Btm_300x250,=
 #ad_rightSidebarSecondBanner, .ad_text_link, .adbox-wrapper, .ads-166-70, =
#topAdsContainer, .footer-im-ad, #adBanner728, .gen_side_ad, #ad-pencil, .a=
d-choices, .ad_warn, .ads5blocks, #Adsense300x250, #advert-stickysky, .ws-a=
d, #ctl00_cphMainContent_lblPartnerAds, #interstitialAdContainer, .hd-adv, =
.advert-sidebar, .ArticlePage-ad, .wpadvert, #center_col > #main > .dfrd > =
.mnr-c > .c._oc._zs, #island_ad_top, .adslotMid, #scrollingads, #below-menu=
-ad-header, #ad_slot_right_top, #preroll_ads, #ad_widget_1, #right_ad_top, =
#b_ad2792, .ad_4_row, .TTButtAd, #search-ad, .tvs-mpu, #ctl00_ctl05_ctl00_t=
dBannerAd, .adfix, .medium-rectangle-ad, #hp_ad300x250, .supp-ads, .variabl=
eHeightAd, #RightAd, .adsmanag, .tc-adbanner, .ad-large-game, .bottomAdsTit=
le, .dfp-ad-rect, .yw-ad, #advert-right, .images-adv, .adsStickyRight, .adv=
-videoad, .sp_ad, .landingAdRail, #adv_adsense_300_dx, .block-bf_ads, #righ=
t_sidebar_ads, #topad728, #left_block_ads, #dfp_ad_mpu, #advertisediv, .wid=
getSponsors, .moduleBannerAd, .paneladvert, .adblock-popup, #xadtop, .heade=
r__ad, #advt_bottom, .sidebar-ad-slot, .sidebar-ads-wrap, .ad640x60, .widge=
t_sej_sidebar_ad { display: none !important; }

.advert-autosize, #adcolContent, #srp_adsense-top, .side-ad-panel, #adsdaq7=
2890, .wp125ad, [ad-id^=3D"googlead"], .advertising-block, #my_ad_mpu, #ctl=
00_ctl00_pnlAdTop, #mason_adv_bp_1, #mason_adv_bp_3, #mason_adv_bp_4, #maso=
n_adv_bp_2, .adplate-background, #rotating_ad, .row_header_ads, .desktoponl=
yad, .ad_perma-panorama, #ads_bar, #bottomAdWrapper, .adWrapper, #AdBar1, .=
ad-top-728, #ad_bottom_728x90, .ad-size-iab-uap-medium-rectangle-300x250, #=
right_global_adspace, .mpu-holder, #cubead2, .adBox-a, .powerinbox, #header=
adwrap, .middle_ad, #ad5_inline, #box-ads-tr, a[href^=3D"http://c.jumia.io/=
"], #dfpAd, .sr-advert, #ad900, #belowAd, .ads-advertorial, .contentleftad,=
 .mb-advert__mpu, .gall_ad, .adv_banner_hor, #advertiseGoogle, #axdsense1, =
#adsensewidget-3, #adspot-620x45-pos-1, #adspot-620x45-pos-2, .bannerAdWrap=
per730x86, #AdsBottomIframe, .homepage-right-rail-ad, #mvp-foot-ad-wrap, .s=
ponsertop, .ad-feature-content, #home_feature_ad, .block-nmadition, .single=
_bottom_ad, #adPopBOTtOM, #Ad-4-Slider, .adchange, .rhsvw[style=3D"backgrou=
nd-color:#fff;margin:0 0 14px;padding-bottom:1px;padding-top:1px;"], .adver=
t300x250, #download-fd-leaderboard-ad-top, .ad-mpu-middle, .cdo-ad, .articl=
e_page_ads_bottom, #adsense728, .adWidgetBlock, .top_big_ads, .rngtAd, .tex=
t-g-net-group-news-half-page-ad-300x600-or-300x250, .advert-home-380x120, #=
live-ad, .detail-ads, .ad-300x250-section, .square_advert_inner, .ad-priori=
ty, .side-ads-block, #sponsored-links-list, a[href^=3D"http://t.mdn2015x1.c=
om/"], .adfbox, #j_special_ad, .adSlice, .inlineAd_content, .post_sponsored=
, .adBox3b, #adLeaderboard-middle, .ads-160x600-outer, .adsonofftrigger, .a=
dsblock, .pubDesk, .single-top-ad, .dsk-box-ad-d, #middle-ad-destin, .adver=
tisement-728-90, .adSlide, #leatherboardad, #ads_big, div[id^=3D"ad_head_ce=
ltra_"], #oas_x70, .ads_sc_tl_i, .AdBoxStyleHome, #ad-sidebarleft-bottom, .=
wazi-ad-link, .np-header-ad, .placeholderAd, .asideAd, [href^=3D"https://hi=
lltopads.com/"], #stationad, #ad-medium, #containerAds980, #ad-banner-deskt=
op, #MPUadvertisingDetail, #sb-ad-sq, .pageAds, .adwrap-widget, #advertoria=
l-box, .mosaicAd, .sidebar-adv-container, .adv-300x250-generic, #bpcads-bot=
tom-footer, #Adc2_AdContainer, #rectangle_ad, #sports_only_ads, .ad160_blk,=
 .fi_adsense, #large-skyscraper-ad, .block-google_admanager2, .block_ad_flo=
ating_bar, a[href^=3D"https://www.camsoda.com/enter.php?id=3D"], #div-adid-=
4000, #innerpage-ad, #ad768top1, #ad_bottombrandtext, #common_right_lower_a=
dspace, #header_ads2, .content-kuss-ads, #bottom_ad_container, #secondAD, .=
s_sponsored_ads, .adbox_366x280, #adzone-parallax_1, .google-ad-widget, .ad=
s_foot, .ad-544x250, .mntl-gpt-adunit, .contentpage_searchad, .mslo-ad-728x=
66, #block-ex_dart-ex_dart_adblade_article, .advertisement_article_center_b=
ottom_computer, .side-ads-wide, .home_ad_300x250, #gallery-ad, #ads-top-728=
, #ad_poster, #my-adsMAST, .adinner, .adv-slide-block-wrapper, #advert-bloc=
k, #ads_box, .block_ad_sponsored_links-wrapper, #ad-billboard-atf, .textSpo=
nsor, .flash_ad, #ctr_adtech_mpu_top, .adsclick, #AdDisplay_TallLink, .pin-=
ad, .headerAdPosition, .regularad, .newsviewAdBoxInNews, #DFP_top_leaderboa=
rd, .live_tv_sponsorship_ad, .newHeaderAd, #dfp-ad-dfp_ad_atf_728x90-wrappe=
r, #content_right_area_ads, .adTitleR, .right-sponser-ad, #advertisement-co=
ntent, .layout_communityad_right_ads, #advert-top-banner, .ad300x100, #ad72=
8Bottom, .ads_disc_lwr_square, .ad300x111, .rightcoltowerad, .gameAd, .TmnA=
dsense, .widget_po_ads_widget, #rhs_block .xpdopen > ._OKe > div > .mod > .=
_yYf, .BtmSponsAd, .ad-vert, .menu-ads, .cont-ad, .box_adv_new, .longAd, .A=
DS-MainContent, .advertHeadline, .ad300x120, .linkedin-sponsor, .rect-ad, .=
onsite-ads-728w, #AD_ROW, .ad_728x90b, #sidebar-main-ad, .c-advertisement--=
rectangle, #adverttext160, .block-thirdage-ads, .ad-text-label, .roundedCor=
nersAd, .adhide, #WNAd103, #lj_ad_row, .nrAds, #ad300x250_336x280_bottom, #=
topMpuContainer, .adsense-review, #aside_ad, a[href^=3D"http://anonymous-ne=
t.com/"], #ad_global_header, .sponsor_div, object[width=3D"140"][height=3D"=
600"], .adsmalltext, .ZventsSponsoredLabel, .ad_728Home, .miniads, .ad300x1=
50, .advertismentText, .media-network-ad, .SponsoredLinksModule, .adNewsCha=
nnel, .adsHeading, .horizontal_adblock, .slideshow-ads, .ad-leader-plus-top=
, .textadtext, a[href^=3D"https://chaturbate.xyz/"], .ad_one, #ADSpro, a[hr=
ef^=3D"https://k2s.cc/pr/"], #area-left-ad, .right-adsense, .adwhitespace, =
#contextad, .GFYY1SVE2 > .GFYY1SVD2 > .GFYY1SVG5, .AdvtSample2, .b-adv, .Ad=
vtSample4 { display: none !important; }

.ad__superbanner, .sidead_300, .mpu_Ad, #rhs_block > script + .c._oc._Ve.rh=
svw, #rhs_block > .ts[cellspacing=3D"0"][cellpadding=3D"0"][style=3D"paddin=
g:0"], .sponsor-ad-wrapper, .booster-ad, .side-ad-160-bottom, .content_adve=
rtising, .Footer_Default_AD_Message_DIV, .zergnet__container, #stickyads, d=
iv[id^=3D"traffective-ad-"], afs-ad, .adlinks, #div-web-ad-billboard, .righ=
trail-ad-block, .sponsor_placement, .shunno_widget_sidebar_advert, .pod-ad,=
 #AD728Top, .right_ad_box, .rect_advert, .spl_ad, #my-adsLDR, .tile-ad-cont=
ainer, .banner-buysellads, .fbs-ad--top-wrapper, .alt_ad_block, #sponsored1=
, .adSeven, .dynamicAdvertContainer, ads-right, #top-ad-right-spot, .sqAd2,=
 a[href^=3D"https://watchmygirlfriend.tv/"], #footerAdBox, a[href^=3D"http:=
//www.babylon.com/welcome/index?affID"], #wide_right_ad, .catalyst-ads, .uk=
n-banner-ads, #closeAdsDiv, #ctl00_tc_ctl19_AdControl, .adSplash, .SitesGoo=
gleAdsModule, .publicidade-dotted, .ad_atf_300x250, .mcx-content-ad, .panel=
-ad, #gameads, .advertisement-300x600, .b_ads_top, .horisont_ads, .topAdBar=
, .adTout, .lastpost_advert, .ad-footer, #leaderboardAdTop, .adhint, #top_m=
pu_ad, #aboveplayerad, #DFM-adPos-bottomline, .google-ad-space-vertical, .D=
etailAdvertisement, #midAD, .advert-label, .advert300x300, .ad_label2a, .fo=
oter-ribbon-ad, #adiframe2_iframe, #ads-panorama-A1, #horizontalAd, .home_a=
dvertorial, .ad-block-in-post, #adsLeftZone1, #adsLeftZone2, .leaderboard_a=
d_container, #outerAd300, #below_content_ad_container, .ad-strip, #large-ad=
s, .big_center_ad, .advertise_carousel, #ad-slideshow2, #floatingAd, .ad_po=
ll, .ad-side-one, .sponsoredlinkscontainer, .ts-featured_ad, .banner_mpu_in=
tegrated, .resultAd, #belowad, #advertising_1, #advertising_2, .iprom-ad, .=
pageTopAd, .rotatingadsection, #ad2CONT, .rhsadvert, #videoPauseAd, #adLead=
erTop, .cornerad, .block-yt-ads, #advHome, #bottomadsdiv, .ADServer, #leade=
rboard-ad-1, #leaderboard-ad-2, #leaderboard-ad-3, #leaderboard-ad-4, #lead=
erboard-ad-5, #headerNewAdsContainerB, .ads-container__inner, .block-adsens=
e, .ad_box300x250, #wl-pencil-ad, .pt_ad03, #resultsAdsTop, #sponsored-ads,=
 #global_header_ad, #holder-storyad, #inlinegoogleads, #adv-leaderboard, #d=
ivAdv300x250, #refine-300-ad, #ad-300-250, #block-adsense_managed-0, .half-=
page-ad, #leaderboardAdLabel, .result-sponsored, .adsense-widget-horizontal=
, .homepage-ad-buzz-col, #HeroAd, #ctl00_ContentPlaceHolder1_toplead_news1_=
dvFlashAd, #bl11adv, #leaderboard-ad-1_iframe, .AD_textinfo, #afc-container=
, div[data-spotim-slot], .blogAdvertisement, #richad, .job-ads-container, .=
ad_300250, .sh-ad-box, #ADVleaderboard, #dfp-ad-slot4-wrapper, .advt_single=
, div[class^=3D"AdBannerWrapper-"], #ad336atf, .ad-panel__googlead, object[=
width=3D"600"][height=3D"200"], #sideAdSub, .advertiseHere, .ad_post, .bloc=
k-ad-middle, #ad-sidebar, .google_add_container, .block1--ads, .wdca_custom=
_ad, #advertisingRightRight, #index-ad, #na_adblock, .google_top_adsense, .=
adSpace950x90, .txtAd, .block-openads, #sponlinks, .google-ads-container, #=
ad-gpt-leftrec, .cmi-content-3ads-horizontal, #idMapAdvertising, .ad_articl=
e_top_left, #ads-box-header-pb, .bottom_adbreak, #ads728x90, .cmam_responsi=
ve_ad_widget_class, .pd-ads-mpu, .boxad1, .ad-sky-right, .ad_caption, .bott=
om-ad2, #left_side_ads, .ads_outer, .mobile_index_ad, a[href^=3D"https://aw=
ecrptjmp.com/"], .adMegaBoard, #LeftAd, #adslist, .homeCentreAd, #header_ad=
sense, #adsensepo, .ad728x90-1, .ad728x90-2, a[href^=3D"http://www.sexgangs=
ters.com/?pid=3D"], .mpuholderportalpage, .ads_bigrec, .table-ad, .boxads, =
#secondad, .bottom-adv, .ablock728, .google-advertisement_txt, #head-ad-1, =
#nbaMidAds, #xlAd, #adBanner3, #adBanner4, #adBanner2, #ad_feedback, .dart-=
advertisement, #adBanner9, .msw-js-advert, .adverserve145, #article_ad_bott=
om_cont, .inner_big_ad, #jmp-ad-buttons, .ad_sidebar_bigbox, #ad_island2, .=
region-ads, #gallery-slideshow-interstitial-ad, #articleview_ad2, .two_ads,=
 .advertisement-space, .ad_pic, #TOPADS, #madskills-ad-manager-0, #madskill=
s-ad-manager-2, #madskills-ad-manager-3, #madskills-ad-manager-1, .adBox_1,=
 .adBox_3, #top_AD, .ads_sidebar_360_b, .scanAd, .square-sidebar-ad, .main_=
ad, #ad_category_middle, .adv-conteiner, .x04-adunit, #ad_skyscraper_1, .st=
oryad300, .contentads1, .contentads2, .chartad, #advertBox, .rail-article-s=
ponsored, .rightbigcolumn_ads, #hdtv_ad_ss, a[href^=3D"http://betahit.click=
/"], #block-advert-content { display: none !important; }

#left-lower-adverts-container, .str-top-ad, #cherry_ads, .diggable-ad-spons=
ored, #dfpad-0, .ad250x250, .site_ad_300x250, .ad468x60Wrap, .skyAdd, .wide=
_ad_unit_top, #rhapsodyAd, .widget-highlight-ads, object[width=3D"240"][hei=
ght=3D"200"], .sidebar-ads-no-padding, .skyscraper_banner_ad, .support-adv,=
 .PrintAd-Slider, #ad300_a, #gallery-advert, #adspot-2a, #adspot-2b, .first=
post_advert_container, .ad300x250, #SitenavAdslot, .widget_evolve_ad_gpt_wi=
dget, #yahoo-ads, .impo-b-stitial, #GamePageAdDiv, #boxAD, .ad_halfpage, .p=
_adv, #ContentAd1, #leftAd_fmt, #ContentAd2, #contentad_imtext, #advert234_=
container, #wow-ads, .bostad, .google300x250, #top_ads_wrap, .ad_right_colu=
mn160, .blockAdvertise, .ad-x10x20x30, .view-ads-under-the-slider, #boxAd, =
#div_advt_right, a[href^=3D"http://cdn.adstract.com/"], .td-a-rec-id-h12_ob=
j_bottom_ad, #BannerAdvert, #adv-scrollable, #Ads_TFM_BS, #contentad-conten=
t-box-1, #ad_banner_example, .right_adlist, .columnAdvert, #companion_Ad, .=
mpu_ad, .advertisement-content, #adl_individual_1, a[href^=3D"http://www.am=
azon.co.uk/exec/obidos/external-search?"], #teaser-adtag-left, .gb-ad-top, =
#compAdvertisement, #ad260x60, #MainContent_ucTopRightAdvert, #SectionAd300=
-250, #sm-banner-ad, #ads-google, .ads_title, a[href^=3D"http://track.adfor=
m.net/"], #ad728Top, object[width=3D"580"][height=3D"80"], .header_advertis=
ement_text, .CommentGoogleAd, #googleAdsense, .adsPlaceHolder, .google_ads_=
sidebar, .widget_better-ads, .block-google-admanager, #topright-ad, #lower-=
ad-banner, #sponsored_v12, #ad_160_sidebar, .ad__desk, #quads-ad2_widget, .=
ad-imagehold, #adzone-middle1, #adzone-middle2, #article_ads, #BotAd, #ad-2=
20x90-1, .header_ads, #banner_pos1_ddb_0, #adxBigAd, .ads-home-top-buttons-=
wrap, .adbox-slider, .frontpage-google-ad, .adsnippet_widget, #advertise_to=
p, .railadspace, #col-right-ad, .pagebuilder_ad, .incontentAd, .advertnotic=
e, .advertismentContainer, #searchAdSkyscraperBox, .advertisementsOutterDiv=
, #horizontalad, #divAdd_Right, .skyscraper_ad, #Ad-Container, #text-linkAD=
, a[href^=3D"http://yads.zedo.com/"], #adleaderboard_flex, .mango_ads, .ref=
reshInarticleAd, #adspot_728x90, #footAd, #Adc3_AdContainer, #rotatingads, =
.google-ad-image, #bottomadbanner, #sidebar-125x125-ads, #ads_center, #home=
page__lead-ad-slot, .advert300x440, #ad-leaderboard-container, .google-ads-=
footer-01, #post-ad-layer, .google-ads-footer-02, #p-googleadsense-portletl=
abel, .fc_splash_ad, .Webnegar_Ad_Core, .vAd_160x600, .sponsorText, #ad_cel=
l, a[href^=3D"https://googleads.g.doubleclick.net/pcs/click"], .white-ad-bl=
ock, .tower_ad, .belowthread_advert_container, .picto_ad, .adsBottom, #ads-=
banner-top, .adbox_br, #blog_ad_content, .galleryRightAd, .adsboxitem, a[hr=
ef^=3D"http://rekoverr.com/"], .component-ddb-300x250-v2, #pagelet_adbox, .=
player-under-ad, .adServer, #adhalfbanner_wrapper, #Adverts_AdDetailsMiddle=
_300x250, #home-advert-module, .adscaleTop, .mpu_gold, #ad-160-long, #medRe=
cAd, #section_advertisements, .advertsLeaderboard, .adspace728x90, a[href^=
=3D"//oardilin.com/"], .ads_ticker_main, a[href^=3D"https://www.nutaku.net/=
signup/landing/"], .top_header_ad_inner, a[href^=3D"http://www.securegfm.co=
m/"], .cwAdvert, .sponsoredBottom, #ad_container_top, #sweep_top_ad, .ad-sh=
ifted, embed[width=3D"600"][height=3D"160"], .sponsoredFeature, #block-adte=
ch-top_300x250, #rr_MSads, .smallad-left, .ad-tabs, .textlink-ads, #adplate=
-content, #adsbottombluesleft, #ad_rr_1, .in-node-ad-300x250, #ads-728x90, =
.halfPageAd, .sideToSideAd, #ip-ad-skyscraper, #sector-widget__tiny-ad, .mi=
ddleAdLeft, .fbPhotoSnowboxAds, .ads_rectangle, .lowerContentBannerAd, #AD_=
rectangle, #button-ads, .textLinkAd, #globalTopNavAd, .type_promoads, #adsx=
pls2, .ad_header_left, a[href^=3D"http://easydownload4you.com/"], .ad_260_2=
10, .c_adsky, #main_col > #center_col div[style=3D"font-size:14px;margin:0 =
4px;padding:1px 5px;background:#fff7ed"], .commentsFavoritesAd, .advertSide=
Bar, .adv-rectangle, #towerad, #adspot-620x270-pos-1, #ft-ad-container, .ad=
Loaded, #dvAd1Data, .adLoader, .widget_text_adsense, #fusionad, .box-entry-=
ad, #adv-middle, .adSpacer, #ad_board_before_forums, .sidebar-ad-box, #side=
bar_ad_top, #ad-manager, .sidebar-adbox, a[href^=3D"https://djtcollectorclu=
b.org/"][href*=3D"?affiliate_id=3D"], .jg-ad-5, #layer_adv1, #adGmWidget, .=
qm-ad-content, #common_right_player_adspace, .module-ads, .fixedRightAd, .a=
d_regular1, .ad_regular2, .ad_regular3, .advt300, .flexiad, #dfp_unit_Deskt=
op_MPU_BTF_1, #dfp_unit_Desktop_MPU_BTF_2, .PU_DoubleClickAdsContent, .home=
pageinline_adverts, .ad250x300, .gms-ad-centre, .js-ad-loaded, .bx_ad_right=
, .gallery_ads_box, #adSpot-twin, #mid_ad_div, #myElementAd, .iframe-ads, .=
newsletter_ad, .advertorial2 { display: none !important; }

#adhead_g, .sideBarAd, .adv-right, #remove_ads_button1, #remove_ads_button2=
, .fl-ads, .flashadd, .searchSponsorItem, .i_ad, .ad-tall, .adHorisontalNoB=
order, .advertisingMob, .tmg-ad-300x250, #br_ad, .ad-permalink, .box-advert=
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01, .ad-02, a[href^=3D"http://callville.xyz/"], object[width=3D"230"][heigh=
t=3D"60"], #theadsADT3, .adbot_postbit, .adsense_single, .adz-horiz-ext, #b=
lock-dart-dart-tag-gfc-ad-top-2, .ads728x90-1, #tripleAdOuter, .header-ad-f=
rame, a[href^=3D"//healthaffiliate.center/"], .landing-feed--ad-vertical, #=
GoogleAd, .grid-sm-ad-300, .ad-integrated-display, .yvp-mode-ad, .google-ad=
-manager__slot, .dartiframe, .ads_slice, #adBoxUpperRight, #wo-widget-wrap,=
 .wrap_boxad, #footer-sponsored, #ad-banner-placement, .leftAdColumn, .home=
-ad--top, .ezAdsWidget, .ad640x480, #adMeld, .quigo-ad, #publicidad-video, =
a[href^=3D"http://www.hitcpm.com/"], .tblAds, #mbEnd[cellspacing=3D"0"][cel=
lpadding=3D"0"], .sidebar-320__box_adv, #hAdv, #header_ad_leaderboard, .adC=
ell, #ad-header-mobile, .advertising-fixed, #baseboard-ad, .rf_circ_ad_460x=
205, #ad-pushdown, #adcell, .categorypage_ad1, .categorypage_ad2, .adLine30=
0x600, #SponsorsAds, .c-adunit--first, .ad180x80, #defer-adright, .adzone-p=
review, #ad-tower, #new-ad-leaderboard, #adsense_ziel, .ad_home_block, .art=
icle__leaderboard-ad, #PhotoAd1, .new_ad1, #ft_mpu, .globalAdLeaderBoard, .=
ads-widget-partner-gallery, #ad6, .pageGoogleAdFlat, #bannerAdContainer1_1,=
 #bannerAdContainer1_2, #bannerAdContainer1_3, #Ads270x510-left, #bannerAdC=
ontainer1_6, #bannerAdContainer1_4, #bannerAdContainer1_5, .advertisespace_=
div, .adv_underpost, .internalAdsContainer, .block_ad_sponsored_links_local=
ized-wrapper, .home-slider-ads, a[href^=3D"http://cp.cbbp1.com"], .lsn-yaho=
oAdBlock, .google-ad-block, .leadAd, #adsponsorImg, #banner_300_250, #ad4, =
.td-Adholder, .advert-sky, .dd-ad-container, .ad-primary-desktop, #div-gpt-=
ad-lr-cube1, .adSummary, .banner-sidebar-300x250, #ad_embed_300x250 { displ=
ay: none !important; }

#ad-main-top, #GoogleADsense, #ad-box1, #ad-box2, .displayAd728x90Js, .widg=
et_advertisment, .largesideadpane, .advertisement1, .ga-textads-bottom, .ad=
s-box-header-wsl, .ads-ul, .home-body-ads, #rightAd_Iframe, #advert-skyscra=
per, .ad-gpt-vertical, a[href^=3D"http://lp.ilivid.com/"], .ads-x1, .banner=
AdSearch, .main_ad_adzone_8_ad_0, .main_ad_adzone_8_ad_1, .adLeaderboard, .=
rt_ad_call, .VideoAd, #ad-double-spotlight-container, #footerAdsPlacement, =
.google-sponsored-ads, #viewer_ads_wrapper, .header-adbox, .ph-ad-desktop, =
._fullsquaread, object[width=3D"980"][height=3D"100"], #ads-right-top, .pho=
toAd, a[href^=3D"https://ads.trafficpoizon.com/"], .AdStandard, .ad1_top, .=
resourceImagetAd, a[href^=3D"https://uncensored.game/"], .downloadAds, .top=
navSponsor, .advertisingFooterXL, #adWrapper, #style_ad_bottom, .pane-ads, =
.block-eg_adproxy, #gallery_ads, .listing-content-ad-container, #inline-adv=
ert, .box_publicidad, #middle_ad, #ad_banners, #liBannerDireita, #advertise=
ments_sidebar, #imageGalleryAdPlaceholder, a[href^=3D"https://www.nudeidols=
.com/cams/"], #frnContentAd, .native-ad-container, .advert-100, #sidebar-ad=
s-content, #ad_midstrip, #content_mpu, .widgetContentIfrWrapperAd, .widget_=
fearless_responsive_image_ad, .sponsor-text, #adlayerContainer, .PageTopAd,=
 #midadd, .rr-300x600-ad, .advertisingTop, #singleADS, #skyadwrap, .ad--rig=
ht, a[href^=3D"http://duckcash.eu/"], .cnt-header-ad, #adSuperAd, .sponsore=
d-headlines, .ad_leaderboard_atf, #buttonAdsContainer, #advertRight, .grv_i=
s_sponsored, .article--adv__before, #bottomAdvertTab, .ad_below_content, .a=
d_unit_rail, a[href^=3D"https://landing1.brazzersnetwork.com"], #ad_728x90_=
content, .insideads, .feed-ad, #horizontalads, .menuAd, #top3_ads, .adSlotC=
ontainer, #MPUAdSpace, #dfp_ad_Entry_EntrySetB_728x90, #adInBetweenPosts, #=
top-ads-tabs, a[href^=3D"https://gamescarousel.com/"], #banner_content_ad, =
.ds-ad-col-container, .content-footer-ad, .slot-top_of_sidebar, .advn_zone,=
 .aroundAdUnit, .ads-long, .r_adbx_top, #ctl00_GoogleAd1, #ctl00_GoogleAd3,=
 .spotim-amp-list-ad, .ad-sense, #headeradsense, .widget_advertisements, #A=
dSenseBottomAds, .adflag, #sponsoredSiteSidebar, #barAdWrapper, .SIM_ad_140=
x140_homepage_tv_promo, .adSpot-twin, .medrect_ad, embed[width=3D"200"][hei=
ght=3D"250"], .search-advertisement, .gallery__footer-ad, #Content_CA_AD_1_=
BC, .wikia_ad_placeholder, .result_ad, .adpic, .weather-sponsor-ad, #view_a=
ds_top_bg_middle, .adintext, object[width=3D"300"][height=3D"276"], .client=
-ad-container, .ozadtop3, .on_player_ads, #ad300x250box2, a[href^=3D"https:=
//atomidownload.com/"], .other-posts-ads, div[class^=3D"largeRectangleAd_"]=
, .lowerContentBannerAdInner, #right_column_internal_ad_container, .xads-bl=
k-bottom-hld, #noresults_ad_container, .ad1-left, #jobs-ad, .dvcvrgtad, .ad=
vg468, #advertisingTopWrapper, .qzvAdDiv, .pl_adv1_wr, .ad_600, .adv-halfpa=
ge, .top-sponsored-header, #Ad-0-1-Slider, #catalyst-125-ads, #dsStoryAd, .=
adboxVert, .bigbox_ad, embed[width=3D"200"][height=3D"500"], #adLContain, .=
adBigBoxSecond, .topbannerad, .textlinkads, .js-ad-imu, #Journal_Ad_300, #k=
aufDA-widget, .advt-block, #ContentPlaceHolder1_pnlGoogleAds, .adpod, objec=
t[width=3D"982"][height=3D"150"], object[width=3D"300"][height=3D"250"], #w=
g_ads, .advertisement-sponsor, .widget_ione-dart-ad, .ad1000, .ad1001, obje=
ct[width=3D"370"][height=3D"170"], #sponsored_container, .adrecom-pic, .top=
Add, .thirdAdHead, a[data-redirect^=3D"https://paid.outbrain.com/network/re=
dir?"], .ad_640, .banner-728x90, .default-teaser__adv, .ads_disc_square, .a=
dwolf-holder, .cb-ad-container, #vertad1, #ads_horz, .homepage-ad-module, .=
liboxads, #block-appnexus-x20-oas-ad, .ad_leader, .inline_ad_title, .sh-ad-=
section, .ad-heading, .adverTag, .articlebodyad, .fusion-advert, .dynamicLe=
adAd, .gp-advertisement-wrapper, .ad-fix, .article-ad-blk, a[href^=3D"https=
://fonts.fontplace9.com/"], .ads_qc1, .ads_qc2, #ad_300x250Ando, .sponsor_l=
ine, #cosponsor, .ad-adsense-block-250, #leaderboard-bottom-ad, .adArea674x=
60, #mpu_div, #bottommpuSlot, #ADbox, .cl-ad-inpager, .atf-ad-medRect, #ap_=
cu_wrapper, .lb-adhesion-unit, .ad_w300i, .bsac, .ads1_label, .dc-half-bann=
er, .leftAdvert, .adContentAd, .leaderAdvert, .ad300banner, .simpleads-item=
, #top_advertising, .ad__in-loop, .ad-RR, #ad_row_home, .supercommentad_lef=
t, #ad300x150, a[href^=3D"https://torguard.net/aff.php"], .advert--vc__wrap=
per, #article_ad_top, #right_column_ad, .article-ad-box, .b-astro-sponsored=
-links_horizontal, .yom-ad-MREC2, .premium_ad_container, #online_ad, #box_a=
dvertisement, .adpos-8, .tallAdvert, .c-ad--text-only, .Ad300x250, div[id^=
=3D"ad-cid-"], .cnt-right-vertical-ad, .rt_ad1_300x90, a[href^=3D"https://t=
ransfer.xe.com/signup/track/redirect?"] { display: none !important; }

#content-ad-side, #A9AdsOutOfStockWidgetTop, .member-ads, .adsmedrect, .ad-=
background-intra-body, .blockid_google-adsense-block, #adssidebar3, .wdp_ad=
Div, #adssidebar2, #advertssection, #div-ad-top, #ad_300x250_content_column=
, .slideshow_ad_note, .adListB, .desktop_ad, .col-ad-hidden, .ibt-top-ad, #=
RadAd_Skyscraper, #ad-mpu2, .pageLeaderAd, .native-ad, .ad_banner_div, .pen=
cil-ad-container, .tpd-box-ad-d, #yan-question-advert, .ad-location, .tpd-b=
ox-ad-e, #bannerAdContainer2_1, #bannerAdContainer2_2, #bannerAdContainer2_=
3, #ap-widget-ad-label, #bannerAdContainer2_4, #MediumRectangleAD, #bannerA=
dContainer2_6, .adTopFloat, .nu2ad, #footer-ad-728, #bannerAdContainer2_5, =
.ads_adsense1, .ads336x280, #leaderboard__advertising, .about_adsense, .hom=
e-ad-links, .gutterAdHorizontal, .top_ad_inner, .getridofAdsBlock, #adverti=
singBottomFull, #ultraWideAdContainer, a[href^=3D"http://get.slickvpn.com/"=
], a[href^=3D"http://adserver.itsfogo.com/"], .header__ads, .googleadcontai=
ner, #btmad, .cct-tempskinad, .ad-dynamic-showcase-top, #ads1_sidebar, .fir=
st_ad, .banner-top-ads, a[data-url^=3D"http://paid.outbrain.com/network/red=
ir?"] + .author, .sidebar-above-medium-rect-ad-unit, #adbanner-middle, #adb=
ar_ads_container_div, a[href^=3D"//go.vedohd.org/"], .plistaList > .plista_=
widget_underArticle_item[data-type=3D"pet"], #adbox-placeholder-topbanner, =
#mobile-ad-container, .widget_wp_ads_gpt_widget, .mrec_advert, a[href^=3D"h=
ttp://www.download-provider.org/"], .sitesprite_ads, #GOOGLE_ADS_13, #GOOGL=
E_ADS_16, a[href^=3D"http://admingame.info/"], .ads-widget-sponsor-gallery,=
 #ad-footer, .general-adzone, #google_ads_wide, .advert-top, #center_col > =
#_Emc, .ad540x90, #adverts-top-left, .main_advert_section, .ad_spons_box, #=
header-advrt, #mod-ad-gemini-rm-1, .cornerBoxInnerWhiteAd, .card-ads, .phot=
oad, .inlineadtitle, a[href^=3D"http://9nl.es/"], .blog_ad, .eniro_ad, #ad-=
leaderboard-top, .adunit-active, #bottomad_table, .my-ads, .bottomAdContain=
er, .burstContentAdIndex, .multiple-ad-tiles, .sky_ad_top, .divAdsRight, #i=
nner-ad-container, .DetailAds, #GOOGLE_ADS_49, .js-gptAd, .zergnet-row, .si=
debar-ad, #WNAd17, #about_adsbottom, embed[width=3D"160"][height=3D"600"], =
.ad-tile, .top_advertisement, #Ad_RightTop, #GOOGLE_ADS_56, .adBgClick, #Ba=
nnerXGroup, .ad.inner, #WNAd20, #morefooterads, .c-ad-size2, .home_advert, =
a[href^=3D"http://www.flashx.tv/downloadthis"], .c-ad-size3, #rhsadvert, .s=
ubheadAdPanel, #ad-block-bottom, #ad-slug-wrapper, .adsbyadop, .centerAdvHe=
ader, #AdDetails_InsureWith, #masterad, #marcoad, .AdsBottom, #Ads_BA_FLB, =
.ad_bgskin, #WNAd43, a[data-redirect^=3D"http://click.plista.com/pets"], #W=
NAd46, #WNAd47, #interstitial_ads, #WNAd49, #branding_ad_header, .flex-ad, =
#category_sponsorship_ad, #sideadscol, #ads-banner, .sponsor_image, #adsifr=
ame, .desktop-ads, #app_advertising_pregame_content, .cs-adv-wrapper, .bann=
er_300x250_2, #ad_wrapper1, #ad_wrapper2, #WNAd52, .ad-ab, .sponsored-resul=
t, #speeds_ads, .banner_300x250_3, .adhalfhome, #ad-banner-lock, a[href^=3D=
"https://mk-ads.com/"], #GOOGLE_ADS_94, #adBar, .menuad, #ad_cna2, #floatin=
gAdContainer, a[href^=3D"http://istri.it/?"], .googleSkyWrapper, #WNAd63, o=
bject[width=3D"100%"][height=3D"90"], #adfactor-label, .adHorisontal, #adve=
rtising_contentad, #textads_right_container, .ad-promoted-game, .ad-bg, .sp=
ons_link_header, #adl_300x250_td, .advert-bot-box, .ad-bt, #plAds, .hero-ad=
-special, #home_lower_center_right_ad, .ad-rac-box, .ew-ad-placeholder, .st=
ory-page-embedded-ad, #bbo_ad1, .inner_adv, .advt_468by60px, .search-sponso=
r, #adPlaceHolder1, #adPlaceHolder2, .advert-txt, a[href^=3D"https://www.mo=
scarossa.biz/"], #subAdsFooter, #csBotterAd, .advert-leaderboard, .item_ads=
, #adv_overlay_content, .googleAdBox, .label-ad, #adtech_1, #adtech_2, .ad-=
dt, #adtech_3, #ad-atf-top, .content-ad-article, #adtech_0, .adverTxt, .mod=
ule_ad_disclaimer, #bottomad300, #dfp_ad_Entry_EntrySetB_300x250, #boxes-bo=
x-zergnet_module, #mediumAdContainer, object[width=3D"1000"][height=3D"200"=
], .ad-ex, #componentAdRectangle, .tileAds, .left120X600AdHeaderText, ifram=
e[width=3D"600"][height=3D"90"], .ad-fi, #AdMobileLink, .ads01, .ads02, .ad=
s03, .ads04, .ads05, .ads07, .ads08, .ads06, .ads09, .dac__mpu-card, .Cheat=
__outbrain, .bannerAdRectangle, .inlineadsense, #leaderboard_728x90, .ss-ad=
-banner, #DivAd1, #DivAd2, #DivAd3, #section_ad, .ads13, .ads14, .ads15, .a=
ds10, .ads11, .ads12, .old-advertorial-block, .googleadsrectangle { display=
: none !important; }

#Ad_RightBottom, .adsenseInPost, #DivAdA, #DivAdB, #DivAdC, #ad_120x600, .A=
dUnitBox, .dfrads, .gAdFour, .houseAd, .google-sponsored-links, .sideadtabl=
e, .ad-ho, .ad_hat_top, .ad_728, .FooterTileAdOuter_Div, #temp-ads, .dfp-bu=
tton, #FooterAd, #rtmod_ad, .homepage-sponsoredlinks-container, .mantis__re=
commended__item--external, #adsTop, .pageHeaderAds, #ad-inside2, #ad_conten=
t_fullsize, .adSize_MedRec, #block-views-advertisements-block, #ad-inside1,=
 #the-last-ad-standing, .carbonad, #adunit_article_center_middle6_computer,=
 #adWrapperLeft, .inhouseAdUnit, .module_home_ads, .ads_before, .ad-engage,=
 #footAds, #adsBoxResultsPage, #adv_BoxBottom, .ads-google-top, .centered-a=
d, .cnnStoreAd, .ad-lb, .cl-ad-slot-post1, .cl-ad-slot-post2, .rmp-ad-conta=
iner, .rockmeltAdWrapper, #adbottomgao, a[href^=3D" http://ads.ad-center.co=
m/"], #ForumSponsorBanner, .nbaTVPodAd, .side_adv_01, .Ad_300x250_holder, .=
ad-mb, #wpladbox1, #wpladbox2, .ad_showthread_firstpost_start_placeholder, =
.netPost_ad1, .adv--desktop-top, .netPost_ad3, .snarcy-ad, .ad--centered, #=
ad-top-wrap, .text-g-nn-web-group-ad-halfpage, .cmg-ads, .affiliation728x90=
, #adspot_220x90, #adtagrightcol, .add_300x250, .adunit125, a[href^=3D"//ww=
w.pd-news.com/"], #eshopad-728x90, #goad1, .lead-ad, .view-advertisements, =
#sidebar-post-120x120-banner, .ra[align=3D"right"][width=3D"30%"], #ds_ad_n=
orth_leaderboard, .widget_maxbannerads, a[href*=3D".ichlnk.com/"], .ad-on, =
a[href^=3D"http://xads.zedo.com/"], .ad-container_row, #adBox, .google-ad-i=
frame, .ad-pb, .content-ad-widget, .adFullWidthBottom, .ads125, .ad_half_pa=
ge, .ads123, .adback, #hometopads, #ad300x250, .rscontainer > .ellip, #goad=
s, .below-ad-border, .banner-ad-footer, #content_4_threecolumnallfocus_righ=
t_0_pnlAdSlot, a[href^=3D"https://uncensored3d.com/"], .boxAdsInclude, .ads=
_rem, #ad-separator, a[href^=3D"http://z1.zedo.com/"], #adInCopy, .wrap-ad,=
 #frontpage_ad1, #frontpage_ad2, #add-top, .ipsAdvertisement, .centerAdBar,=
 .ad-rh, .ad-ri, .adunit160, .reclamTable, .video-right-ads, #bg-footer-ads=
, #content_bottom_ads, a[href^=3D"http://liversely.com/"], .ad_deferrable, =
#content-advertising-header, .cube-ad, .advert-three, .banner125x125, #ad_r=
ight_content_article_page, .ad-sp, .bottomAdvt, iframe[width=3D"468"][heigh=
t=3D"60"], .commercial-unit-tiles-immersive, .ehs-adbridge, #big_ad, .ads16=
0, .PartialProgrammaticAd-ads, .ad-gpt, #ad368_2578, #advertisement728x90, =
.ad-v2, .ad_bg_300x250, #searchAdFrame, #ads_zone27, #ctl00_ctl00_ctl00_tab=
leAdsTop, .jLinkSponsored, .td_left_widget_ad, .cm-take-a-break-ad-area, #s=
idebar-advertisement, #wallpaper_flash_ad, #dvad2main, .pane-mp-advertiseme=
nt-rectangle, a[href^=3D"http://codec.codecm.com/"], #contentAds, .ad-us, .=
story-ad-container, #yw-sponsoredad, .zerg-widget, .dart-leaderboard-top, #=
ad_ros_tower, .ad-grp, .block-heremedia-ads, .ld-ad, #advert-placeholder-po=
st-content-image-1, .slideshow-advertisement-note, .adslogan, .mastheadAds,=
 .ad980x120, .ads-small, a[href^=3D"https://gogoman.me/"], .cdsidebarSearch=
AdParent, #ads_title, #bottom_ad_wrapper, .logoutAdContainer, .trafficjunky=
-ad, .pb-f-ad-flex, .region-dfp-ad-content-bottom, #DARTad300x250, #downloa=
d-leaderboard-ad-bottom, .sidebox-ad, .pageGoogleAdSubcontent, #ad_bg_image=
, .info-advert-160x600, #header_adbox, .midAdv-cont, #CompanyDetailsWideGoo=
gleAdsPresentationControl, #right_ad, .adWarning, #main_ads, .advert--place=
holder, #Body_Ad8_divAdd, #toolbarSlideUpAd, .banner-ad-below, #afterpostad=
, #dfp-ad-dfp_ad_atf_728x90, #Adv_Main_content, .mod > .gws-local-promotion=
s__border, #left-lower-adverts, .adunit_210x509, .mobileAppAd, #text-link-a=
ds, .widget_island_ad, .adband, #google468x60, #pgFooterAd, #GOOGLEADS_BOT,=
 #story-sponsoredlinks, #PREFOOTER_RIGHT_BOXAD, .advert-300, #advertisement=
-rightcolumn, #region-regions-ad-top, #ad_related_links_div_program, .block=
_bigad, #smallAd, #adSlot1, #adSlot2, #adSlot4, #adSlot3, .in_ad, .ticket-a=
d, #sponsoredlinks_left_wrapper, .ad-chartbeatwidget, .ads300n, .adrec, .re=
ctangle-embed-ad, .rt-ad-side, .reklam_mgid, .ads300x, .ads_big_right_code,=
 a[href^=3D"https://www.what-sexdating.com/"], .in-content-ad, #block-sideb=
arad1, #adsBottom, #middleads, a[href^=3D"http://www.graboid.com/affiliates=
/"], #ad72890foot, .sfadSlot, #shoppingads, .nativeMessageAd, #ad-bottom-ba=
nner, #top_adv_728, .bnr_ad, #comments-ad-container, .advert_main, .yui3-ad=
, .chrt-subheader__adv, #div-ad-1x1, .adbase, .widget_728x90_advertisement,=
 #ad-120x600-other, #inline_ad_section, .widget_ad_300x250_atf, #ctl00_Adsp=
ace_Top_Height { display: none !important; }

.add300top, .mainRightAd, #content_3_twocolumnrightfocus_right_bottomright_=
1_pnlAdSlot, .ad01-obj, .bo-top-right-ad, .adv__box, .gtop_ad, #full_banner=
_ad, .bot_ad, .entry_sidebar_ads, .bomAd, .nn-mpu, .houseAd1, .ad--468-60, =
.cate_right_ad, .adMastheadLeft, #topadsdiv, .cp-smalladv, #adsHeadLine, .a=
fterpostadbox, .moduletable_ad300x250, #footer_ad_modules, .lt_ad, .rec-spo=
nsored, #Adv-div, .sponsors_box_container, .sponsor-btns, .single-post-ad, =
#adClickMe, .adEmployment, .GRVAd, #baseboard-ad-wrapper, .ad-siderail, #ad=
_rec_01, #ad-mrec, .skyscraper-ad-1, .advert1, .wingadblock, .advert4, .adv=
ert5, .advert8, #galactic_sponsors_sidebar, .yom-ad-moneyball, #blox-tower-=
ad, object[width=3D"610"][height=3D"130"], .advertiseBlack, .banner_reklam2=
, #sideadbox, .ad-sidebar300, .FlowersAdContainer, .ad-expand, .app_ad_unit=
, a[href^=3D"http://www.myfreepaysite.com/sfw.php?aid"], .divTopADBanner, .=
ss-ad_mrec, .ad-identifier, .box-taboola-content, .horizontaltextadbox, .ad=
Top_placement, #ad_messageboard_x10, .ad_300_120, .adLabelLine, .ad-hdr, .s=
ponsorBannerWrapper, #PPX_imBox_Container, #ad-space, #slideshow_ad_300x250=
, .article_inner_ad, #printads, #tsad1, #bottomRightAdContainer, .adsanity-=
group, #ad2-label, .housead, .rightAdContainer, #tsad2, #c-adzone, .adsense=
_bdc_v2, a[onmousedown^=3D"this.href=3D'https://paid.outbrain.com/network/r=
edir?"][target=3D"_blank"] + .ob_source, .adv_code, .adrow, #adSpaceBottom,=
 .add_baner, .postbit-ad, .adv-text, #header-lb-ad, .ad-sponsor-text, .bann=
er160, #Ad300x250_0, .tmz-dart-ad, .sponsorship_ad, .mod_r_ad, #icom-ad-top=
, #top_sponsor_ads, a[href*=3D".inclk.com/"], #pmad-in1, .adbanner-300-250,=
 .sponsored-ad, #divAdMain, .plista_widget_i300x250, .AD_MOVIE_ITEMLIST, .o=
penx_3, .openx_4, #dfp-middle, div[id^=3D"adspot-"], .related-content-story=
__stories--sponsored-1, #sideBarAd, .related-content-story__stories--sponso=
red-2, #bigboard_ad_ini, #adv-right, .adrrr, .ad-260x60, .related-content-s=
tory__stories--sponsored-3, #common_right_lower_ad_wrapper, .articleHeadAdR=
ow, .box_adv_728, #hiddenadAC, #google_ads_box, #rtm_html_920, .ad-skyscr, =
#header-top-ads-text, #ad-sky-atf, .rightAdBox, #ad_wide, #ctl00_tc_ctl03_A=
dControl, .ad-panorama, .ads-leaderbord, .site-top-ad, .showAd_Yes, #AdTrac=
kVideoPlayer, #adv_IntropageOvl, .adsense_336_280, .dfp-dynamic-tag, .tl-ad=
-dfp, .sec-ad, img[alt^=3D"Fuckbook"], #footeradvert, .button_advert, a[hre=
f^=3D"http://t.mdn2015x2.com/"], #adCol, .mvAd, #top_wide_ad, div[id^=3D"ad=
-div-"], .ad-unit-970x90, .taboola-partnerlinks-ad, #icePage_SearchLinks_Do=
wnloadToolbarAdRightDiv, #vsw-ads, .exo-native-widget-outer-container, .ads=
ense_container, #ad_cont, #google_ads_div_Blog_300, .adsYN, .SidebarMiddleA=
dContainer, #blog-advert, .ads-here, a[href^=3D"http://install.securewebsit=
eaccess.com/"], .ads_sep, #ntvads, .headerAdContainer, #ad_content_wrap, #m=
ain-content > [style=3D"padding:10px 0 0 0 !important;"], .ad_unit_300_x_25=
0, .article_ads_banner, .vw-single-header-ads, .smallsideadpane, #adMonster=
1, .bottom-ad-large, .adPanelContent, .top_advertising_lb, #block-adsense-0=
, .ads250, #block-adsense-2, .ad-hor, .advert-image, .google-ad-160-600, #I=
mageRotaAreaAD, .topad-bar, #sidebar2ads, .thumb_ad, .__xX20sponsored20bann=
ers, .articlepage_ads_top, .M__leaderboardAdvert-image, .advr_top, .AdModul=
e_ContentLarge, #ad_160_600, .z-lockerdome-inline, .banner_468_60, .adstxt,=
 .ads_wrapperads_top, #commentAdWrapper, .ads-wrap, #rbAdWrapperTop, object=
[width=3D"250"][height=3D"250"], .homepage__ad--top-mrec, #gtv_tabSponsor, =
.sponsBox, #sidebar-advertise-text, .ml-adverts-sidebar-bottom-1, .ml-adver=
ts-sidebar-bottom-2, .ml-adverts-sidebar-bottom-3, #leadad_1, #leadad_2, .i=
nlineAdContainer, .publicidade-abre_padrao, .ad-block__ad300, #ad_header_co=
ntainer, .google_ad_first, #ads72890top, #adspot-300x110-pos-1, #tr-adv-ban=
ner, .ads_3, .ads_1, .ads_4, .lqm-ads, #premiumAdTop, .ads_2, a[href^=3D"ht=
tp://www.streamtunerhd.com/signup?"], .desktopads, #RightSponsoredAd, .rect=
angleAd, .rhs-advert-container, #adSpotSponsoredLinks, .right_box_ad, #amaz=
on-ads, .UnderAd, #ad_link, #rightColumnSkyAd, .ad_lnks, #adBreak, #footerG=
oogleAd, .horizontal_Fullad, #ft-ad-1, .ads_h, #my-medium-rectangle-ad-1-co=
ntainer, .dynamic-ads, .ads_r, .GreenHomeAd, #blogImgSponsor, .c-adunit--bi=
llboard, .ad-bigbox, #upper_advertising, .puFloatLine > #puFloatDiv, #right=
_player_ad, .g_ads_200, #top_ad_zone, .ad-rect, object[width=3D"250"][heigh=
t=3D"500"], .ads_leader, .ad_block_300x250, .ad_eniro { display: none !impo=
rtant; }

#sky-ad, #inside-page-ad, #ad-box-leaderboard, .adv_link, .ads_brace, .goog=
le_ads_header11, .Cheat__footer-ad-container, #adxSponLink2, .left_col_ad, =
#synced-ad, .adverts-125, #adxSponLinkA, #ContentPlaceHolder1_adds, .rowgoo=
gleads, #bg_YieldManager-300x250, #ad_300x60, .adbbox, .app_advertising_sky=
scraper, #homepage__desktop-lead-ad-wrap, #gsyadtop, .ads-block-top, .itw-a=
d, a[href^=3D"http://adserving.liveuniversenetwork.com/"], .adfront-head, .=
rightColAdBox, #banner_ad_bottom, #advert_sky, .advertisement__label, .blog=
ads, .sidebar-advertisement, #smallad, .adsep, .adset, #adsense-link, div[i=
d^=3D"div_ad_stack_"], .profile__ad-wrapper, #content > #center > .dose > .=
dosesingle, .inlineAd, #hometop_234x60ad, .cdmainlineSearchAdParent, .vjs-a=
d-iframe, #ad_300x90, #leaderboardAds, .billboard300x250, .adv-format-1, .m=
odule-image-ad, .advertisement_box, #adsd_txt_sky, .widget_ad_300x250_btf, =
#top-ad-container, .bsa_ads, .advertisement_caption, object[width=3D"180"][=
height=3D"107"], #banner-728, #hdrAdBanner, .sponsorBox, .adshl, dfp-ad, .O=
uterAdvertisingContainer, .adMediaNet, .ad-ldrbrd, .adshp, .post_sponsor_un=
it, .advertIslandWrapper, .marketplaceAd, .Post5ad, #adv_Reload, #ctl00_hea=
derAdd, a[href^=3D"http://c.actiondesk.com/"], .advertisement_header, .advt=
Block, #dict-adv, .promoAds, .adsjx, #squareGoogleAd, .tto-sponsored-elemen=
t, #div-web-ad-marginale-1, #advertising_728, #div-web-ad-marginale-2, #div=
-web-ad-marginale-4, #div-web-ad-marginale-5, .ad-nav-ad-plus, #div-web-ad-=
marginale-3, .ad-textads, .gp_adbanner--top, a[href^=3D"http://earandmarket=
ing.com/"], #hideads, .Ad247x90, #ad-block-125, .ad_stream, .ads_160, #adsp=
ace-728, .advertisement_btm, .wide-ad-outer, #adbanner-top-left, #js-image-=
ad-mpu, #sponsored-widget, .mainLinkAd, .region-regions-ad-top, .acm_ad_zon=
es, #adMid1, #adMid2, .google_ads_content, #post-bottom-ads, #AD_gallery, .=
ads-120x600, .rside_adbox, .Advert300x250, .ads_180, .adv__container--300x2=
50, .section-advert-banner, #ads340web, .ad_728_90_1, #ad_336_singlebt, .ad=
padtwo_div, #content_right_side_advertisement_on_top_wrapper, .fixed_ad_336=
x280, .adsns, .js-ad-prepared, .leaderboard_ad, #adiframe3_iframe, .c-tease=
r__advertising, #banneradrow, .afns-ad-sponsor-logo, #FIN_728_90_leaderboar=
d_ad, #td-applet-ads_container, #widget_ad, .leftAds, .ads-middle, .RightAd=
Wrapper, .ad_native, .adv_box_narrow, #wideAdd, .sidebar_small_ad, .screens=
hots_ads, #ADsmallWrapper, .ad_300_250, .adsplash-160x600, #ad-banner-970, =
.rt_ad_300x250, #first-300-ad, #mrec-advertisement, .peg_ad, .lowerAds, .to=
p_ad_disclaimer, .ga-textads-top, .adv_aff, .ads-sponsors-125-left, .gpadve=
rt, .insert_advertisement, #vdls-advs, #AdsWrap, #ad-banner-980, .ad-970x50=
, .ad100, #container_ad, .outbrain_dual_ad_whats_class, .cm-ad-row, #adjace=
nt-list-ad, .hp_ad_cont, .module_header_sponsored, #BottomPageAds, #interst=
itial_ad, .AdsBoxBottom, #cobalt-ad-1-container, #adv_google_300, #ad-links=
-content, #ad-sky-btf, .vce_adsense_expand, .scroll-ads, .eight8_advertisme=
nt_box_all_posts, .entry-ads-110, #top_right_ad, .ADPod, .alt-ad-box, .ads3=
00, .rc_ad_300x100, #topads-spacer, #ad_left_skyscraper, #right_advertising=
, #topadwrap, .Cheat__top-ad, #AdShopSearch, .ad125, .ad120, #yreSponsoredL=
inks, #bannerAdLInk, .Ads-leaderboard, .ads315, .wrb3_ls1_adv, .block-ads-e=
planning-300x250top-general, .sideadmid, #mediaget_box, .sub-ad, .banner-30=
0-100, #leaderboard-ad-2_iframe, .cnbc_leaderboard_ad, .sideAdv, .fi-adv-ha=
lfpage, .LeftWideSkyscraperAdPanel, .ad140, .adfoot, embed[width=3D"180"][h=
eight=3D"530"], a[href^=3D"https://incisivetrk.cvtr.io/click?"], #nbaLeft60=
0Ad, .bullet-sponsored-links-gray, .sponsoredresults, .bottomAdBlock, .fa-g=
oogle-ad, #js-ad-leaderboard, .ad-970x90, .bg-ads, #hide_ad_section_v2, #ph=
otoAndAdBox, .ss-ad-thumbnail, .rightAdvert, #ad-leader-container, #adposit=
ion-TOCSS, .ad_linkunit, .adframe_rectangle, #adrighthome, .advads_widget, =
.ad160, .adv-comments, #adsense-letterbox, .SponsorIsland, .internal-ad, #b=
ig-ad-switch, .ad-index-main, object[width=3D"800"][height=3D"90"], .sectio=
n-ad-related, .adleader, .moneyball-ad, .Video-Ad, #blogad, a[href^=3D"http=
://www.1clickmoviedownloader.info/"], .ad180, .wallAd, #adkit_rnav-bt, .sid=
ebar_ad_1, #AdBlock, #adbg_ad_0, #adbg_ad_1, .sidebar_ad_2, .browser_boot_a=
d, .adSquare, .anchor-ad-wrapper, .sidebar_ad_3, .footer_ad_container, .csa=
-adsense { display: none !important; }

.ads_tit, #adrow-house, .ad-200-big, #display_ads_footer_last, .ad-grid-125=
, .advttopleft, #div-dfp-BelowContnet, #midrect_ad, .advert_surr, #sponsore=
dProducts2_feature_div, #banner-300x250-north, #adspace300x250, #side_ad_co=
ntainer_A, .adsboxBtn, #monsterAd, .fixed-ad-bottom--banner, .grey-ad-line,=
 .rectanglead, #divAdd728x90, #ads-vers7, #adRContain, #adkit_rnav-fb, .adv=
_120x240, .spnsrCntnr, .bmg-sidebar-ads-125, #leftAd_rdr, #featureAdSpace, =
.visuaAD400, #adsense_box, .right_block_advert, #content-adwrapper, #home-p=
age-listing-ad, .google-ad-top-outer, #dfp-ad-homepage_300x250-wrapper, .se=
-ligatus, .ad_rightSky, .br-ad-wrapper, #adsense300x250, .adtab, .widget-te=
xt-ad, .adtag, .ad_long, .mo_googlead, .cnn_728adbin, #center_col > #result=
Stats + #tads, #double-inline-ads, #rightad2, #rightad1, a[href^=3D"http://=
track.trkvluum.com/"], .ziffad-wrapper, .panel__column--vc-advert, #header_=
ad_728, #adsense_honeytrap, a[href^=3D"http://data.linoleictanzaniatitanic.=
com/"], #headadvert, .content_left_advert, #ad-footer-728x90, .bq_rightAd, =
.companyAdsSquare, .adSenceImagePush, #rightadg, .g_adv, #addspaceleft, #aw=
esome-ad, #dfp-ad-half_page_sidebar-wrapper, #rightads, .AdMultiPage, .trb_=
pageAdHolder, .section-sponsors__label, .view-advertorials, .ad-salutations=
, .ad-slot-300-250, .sideskyad, #ad_island_incontent, #ad520x85, .beteasyad=
txt, .wfb-ad, #home-rectangle-ad, .commentsbannerad, #adVcss, .ad_word, .ad=
-container-bot, #ad-banner-wrap, #header-ad-placeholder, #apt-homebox-ads, =
#ad300x600pos2, #leaderAdContainerOuter, .mod-trbad, a[href^=3D"http://api.=
ringtonematcher.com/"], .leftrighttopad, #leftAdCol, #adsctl00_AdsHome2, #c=
omponentAdSkyscraper, #bottomBannerAd, .slide-advert, .eng_ads, #BBCPH_MCPH=
_MCPH_P_OasAdControl1Panel, .column2-ad, .sidebar-box-ad, .sb_adsWv2, .dn-a=
d-wide, .inlinead, #ads-left-top, .jw-ad-block, .bottomad-bg, .ads_big-half=
, .artAdInner, #cbz-comm-advert-1, #ads-sponsored-boxes, .block--advertisin=
g, .headerAdspace, .ad-slot-sidebar, .multiad2, #advert_top, .adsFixed, .ad=
thx, #dotnAd_300x250_c20, #divFoldersAd, .simple_ads_manager_zone_widget, .=
topadsection, .rightAdColumn, object[width=3D"990"][height=3D"206"], .conta=
iner-lower-ad, .adv-336-280, .adv-4, #adxtop2, .botad2, .btm_ad_container, =
.adsBelowHeadingNormal, .embeddedAd, .header-ads-holder, .section-adtag, .a=
diframe250x250, .cat-adv, .WiredWidgetsDartAds, .widget-entry-ads-160, #skc=
olAdSky, object[width=3D"256"][height=3D"300"], #ads_top_banner, #lowertop-=
adverts, .adv-p, #devil-ad, .ad-media-marquee, .sideBySideAds, #adzone-tead=
s, .x-tile__advert, .container--advert, .Ad_468x60, #block-fan-ad-fan-ad-fr=
ont-medrec-top, .ap_str_ad, .dfp_ad_content_top, #bottom_adbox, .post_seper=
ator_ad, #related_ads, a[href^=3D"http://bs.serving-sys.com/"], .ad_spotlig=
ht, #dfp_ad_Result_728x90, .widget-ad-sky, #ringtone-ad-top, #ad_frame, #ad=
_700_90, .ads-in-article-view, .banner336, .jc_ad_container, .adv-300x250, =
.openxbuttons, .is-sponsored, .ads-by-google-0, .tdad125, #tilia_ad, #ad_ga=
llery, object[width=3D"188"][height=3D"290"], #ad-anchor, .msg-ad, .ad-355x=
75, #below-listings-ad, .o-ads, #pageAdvert, .art_ad_aside, .market-ad, .ad=
Recommend, .ad_thumbnail_header, #text_ad, .banner350, #lb-sponsor-right, .=
adrotate-sponsor, .cntrad, .adv300_100, .ads-rotate, .ad-unit-top, #forum_t=
op_ad, .adv_90, #dfp_ad_InternalAdX_300x250_right, #content_11_pnlAdSlot, .=
side-adverts, .widead, .ad_cheat, [lazy-ad=3D"leftbottom_banner"], .module-=
ad-small, .lazyload_ad, .ads-box, .ad200, .sponsored_links, #headAd, #adv_v=
ideo_sidebar, #btm_ads, #leaderad, .in-content-ad--container, #skinad-left,=
 .wrb6_x1_adv, #right_ads_box, #ad468_hidden, #vidAdBottom, .bottom-ad-wrap=
per, #adSpotIslandLarge, .adContainer_728x90, #cmn_toolbar_ad, .ads_top_pro=
mo, .adageunicorns, .article-adv-right-sideBar, .mod_ad, .mpu_advert, #ad_P=
ushdown, #ads_back, .gamesPage_ad_content, #sideAdLarge, .ad--fullsize, .ad=
NoticeOut, .ad_right_column, #sidebar_ad, div[id^=3D"zergnet-widget"], .mtv=
-adChoicesLogo, .right_ad_unit, a[href^=3D"https://clixtrac.com/"], #divWra=
pper_Ad, .ad230, .ad234, .homeadwrapper, #bottom_banner_adsense, #topAdvert=
-09, .ad-slot--inline, .adsenseformat, .AdCaption, .ad-incontent-ad-plus-to=
p, .bottomvidad, .ad240, object[width=3D"240"][height=3D"400"], .advert_dja=
d, a[href^=3D"http://partner.sbaffiliates.com/"], #AdBox2 { display: none !=
important; }

.ads-btm, #article-content-ad, .nr_partners, .AdsLinks1, #adTopbanner, .Ads=
Links2, .adv728_90, .ad250, #topBannerAdContainer, .ad257, .rectangle-ad-co=
ntainer, #tcwAd, #ad-page-sky-left, .ad_left_cell, #ad-results, #network_he=
ader_ad_1, #footer_text_ad, #advert-box, .AdWidget_ImageWidget, a[href^=3D"=
http://www.clickansave.net/"], #featuredAdWidget, #adpostloader, .ad260, #p=
ersistentAd, .adtxt, a[href^=3D"https://refpaano.host/"], .adunit468, .r_ad=
s, #ad_global_300x250, .atf-ad-medrec, .header-article-ads, .pane-ad-manage=
r-middle1, .rc_ad_300x250, .ad-blogads, #ads-hoster-2, .ad-TOPPER, .banner-=
advert, .ads460, .button-ad, #gpt2_ads_widget-6, #gpt2_ads_widget-7, #gpt2_=
ads_widget-8, #gpt2_ads_widget-9, .ads468, .content_adsq, .banner-300-250, =
#txtAdcontainer2, iframe[width=3D"104"][height=3D"464"], #adunit-mpu-btf-si=
debar, .half_ad_box, .adv_box, a[href^=3D"http://wct.link/"], .ad290, #ads_=
tower1, #leaderboard_ad_unit, .AdvertorialTeaser, #rtAdvertisement, .extern=
alAdComponent, .floated_right_ad, #sidebar-scroll-ad-container, .widget_sup=
ernews_ad, #ad_container_sidebar, .advertisment-left-panal, #googleAdMid, .=
rect_ad_module, .RealtorAd, .wallad, #ad160600, .mod-adopenx, #ad_NorthBann=
er, #dfp-ad-boombox, .card--article-ad, #postpageaddiv, .gallery__bottom-ad=
, .support_ad, .adtext_gray, #ads300x250_single, #related-projects-sponsor,=
 [onclick^=3D"window.open('https://www.brazzersnetwork.com/landing/"], .con=
tent_advt, .sidead_300250_ht, #mpuWrapper, .ADITION, .detailMpu, .ad-728-ba=
nner, .aa_AdAnnouncement, #reklama_left_body, .homesmallad, #adText2, .tj_a=
d_box_top, .apxContentAd, .advertasingtxt, .body_sponsoredresults_top, #ad-=
lb-secondary, #adPageContainer, #gnadww, #bottom_ad_desktop, .advertisement=
_article_center_middle4_computer, .vs_dfp_standard_postbit_ad, #wallpaper-a=
d-link, .banner_ads_home, #adv_border, #box-ads-x600, .topadspot, #ads-righ=
t-bottom-sidebar, #advertise-now, #skin-ad, .m-header-ad--slot, .navadbox, =
#sidebargooglead, .advertMiddle, #sponsored-not, .frn_adbox, .horizontal_ad=
s, .ad-block-big, #med-rectangle-ad, #oanda_ads, a[href^=3D"http://hyperlin=
ksecure.com/go/"], .adChoice, .top-adverbox, .sponsor-services, .adsponsor,=
 .c-sitenav-adslot, #bannerAd_ctr, #adColumn3, .block-openx, .Adv300x250Box=
, .top-ad-div, #column4-google-ads, #div_ad_TopRight, .ad_tower, .ads_tople=
ft, #bigBoxAdCont, a[href^=3D"https://chaturbate.jjgirls.com/"][href*=3D"?t=
our=3D"], #adcontainsm, .dfp_ad_caption, #rm_ad_text, #HomeAd1, .ads-smartp=
hone, #ad-space-big, .ads_300, .ads_305, .rev_square_side_door, #ad-spot-on=
e, .banner-ad-row, .ctn-advertising, .rr-300x250-ad, #GoogleAdsense, #ad_ti=
le_home, .advertisement-title, .sub_cont_AD01, .googleAdv1, .sub_cont_AD02,=
 .sub_cont_AD04, #yahoo-sponsors, .adGoogle, .sub_cont_AD07, .sub_cont_AD06=
, .news_ad_box, a[href^=3D"https://www.camyou.com/?cam=3D"][href*=3D"&track=
=3D"], #ads_sponsFeed-left, .ads_320, .wg-ad-square, .adhref_box_ads, .main=
_ad_container, .tncms-region-ads, #topad-728x90, .mj-floating-ad-wrapper, .=
views-field-field-html-ad, .ads_330, .tz_ad_widget, .mobile_featuredad_arti=
cle, a[href*=3D".allsports4you.club"], #ADgoogle_newsblock, .page-ads, #adb=
anner-container, #fb_300x250, #main-ad160x600-img, #ctl00_BottomAdPanel, #d=
fp-ad-medium_rectangle, .ezmob-footer, .adAreaNative, .supercommentad_right=
, .medium-google-ad-container, #adsense_200_200_article, .ads-box-header-ma=
rketplace-right, #votvAds_inner, #hl-ad-MON-0, #icePage_SearchResults_ads3_=
SponsoredLink, .ads_350, .advertisementonblue, .adspace_bottom, .ad-leaderb=
oard-marquee, #ad_leaderboard_top, #dsk-banner-ad-b, .floatAdv, .adsense_20=
0x200, #AdDetails_SeeMoreLink, .us-txt-ad, .widget_wnd_ad_widget, .advert-o=
verlay, .adsense_unit, #rightadd300, #adSenseResults, a[href^=3D"//api.ad-g=
oi.com/"], .TimelineAd, .widget_arvins_ad_randomizer, #DivAdForumSplitBotto=
m, #adverthome, #ad_468x60, .MarketGid_container, .ad-desktop, .square-ad, =
#post-ads, .advertising-leaderboard, .adsense_bottom, .center_adsense, .dfp=
-leaderboard, #wrapCommentAd, #topad_holder, .ads-bigbox, .place-ads, #ad_f=
eature, a[data-widget-outbrain-redirect^=3D"http://paid.outbrain.com/networ=
k/redir?"], object[width=3D"265"][height=3D"300"], .mid_article_ad_label, #=
lbAdBarBtm, #AdBar, .centralizer-adx, #mpuholder, .box-footer-ad, a[href^=
=3D"http://ads.affbuzzads.com/"], .gAdvertising, .main-tabs-ad-block, .post=
-adsense-bottom, #article-ad-container, .adfloatleft, #thistad, #bn_ad, #ho=
rizontal-adspace, .big-box-ad, .southad, .adsenseContainer, .__zinit .__y_i=
tem, .site-footer__ad-area, #ctl00_tc_ctl15_AdControl, #boxes-box-ad_300x25=
0_1, .ads-superbanner, .banner468, .rect-ad-1 { display: none !important; }

.on-demand-ad, #ad-wide-leaderboard, #ad300x600, .ad-block-240x400, .header=
-ad-box, .adInnerLeftBottom, .bq_adleaderboard, .ad_new_box01, .ad_new_box0=
2, #adSuperbanner, #bottomAd300, .bunyad-ad, .IABAdSpace, #ctl00_ctl08_ctl0=
0_tableAdsTop, .photo-ad, .AdUnit300x250, #admaru_reminder, .home-ad-contai=
ner, .ad310, #cubead-2, #headad, .ad-unit-300, #mc-videoads-overlay, .Googl=
eAdv, #adPlaceHolderRight, .ad315, .articlePage3rdPartyContentStrip, #c4ad-=
Middle1, #sidebar-ad_dbl, .advImagesbox, .qm-ad-content-news, .iframeAd, #s=
ide_skyscraper_ad, #adFot, #homepageadvert, .bxad, .ad336, .ads_125_square,=
 .adLabels, .gallery_ad_wrapper, #section-pagetop-ad, .monitor-g-ad-300, .a=
dv--leaderboard, .h11-ad-top, .queue_ad, .gp_adbanner--bottom, #adFps, .ad-=
140x45-2, #sidebar-ad-space, #side-banner-ad, .ad-lower_river, .pagenavinde=
xcontentad, .ad-lower_rec, div[id^=3D"ads300_100-widget"], .ad350, #hAd, #a=
d_mpu_1, #div-gpt-ad-spotlight, .advertising-srec, .adBottomLink, .adLeft, =
.aopsadvert, .ad360, .widget_advertisement, .ThreeAds, .boxAdContainer, #ad=
PlaceScriptrightSidebarSecondBanner, #adleft, #adsright, #mn #center_col > =
div > h2.spon:first-child, .ad-vendor-text-link, .rightAdverts, #WNAd1, #mo=
zo-ad, #largeAds, #raw-search-desktop-advertising-tower-1, a[href^=3D"http:=
//www.usearchmedia.com/signup?"], .item-ad-leaderboard, #sponsorLinkDiv, #b=
ackgroundadvert, #walltopad, a[href^=3D"http://goldmoney.com/?gmrefcode=3D"=
], .p75_sidebar_ads, #adtoniq-msg-bar, #block-ibtimestv-player-companion-ad=
, #show-player-right-ad, .advertisement--appnexus, .widget_etcenteredadwidg=
et, .adv_cnt, .wnMultiAd, #advertorial_block_3, #hd_ad, #ga_300x250, .foote=
r-advert-large, .Ad-Container-976x166, #adjs_id, #div-id-for-interstitial-a=
d, .m-ContentAd, .advertisment-module, .gm-ad-lrec, .square_button_ads, .co=
ntent-module.ad, #boxes-box-ad_728x90_1, .bmg-sidebar-ads-300, #YahooAdsCon=
tainer, #ad_mpuav, .ad_promo1, .innerBanner, #ad_billboard_ifm, #ovAdWrap, =
.ad1x1, .adv_1, .bb-adv-160x600, .adv_bg, #ad-large-header, .ad-wrap01, #gl=
obalHeader_divAd, #headersponsors, .ad-wrap02, .ad_square, .adv_2, .homepag=
e300ad, #ft-ads, .adBox-mr, #adunit_main_right_top_computer, .blog2AdIntegr=
ated, .adnSpot, .advertisement-banner, #supp-ad1, .md-adv, .pane-frontpage-=
ad-banner, #adPosition14, #parade_300ad2, .yvp-adsview-show, .main-advertis=
ing, #ad_channel, .box_ads728x90_holder, .ad_head, .ad-banner-label, #ad-fu=
llbanner2, #browsead, .adsbox_300x250, #advertisement-text, .l-adsense, #BB=
1-ad, .sponsorshipbox, .columnBoxAd, #ad-special, .adsCategoryTitleLink, a[=
href^=3D"https://zononi.com/"], #ad_medium_rectangle, .adReportsLink, #adun=
it-pages1x1, .ads_text, .content_bottom_adsense, .adfieldbg, .ad-bottom-con=
tainer, #l_home-keen_ad_mask, .Ad_D_Wrapper, .RightGoogleAd, .trb_ar_sponso=
redmod, .middle_ads, #PublicidadSuperior, #button_ad_wrap, #ffsponsors, .si=
de-sky-banner-160, .advert-competitions, .adchoices, .featured-ads, #advert=
ising-mockup, a[href^=3D"http://greensmoke.com/"], object[height=3D"250"][w=
idth=3D"175"], #advert_mpu_1, #advert_mpu_2, .ad-refresh, #footer-ads, #foo=
ter-adv, .ad-innr, .ads-970x90, #mc_ad, .dfp-top1, .ads-bing-top, .advert-7=
28, #right-uppder-adverts-container, .this_is_an_ad, #advertistop_td, objec=
t[width=3D"480"][height=3D"100"], .partnerad_container, .txt_ad, #divAdvert=
isingSection, #sidebar-top-ad, .fp-adinsert, .web-result-sponsored, .advert=
isment_two, #content-ads, #left-ad-col, .adRoller, .mpu-top-right, .avantga=
rdia-ad-widget, .hm_advertisment, #left_adspace, .top_ad_holder, .ad_widget=
, .block--views-premium-ad-slideshow-block, .ampad, #bottomAdCCBucket, a[hr=
ef^=3D"https://www.brazzersnetwork.com/landing/"], #advertiseLink, .big-adv=
ertisement, #adspot-468x60-pos-2, .banner_header, #mpr-ad-leader, .spon-lin=
ks, .dart-leaderboard, #tileAds, .ingameadbox, .advert-760, .adBoxContainer=
, #mini-panel-top_ads, .Post8ad, .skinad-l, .advertisementsubtitle, #ad_con=
tainer_marginal, .ad-cluster-container, #box_advertisment, .skinad-r, .bloc=
k-ads-yahoo, .ad-placeholder, .adserverad, #chatAdv2, .header-ad-wrapper, .=
mod_index_ad, .ad-story-top, .ads-side, .display_advrst, .ad-300-b, .sidead=
vert, a[href^=3D"http://n.admagnet.net/"], .GoogleAdsItem, .JobListMidAd, #=
mrecPlacement, #houseAd, #topadvertisements, .stProAd, #comment_ad_zone, .w=
ppaszone, .ad_info_block, #leaderad_section, .topAdContainer, .ads_468 { di=
splay: none !important; }

.insertAd_AdSlice, .pane-two-column-ads, #comments_advert, .bannerAdSidebar=
, .hp_ad_300, .sidebar_ads_336, #viewAd1, .ads-div, #boxLightImageGalleryAd=
, a[href^=3D"http://www.adbrite.com/mb/commerce/purchase_form.php?"], .fixe=
dAds, .right_adskin, .advert_wrapper, #banner_ad_module, #lowertop-adverts-=
container, .sponsor_logo, #sponsored-search, .adBox728X90_header, a[href^=
=3D"https://ads-for-free.com/click.php?"], #ad-front-sponsoredlinks, .ad-sp=
ace-mpu-box, .inline-ad-wrapper, #sponsoredList, #right_advert, .ww_ads_ban=
ner_wrapper, .ct-ads, #ads_r_c, embed[width=3D"200"][height=3D"230"], .squa=
readMain, .adslot_1m, .popup-ad, #iqadcontainer, .content-item-ad-top, .adv=
ertisementText, #bottom_banner_ad, #adkit_footer, #AdMediumRectangle1300x25=
0, .adslot_2m, #Ads-D-728x90-hori, #promoFloatAd, .koadvt, .top_corner_ad, =
#ads_combo2, #layerTLDADSERV, .adv_tr, .display-ad-block, .gutter-ad-right,=
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ogle, .adCenterAd, .adslot_3m, .sponsor-ads, .trb_masthead_adBanner, .ad_si=
de_box, #RadAdSkyscraper, .sr-side-ad-block, #taboola-right-rail-stream-2nd=
, #textad3, a[href^=3D"http://tracker.mybroadband.co.za/"], #AdHouseRectang=
le, .ad-rectangle, .ad-bigboxSub, .ad-leadtop, #footer-adwrapper, .ad400, o=
bject[width=3D"480"][height=3D"60"], .rightad_2, .rightad_1, .rev-content-s=
ponsored, .landing-page-ads, .top-fbs-ad-sticky, #aboveGbAd, .sponsoredLink=
sGadget, #ad-sidebar-mad, .adv200_border, .tile--ad, .ad_hat_728, #bannerad=
vert3, #adSpot-banner, #right-ad-skin, #googleAds, .ads600, #rightAdsDiv, .=
quigo, .ads_topright, .InArticleAd, .advertis-left, .pm-ad-unit, .banner_ad=
v, #ad-container-fullpage, .ad-table, .Ad-Header, .lg-ads-311x500, #box-ad-=
sidebar, a[href^=3D"http://adserver.adtech.de/"], #vert_ad_placeholder, .se=
ction-adbox-bottom, .ads-600-box, .div-gpt-ad, #divSponsoredLinks, .h-ad-72=
8x90-bottom, #gl_ad_300, .iframead, #pauseAd, #ad-div-leaderboard, .ad_area=
, .head-ad, .ad728x90_wrap, #gft-adChoicesCopy, .Ad_120x600_holder, .group_=
ad, .ad_lrec, .adunit_leaderboard, .box-ad-grey, .ad450, .ban980x90, #medRe=
qAd, .front_ad, .sponsoredibbox, .advertDownload, .ad120x120, .advertisemen=
t_block_468_60, #divAds, .article_ad_text, .src_parts_gen_ad, .box1-ad, .ad=
_descriptor, #menu-ads, .masthead-ads, a[href^=3D"http://banners.victor.com=
/processing/"], #contentad-adsense-homepage-1, #ad-halfpage, #contentad-ads=
ense-homepage-2, .article-ad-left, .betteradscontainer, #TopAdPlacement, .n=
w-top-ad, .ads-site, .quotead, #SidebarAd, .adv-list_inner, .mvAdHdr, .cnn_=
adbygbin, div[role=3D"navigation"] + c-wiz > div > .kxhcC, #ctl00_ctl00_ctl=
00_divAdsTop, #ad375x85, .ad_iframe2, .ads_big_right, .widget_appmanager_sp=
onsoredpostswidget, .leaderboard-ad-main, .storyad, .fs_ad_300x250, .monito=
r-g-ad-468, #article_ad_bottom, .advertising2, .quick-tz-ad, .adZoneRight, =
.ribbon-ad-container, #spotlight-ad_iframe, .adBoxBorder, #annoying_extra_a=
d_wrapper, .topAdLeft, .dfp-adspot, .postads, a[href^=3D"http://secure.cbdp=
ure.com/aff/"], #FIN_300_250_position2_ad, .greyad, .ad-pushdown, .advert-w=
ide, .detail_top_advert, .ads-header-right, .youtubeSuperLeaderOverallAdAre=
a, #ad_pr_info, #showcaseAd, .ads-block-top-right, .sponsorship-container, =
.bottomadtag, .ads_box_headline, .ads_upper_right_wrap, a[href^=3D"http://t=
raffic.tc-clicks.com/"], .banneradsensetoptitle, .pencil-ad, div[id^=3D"q1-=
adset-"], #IC1-ad, #ad-center, #page_content_top_ad, #view-photo-ad, #ads30=
0k, .staticad_mark125, #topbarads, a[href^=3D"https://www.bebi.com"], .spri=
te-ad_label_vert, .videoAd300, .sponser-link, .wpi_ads, #dnn_ad_island1, #m=
ason_adv_rn_2, .rgt-ad, .specialAdsLink, object[width=3D"120"][height=3D"60=
0"], .ad_container_5, .ad_container_6, .ad_container_7, .adrighttop, .ad_co=
ntainer_9, .ad_choice, #block_advertisement, .ad_container_8, .Ads_3, .Ads_=
4, .ads_up_big2, #ctl00_ucAffiliateAdvertDisplay_pnlAffiliateAdvert, .ad-cu=
rtain, .adUnitVert_noImage, #ka_adFullBanner, .bonnier-ads-ad-bottom, #dfp_=
ad_1, #dfp_ad_2, #dfp_ad_3, #secondrowads, #dfp_ad_7, #panel-ad, .divAdsLef=
t, .ad-top1, #content_2_pnlAdSlot, .ad-top2, .ads720x90, #topAdBar, #inside=
r_ad_wrapper, .sponsors-box, #header-advert-panel, .ad-box-300x250, .ad-adc=
ode, .adf_tisers, #blog-header-ad, #ad-cube-sec, .block-ad_tag, .cards-cate=
gorical-list-ad, #adPUSHDOWNBANNER, .videos-ad-wrap, .streamAd, #ads_horizo=
ntal, .layout-ad, .ad-div-t0-wrapper, iframe[width=3D"200"][height=3D"300"]=
, .adtech-top-ad, #adpos_3, .vw-header-ads-leader-board { display: none !im=
portant; }

.premium-ad, a[href^=3D"http://ul.to/ref/"], .addivwhite, .markplace-ads, .=
aol-twist-flyout-ad, .advert-note, .rhs-advert-title, #topadbanner, .ad_goo=
gle, .mini-ad, .Post9ad, .jsOneAd, #content_7_pnlAdSlotInner, .home_adholde=
r, #headline-sponsor, .adBlockSpacer, .publicidade-vertical-layout, #varian=
t_adsLazyLoad, #sensis_island_ad_3_column, .ad200x60, #adverti, .ads-image,=
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dcenterRowWrapper, .full-width-ad, .widgetYahooAds, .m-ad-region, .adrechts=
, a[href^=3D"http://webgirlz.online/landing/"], .ban420x200, .section-adver=
tisement, .advertRight, .ad_300_600, .ad_no_border, .after-post-ads, #stick=
y-ad, .adPlaceholder35, .adlateral, .ad_300_608, .slideAd, .banmanad, #ad-t=
op-250, #ad_300_wrapper, .googad, #ad-holder, .ad_movFocus, .hideAdMessage,=
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nt, #adsenseskyscraper, .adv_amazon_single, .AD300Block, #story-separator-a=
ds, .simplead-container, .not-an-ad-header, .adPlaceholder54, .hp-ad-contai=
ner, .ad-med, .block-altads, .ntnlad, #adsbottom, .bottomadtop, .power_by_s=
ponsor, .AD_336_120, div[id^=3D"ad-server-"], img[title^=3D"advertisement"]=
, #ad_TopLongBanner, #adtext-top-content, #divWNAdUnitLanding, #ad-pan3l, .=
adsense_sidebar_top, .inline-ad-card, #second-right-ad-tray, #homepage_top_=
ad, #msnAds_inner, .ad_flash, .adsCell, .rightbox_content_ads, .bz-ad, #goo=
gle_ads_frame_quad, #ad-bottom-300x250, a[href^=3D"http://www.pheedo.com/"]=
, #ad1-468x400, #MainAd1, #adsense-head-spacer, .bps-advertisement-placehol=
der, .ad236x62, .lb-advert-container, .ad-article-breaker, .rot_ads, .ad300=
x250_box, .CG_adkit_leaderboard, .ban420x260, #yandex_ad, .postgroup-ads-mi=
ddle, .ez-clientAd, a[href^=3D"https://rev.adsession.com/"], .contentadstop=
1, #rightadsarea, .fe-blogs__sidebar-ad, .contentadarticle, #advertisement_=
banner, #Adv_Footer, #hot-deals-ad, .ad-marketplace, #adsIfrme1, #adsIfrme4=
, .logo_AdChoices, .adboxRightSide, .eads, #right_mini_ad, #ads-post-468, o=
bject[width=3D"1000"][height=3D"300"], .ad-iab-txt, .adslot-rectangle, .ds-=
ad, .largeRecAdNewsContainerRight, #topAdBox, #proj-bottom-ad, #box_ad_cont=
ainer, .ADTop, .adscontentcenter, .js-ad-slot, .rightbigcolumn_ads_nobackgr=
ound, #TitleAD, .mslo-ad, .adsRectangleMedium, .ad530, .adCentered, #adv_go=
ogle_728, .bottom-ad-desktop, .ad_label1, .advert--header, .ads-468x60-bord=
ered, #ad_sitebar, .AdRingtone, #af_ad_large, .views-field-field-ad, .ads72=
8, .element-adplace, #googleAd_words, .google_728x90, #AdDiv, .dfp_ad_conte=
nt_bottom, #dfp_ad_Home_300x250, .affiliate-ad, #head_advert, #mastercardAd=
, #adcontainer___gelement_adbanner_2_0, .right_content_ad, #ts-ad_module, #=
taboola-below-article-thumbnails-3rd, .ad--mid-content, .stickyMultiAd-proc=
essed, .divad1, .adComponent, .divad2, .divad3, .hp-ss-service-ad, #anyvan-=
ad, #inlineAdtop, #advertising-caption, .ad_network_content, #div_content_m=
id_lft_ads, #tgAD_imu_2, #tgAD_imu_3, #tgAD_imu_4, .adnation-banner, .adver=
tisebtn, .sponsor-link-banner, .ad-mod, .rightColumnAdsTop, .sponsoredlinks=
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iendlyduck.com/"], #adv_banner_featured, .cpmstarText, .top_header_ad, a[hr=
ef*=3D".orange2258.com/"], #rightadBorder1, #rightadBorder2, .consoleAd, .a=
d-mpl, .adv_120x600, .ad-mpu, .divads, .container-type-banner-advert, #goog=
le_ads_frame1_anchor, #h-ads, #ad_sense_help, a[href^=3D"http://adserver.ad=
techus.com/"], .cA-adStack, #ads_sky, .post-pick-ad, #long-ad, .moads-widge=
t, .smallAds, .wrapperAdSky, .smallAdv, .ad590, #ad_comps_top, #ad_top_bann=
er, #dfp-ad-ne_column3a_300x250-wrapper, #divBottomad1, #divBottomad2, .ads=
Column, #adTag1, #adTag2, #mpu-sidebar, #ad336x280, .bt_ad, .ad-msg, .sl-ar=
t-ad-midflex, #ad-rect, .ad-msn, #ad_728x90_container, .ad_mrectangle, #adl=
anding, .c_google_adsense_nxn, .yam-plus-ad-container, #centerBelowExtraSpo=
nsoredLinks, #infinite-adslot-1, .adPlaceholder, #content_0_storyarticlepag=
e_sidebar_0_pnlAdSlot, .buzz_ad_wrap, .ad-top-lboard, .tx-aa-adverts, #txtT=
extAd, .adUnitVert, .block--bean-artadocean-text-link-1, .block--bean-artad=
ocean-text-link-2, .ads_admeld, .card-ad, .ad_default, a[href^=3D"//adbit.c=
o/?a=3DAdvertise&"], #xybrad, .adDomOutter, .ad-caption, .ad_btf_728x90, .a=
dvertBlock, #ggogle_AD, .dc-widget-adv-125, .moduletable-centerad, #newads =
{ display: none !important; }

#advert_leaderboard, .adb-bottom-outer, #sponsored_game_row_listing, #spons=
ored_news, .MiddleAdContainer, .top-banner-ad-wrapper, #blogads, .image-ad-=
336, #header-adsense, .adMeldGuts, .wrapper-sidebar_ads_half-page, .box-ad,=
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boola, #advertisementBottomThreadUser, #ad_728h, #ad728foot, .adsenseGreenB=
ox, #say-center-contentad, .box-sidebar-ad, .g_ads_728, .dfp_unit, .LeaderA=
dvertisement, .lb-ad, .view-id-simpleads_advertisements, .ibm_ad_bottom, .w=
_AdExternal, a[href^=3D"http://adtransfer.net/"], .msn_ad_wrapper, .legal-a=
d-choice-icon, .wrapper-google-ads, #top_ads_container, .advText, #spotligh=
t-ad-container-block, .footertextadbox, #leftAdSpace, .ad__mobi, #video-in-=
player-ad, .adLabel, #wgtAd, .w-ad-box, .content-single__block_top_ad, .spe=
cial-ads, .ad_300x250_live, #advertisment-horizontal, div[data-mediatype=3D=
"advertising"], .adgeletti-ad-div, object[width=3D"220"][height=3D"320"], #=
pinned_advert_top_wrapper, .advertisedBy, #show_ads1, a[href^=3D"http://www=
.friendlyduck.com/AF_"], .bigadright, .bam-dcRefreshableAd, .mt_adv_v, div[=
class^=3D"gemini-ad"], #sponsoredResultsWide, .searchSponsoredResultsBox, #=
invid_ad, .ad_size_160x600, .side-ad-160-middle, #sideAD, .bpcads-top-leade=
rboard, .customAd, #ContentPolepositionAds_Result, .adright300, .Advertisme=
nt, #dfp-ad-pencil_pushdown-wrapper, .ad_strip_noline, #ad_bottom_1x1, .lea=
derboard-ad-inner, .attachment-dm-advert-gold, #top_google_ads, #googleadst=
op, #resultsAdsBottom, #taboola-below-home-thumbnails-homepage, #video-cove=
rage-ad-300x250, #baseAdvertising, #adLeaderboardUp, .relatesearchad, .spon=
sored-header, #ads_160, #top_ad_banner, #qpon_big_ad-teaser, #exoAd, .ad__m=
pu, #banner_pos2_ddb_0, .ad-gpt-container, .myadmid, .mid_page_ad_big, #ina=
dspace, .advertising-header, .Ad_Label, #external-links-column-ad, .G_ads, =
.serviceAd, #bh_adFrame_bh_300x250_atf, .sponsor_footer, #ad_120_sidebar, .=
article_ad250, .sidebarad_bottom, .carouselbannersad, #BottomAd0, #ad-728x9=
0-top, #gBnrAd, .pj-ad, #ad_menu_header, .ad-catfish, iframe[src^=3D"http:/=
/static.mozo.com.au/strips/"], .adDefRect, .ads-fif, .ads_square, .lv-Aduni=
t, embed[width=3D"100%"][height=3D"100"], .aadsection_b1, .advert_source, .=
aadsection_b2, .adxli, a[href*=3D"=3DAdtracker"], .commercial-unit-desktop-=
rhs > .iKidV > .Ee92ae + .P2mpm + .hp3sk, .logoAd-hanging, #ads-bottom, .ze=
rg-colm, #shell-ad_rect_btf_01, .pane-tw-ad-master-ad-300x250a, a[href^=3D"=
http://www.wantstraffic.com/"], .ads_672, .ADwidget, .col_header_ads_300x25=
0, #socialBarAdMini, .advertSign, .js-adfliction-standard, .ad-slot-sidebar=
-b, .banner728, #leftAds, #right_rail-zergnet, .idGoogleAdsense, #content-r=
ight-ad, #advertspace, .slidead, .ad-noline, #divAdsTop, .zeti-ads, a[href^=
=3D"http://www.ringtonematcher.com/"], .topArticleAds, .ad_320x360, #adsens=
e_banner_top, .articlepage_ads_1, .sponsor_block, .advart, .sb_ad_holder, #=
mts_ad_widget, #Ad-Top, #gallery-ad-container, #adScraper, #top_adspace, .a=
dminister-ad, #ad-top-slot, .top-bar-ad-related, div[role=3D"navigation"] +=
 c-wiz > script + div > .kxhcC, .ad-new, .adblade, #ad_kvadrat_under_player=
, .master_post_advert, .ad300Block, #AD-HOME-LEFT, #dfp-ad-stamp_2-wrapper,=
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orceads, .adsdisplaygames, .sponsored-container, .ads-feed, .column_3_ad, .=
banner-ads-sidebar, .big-right-ad, #adv2_ban, #sideAd1, #sideAd2, a[href^=
=3D"https://lingthatsparleso.info/"], .js-dfp-ad-bottom, .mobile_featuredad=
, #ad-cube-top, .sp-ad, .strawberry-ads, #shortnews_advert, #dfp-ad-content=
_1-wrapper, #searchPaneGoogleAd, .headerAd1, .google300x250TextDetailMiddle=
, .ad600, a[href^=3D"http://ads.integral-marketing.com/"], #partnerAd, #adS=
pace0, #adSpace1, #adSpace2, #adSpace3, #adSpace4, #adSpace6, #adSpace7, #a=
dSpace8, #sideAds, #adSpace9, #adSpace5, #lateralAdWrapper, .story_body_adv=
ert, #adops_cube, .ad__leaderboard, #dfp_container, .ad-related, #ad_hdr_2,=
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], .right_ad_160, ._iub_cs_activate_google_ads, .c-res-ad, .adArticleSideti=
le, .b-ads_300, .ui-ad, #gpt_ad_panorama_top, .AD_336_280, #adSpacer, #ads-=
right-last-sidebar, #ctl00_leaderboardAdvertContainer, .ad-auction-footer-c=
ontainer, .bcom_ad, .ads_widget, #pregame_header_ad, #yom-ad-tbs-as, .sideb=
ar-advert, #rightBlockAd, .sml-item-ad, a[href^=3D"http://www.incredimail.c=
om/?id"], .adGlobalHeader, .ad644, #home_spensoredlinks, .ox_ad, .right-col=
-ad, #adTopBanner1 { display: none !important; }

#mainPlaceHolder_coreContentPlaceHolder_rightColumnAdvert_divControl, .ad65=
2, .adsense-mod-border, #x-houseads, .portal-advert, .middle-ad, a[href^=3D=
"http://tezfiles.com/pr/"], #ad-88-wrap, .nomobilead, .admiddlesidebar, .ad=
-unit-panel, #adsense_testa, .dfads-javascript-load, #adspaceBox300_150, ob=
ject[width=3D"180"][height=3D"300"], .ad-boxes, .moduletable-adsponsor, #mo=
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sTop, .ads_banner_between, .video-player-ad-center, .articleEmbeddedAdBox, =
#bottommpuAdvert, .google-ad-sidebar, #ad-homepage-content-well, #ads-slot,=
 .bottomleader, .paragraphs-item-advertisement, .links_google_adx, .profile=
-ad-container, #FRONTADVT2, #FRONTADVT3, #FRONTADVT4, #FRONTADVT5, .toaster=
-ad, #FRONTADVT8, #adSuperSkyscraper, #article-agora-ad, .rightSideSponsor,=
 .firefly-sidebar-ad, .blockad, #adunit-mpu-atf-sidebar, .searchCenterTopAd=
s, #dItemBox_ads, #DealsPageSideAd, .fireplaceadright, .adunit_300x250, .bo=
tton_advertisement, .sb_adsN, #adsense_leaderboard, .sb_adsW, .googleAd, #d=
fp-ad-schedule_300x250-wrapper, .adSlot, #AD_160, #oba_message, .advrst, #a=
dvertisementLigatus, #article_gallery_desktop_ad, #adwidget3_hidden, #adslo=
t, #sidebar_ad_adam, #adcontainer250x250, .ad_inline, #headerTopAd, #sideba=
rAdSpace, #indexSquareAd, .element--ad, #_ads, #adwrap-966x90, .squareAdd, =
#indexsmallads, .artnet-ads-ad, .videoAd-wrapper, .sideheadnarrowad, .squar=
eAds, a[href^=3D"http://adclick.g.doubleclick.net/"], a[href^=3D"http://go.=
trafficshop.com/"], .fe-blogs__desktop-ad, #advertise-sidebar, .adTopboxrig=
ht, .widget_awpcp-random-ads, .right_advert, #topAd728x90, #sideadzone, .ad=
unitrd, .adv-mid-rect--right, .adslot_728, .adv-dvb, #spr_ad_bg, .ads728_90=
, .adnotice, .story-top-ad-fix, #adspot_300x250A_desktop, #DivAd, .homepage=
-ad-block-padding, [id*=3D"MGWrap"], .ads-sponsors-125-right, object[width=
=3D"760"][height=3D"90"], .pb-f-advert-dfp-double-mpu, object[width=3D"940"=
][height=3D"120"], #ctl00_ctl00_RightColumn1_ctl04_csc300x250Ad1, .googleSu=
bjectAd, .js-header-ad, #page_ad, #div-ad-1x1_3, .associated-ads, #ClickSto=
ry_ViewAD1, .adSlug, a[href^=3D"http://adsrv.keycaptcha.com"], #dfp-ad-home=
_1-wrapper, #header-ad-wrapper, #adlabelFooter, #thefooterad, #rightcol_mgi=
d, a[href^=3D"http://www.bitlord.me/share/"], .ad-medium-two, #blog_ad_top,=
 .LL_Widget_Advertorial, #SponsoredResultsTop, #bottom-pinned-ad, #realEsta=
teAds, .xads-blk-top2-hld, #id_SearchAds, .linkAD, .ad-fadeup, .adsense-ima=
ge-detail, .ad-push, .home_advertisement, #ads_top_right, #advertismentBott=
om728x90_, .googleads-bottommiddle, #video_vert_right_ads, #rightAdHolder, =
#center-ads-72980, #gglads, #adBox350, .bottom-main-adsense, .ad_wrapper_fa=
lse, #adkit_content-foot, .billboardAd, #stickyBottomAd, .tr-ad-adtech-plac=
ement, .tribal-ad, .adSidebarButtons, .ads_takeover, .AdvertiseWithUs, .bud=
get_ads_bg, #XEadLeaderboard, .search-message-container-ad, #squareAdTop, #=
internalAdvert, .miscAd, object[width=3D"190"][height=3D"700"], #topadzone,=
 #footer_advertising, .thirdage_ads_300x250, .instructionAdvHeadline, .head=
er3-advert, #mBannerAd, .advertisementBannerVertical, .publicidadtxt, #ad-n=
orth, .TextAd, .ads_player, .ngs-adv-async, #adBox390, .ad-bigsize, #sponso=
red_head, #weather_sponsor, #ad-container-adaptive-1, #ad-container-adaptiv=
e-3, #global_header_ad_area, .mod-ad-lrec, #ad-wrapper-728x90, .tone_adspac=
e_300x600, #ad_sec, .fdDisplayAdGrid, .aftContentAdLeft, .adv-phone, .ad-no=
te, a[href^=3D"http://cpaway.afftrack.com/"], .ad-line, .b-adv-art, #google=
ad-sidebar-middle, a[href^=3D"http://wxdownloadmanager.com/dl/"], #articlea=
d300x250r, .ad-in-read, .ad-homepage-one, .cls_PostBottomInArticleAdsence_d=
ivContents, #coAd, #ad_slot_bottom, #mi_story_assets_ad, #cnnAboveFoldBelow=
Ad, #ad_sgd, .adtv_300_250, .ad-medRec, #dfp-home_after-headline_leaderboar=
d, #ad_stck, #ctl00_phContents_ctlNewsPanel_rptMainColumn_ctl02_pnlLigatusA=
ds, #kamidarticle-middle-content, .mpsponsor, .adsense_afc_related_art, #ad=
TextLink, #sidebar_mini_ads, .lefttopad1, #layerad, .top-ad-anchor, #Sponso=
redAds, .g-adblock3, .advertisingarea, .entry-top-ad, .LeftButtonAdSlot, #A=
DVERTISE_RECTANGLE1, #ADVERTISE_RECTANGLE2, .ad--BANNER, .adspot_468x60, .a=
dbox-sidebar { display: none !important; }

.question_page_ad, .sugarad, .ads_space_long, .slideshow_ad_300, .topBanner=
Ad, .ad-container-728x90, .mvp_block_type_ad_module, #hl-sponsored-links, .=
ad-marketswidget, .adFrameContainer, a[href^=3D"https://ads.ad4game.com/"],=
 .headerAdCode, .livingsocial-ad, #ad_mast, #Ad3Right, #ctl00_tc_ctl14_AdCo=
ntrol, .moduleAdvertContent, .str-slim-nav-ad, #__BULLETIN__bdiv[style=3D"p=
osition"], #TopAd0, #advertisingModule160x600, .index_ad, .adblade-containe=
r, #ad-leaderboard-bottom, #overlay-advertising, #ctl00_adFooter, #ad_sky, =
.pane-ad-manager-right, .StandardAdRight, .ck-ad, #AdvContainerTopCenter, .=
advertising--tablet, .AD_300x100, #rightAd160x600, #headeradbox, .channel--=
ad, a[href^=3D"http://googleads.g.doubleclick.net/pcs/click"], a[href^=3D"h=
ttp://vinfdv6b4j.com/"], #divAdSpecial, .ads_layout_sky, #adsZone_1, .Ad_Ri=
ght, .spc-ads-sky, #ad_right3, #divArticleInnerAd, .inner-ad, .tynt-ad-cont=
ainer, #adv_top_1, .ad-sidebar-btf-1, .cnnStoryElementBoxAd, #subpage-ad-ri=
ght, .ads__leaderboard--footer, .internalAdSection, #Ads_BA_CAD2, .universa=
lboxADVBOX04a, .panoramic_ad_placeholder, #adsection, #base-board-ad, .play=
er-ad-overlay, #rightcollongad, .wide_google_ads, .blog-ads-container, .con=
tainer-adwords, .ad-square2-container, .adsHeaderFlog, #adPlaceScriptrightS=
idebarFirstBanner, .adv_x_2, #ignad_medrec, #abovepostads, .bsaProContainer=
, #top_ads_region, #boxAdvert, .adv_x_1, #belowNodeAds, #tbo_headerads, .si=
debar-ad-box-caption, #advTop, embed[width=3D"300"][height=3D"250"], .ez-ad=
, #wp125adwrap_2c, .AdZone120, #adbox300x250_1, #adbox300x250_2, .side-ad-1=
20-middle, .ad-noBorderAndMargin, .Post-All-Advertment, #rightColumnAds, #a=
d_rect_body, #dlads, #b5_ad_sidebar1, #ad_rect_bottom, #KH-contentAd, .spon=
sLinks, .WP_Widget_Ad_manager, a[href^=3D"http://www.firstclass-download.co=
m/"], .adv_flash, object[width=3D"468"][height=3D"40"], #adl_250x250, .ad_h=
ome_top_bnr, .td_reklama_bottom, .adbox_left, .adv-lshaped-wrapper, .ads-fa=
vicon, .bottom-mpu-ad, #ad_promoAd, #home-banner-ad, .ad-wrapper--flexiblep=
ortrait, #AdLeaderboardTop, #div-gpt-ad-top_banner, #fpad1, #fpad2, .ad-con=
tain-top, #rightadcell, a[href^=3D"https://www.incredimail.com/?id"], .home=
page_ads_firstrow, #ad-ads, .cubead-widget, .adsWrap, #oem_ad, #adl_300x250=
, #dfp-ad-local_300x250-wrapper, .adHeaderAdbanner, .pm-ad-zone, #popupBott=
omAd, .box_adv1, .box_adv2, #ad-lead, .ad-update, .indy_googleads, .underpl=
ayer__ad, #ad_iframe_160_by_600_middle, .ad-national-1, .cldt-ad-top, #ad-g=
oogle-chrome-sidebar, .home_ad_bottom, object[width=3D"626"][height=3D"75"]=
, .str-300x250-ad, .smallbutton-adverts, .player_ad_box, a[href^=3D"http://=
www.gamebookers.com/cgi-bin/intro.cgi?"], .mod_ad_t25, .google_ads_bom_bloc=
k, #article-sponspred-content, .adsArea, #CONTENTAD, .gallery-sidebar-ad, .=
advertAreaFrame, .etad, .Advertisehere2, .news_footer_ad_container, .google=
ad, #adCirc300x300, .ad_module, #ad2gameslayer, #pageLeftAd, #adHolder1, #a=
dHolder2, #adHolder3, #adHolder4, #adHolder5, #adHolder6, .sponsoredtextlin=
k_container_ovt, .ads-loaded, #ad_160, .unSponsored, #dfp-ad-tower_2-wrappe=
r, .ad_topic_content, .cp_ad, .view-promo-mpu-right, .sponsored_links_box, =
.ads-articlebottom, #adPosOne, #ad-left, .adstext, .dart-ad-content, #head_=
ad0, #dfp-ad-boombox_3-wrapper, .yahoo_ad, div[id^=3D"drudge-column-ads-"],=
 .pads_bulk_widget, .adverteaser, .ad_masthead, .adrotate_top_banner, #liga=
tus_adv, #left_skyscraper_ad, #adv_sky, #rightside-ads, #ads-125, #ctl00_Co=
ntentPlaceHolder1_AdRotator3, #pagelet_search_ads2, #Ad-5-2-Slider, .ad250w=
rap, .little_vid_ads, .block-nst-googledfp, #rxgcontent, .primary_sidebar_a=
d, #block-dfp-mpu-1, #block-dfp-mpu-2, #block-dfp-mpu-3, #homepageAdsTop, #=
head_ads, .ad-top-rectangle, .ad-above-header, .ad--stroer, .hori-play-page=
-adver, #section-ad-1-728, .ad_placeholder, #billboard-ad-container, #deskt=
op-atf_sidebar_sticky, .topadtxt300, .publication-ad, #weatherad, #adbanner=
box, .lr-ad, .adsense-sticky-slide, .region-top-advertisement, #video-embed=
-ads, #body-ads, #fav-advert, #admanager_top_banner, .rt-ad-body, .header-a=
dplace, .zergnet-widget-container, #mpubox, #ad_squares, .ads--square, .ads=
_topbanner, .block-ad-leaderboard, .sponsoredShowcasePanel, .dfp_ad_inner, =
.addbanner, #addvertise_area, .adg_table_row, .sidebar--mps_ad, #adverttext=
, #adv_left_1, #ad_right_rail_flex, #divTopAd, #pgAdWrapper, #footer_ad_clo=
ud, .google728x90TextDetailTop, #top-adspot, .gx_ad, #c_ad_sky, #ad_tbl, #A=
dvertsBottom, #divFooterAd, .gads300x250, .adFtr, a[href^=3D"http://eclkmps=
a.com/"] { display: none !important; }

#ad-tail-placeholder, #adWrapper1, .adblock-wide, #adrightrail, .bean-adver=
tisment, .cinemabotad, .game-category-ads, #adv_banner_sidebar, .adpane, #m=
iddle_sponsor_ads, .leaderboardAd, #ad_leaderboard_flex, #dart_ad_island, #=
adMpuBottom, .ad-hideable, #dvad6main, #google_adsense_home_468x60_1, #firs=
tAdUnit, .adlayer, .content_inner_ad, #containerLocalAds, .product-bar-ads,=
 .belowNavAds, #ad_frame1, .wAdvert, #adrightgame, .adlabelleft, .ads-befor=
econtent, #ad_under_game, #advertising_300x105, #skin_adv, .frontpage-right=
-ad, .dmRosMBAdBox, .advertisement-160-600, .sponsor-300, .page-ad-containe=
r, .ad-postText, .Ad_Tit, #pnl_BannerAdServed, .google_ad, #ad_leaderboardt=
wo, #ad_display_300_250, .dynamic_adslot, .ad940x30, #ad-west, #RHS2Adslot,=
 .adv_630, #SIM_ad_468x60_homepage_pos1, #SIM_ad_468x60_homepage_pos2, #SIM=
_ad_468x60_homepage_pos3, #pf-dialog-ads, .adunit-title, .sidebar-zergnet, =
#google_ads_div_video_wallpaper_ad_container, #adoptionsimg, .rh-ad, #ads-r=
ight-skyscraper, .mpu-top-left-banner, .fblockad, .block-skyscraper-ad, .ed=
itor_ad, .single-ad-anchor, .mod > ._jH + .rscontainer, .ad_120x60, .sponso=
r_div_title, #commercial_ads_footer, .gameplayads, .bigCubeAd, #p-googleads=
ense, .adonmedianama, #ad-sidebar-right_300-1, #ad-sidebar-right_300-2, #ad=
-sidebar-right_300-3, #googleAdsenseBannerBlog, .amp_ad_header, .ads-in-con=
tent, .advertising-inner, .pane-textlinkads-26, .googleAds728, .promo-class=
-brand-getprice, .AdIndicator, object[width=3D"175"][height=3D"220"], .port=
alCenterContentAdMiddle, .the_list_ad_zone, .top-ad-multiplex, .my_ad, .tl-=
ad, .wp_bnn, .ad_120x90, .bottom-adv-container, .googleadbottom, #featured_=
ad_widget_area, .ad_300x100, .widget_ad_300, object[width=3D"185"][height=
=3D"228"], .ads-to-hide, .ad_buttom_banner, .news_article_ad_google, #block=
-display-ads-leaderboard, #rightAdColumn, .sponsored-by__label, #left_globa=
l_adspace, .listicle--ad-rail, a[href^=3D"http://www.accuserveadsystem.com/=
accuserve-go.php?"], .ad-slot-tall, .bq_ad_320x250, #outsideAds, #footerads=
, #top-ad-unit, #ADSLOT_1, #ADSLOT_3, #ADSLOT_4, #AD_300, #big-box-ad, #hom=
e_sec2_adverts, #bottom_text_ad, #ADSLOT_2, #header-advertising, #ad-ban, .=
ad-square300, #banner468x60, #ad-bar, .footerAd, #ad-inner, .block-adsense-=
managed, #ad_banner_1, .section-ad2, .AD_300x250, .bo-top-left-ad, #ads_ful=
lsize, .ad_728_top, #sideBySideAds, .scb-ad, .advtop, .ad-container-728, #a=
d-software-sidebar-300x250-placeholder, .AD_300x265, .ob_nm_paid, .U210-adv=
-column, .AD300x250, #bottom-side-ad, .cnbc_banner_ad_area, .section-ads, .=
section-adv, .lg-ads-160x90, .ad_72890_box, #playvideotopad, .advertise-squ=
are, #adsdiv_close, bottomadblock, #slideshowAd, #post_adspace, .reklam-blo=
ck, .ADFooter, .adv200, .side-ad-300-middle, .content-footer-ad-block, .mod=
uleAd, #adzoneBANNER, #ad_Bottom, #ad-output, .advTicker, #ad-top-leader, #=
ctl00_ContentPlaceHolder1_ad12_adRotator_divAd, #ads-top, .AdvtSample, #ad-=
stickers, .advertisement_main_right_middle2_computer, #logoAd2, #topAdconta=
iner, .adInteractive, #ad_two, #ad_250, .another_text_ad, .r7ad, .fl-adsens=
e, #googleadsense300x250, .premiumInHouseAd, .affiliateAdvertText, #adition=
_Skyscraper, .ads-300-box, #ad_xrail_top, #LittleAdvert, .gam-300x250-defau=
lt-ad-container, #ad_txt, .b_adLastChild, #ad-big, .longBannerAd, #ad_foot,=
 .box_content_ads, #adv468x90, #ads-200, #header-ad-container, #apolload, #=
contentarea-ad-widget-area, #ad-left-sidebar-ad-2, #ad-left-sidebar-ad-3, #=
ad_right_skyscraper, #leaderboard-ad-4_iframe, .footer_ad336, .adv250, .ads=
-horizontal-banner, #ad-left-sidebar-ad-1, .article-ad-align-left, #textAds=
Top, .ad-slot--top, .aalb-pc-ad-unit, #td_adunit1, #add_720bottom, #td_adun=
it2, #ad-header-right, #layout_topad, .banner_ads1, #bottomRightPanelAdCont=
ainer, .spn_links_box, #SIM_ad_300x100_homepage_pos1, #ad160-2, .adgear_hea=
der, #top-adds, #gm-ad-lrec, .adsrecnode, #bott_ad2_300, #slide_ad, .ln-sid=
ebar-ads, .LoungeAdsBottomLinks, .articleads, .ui-advertising__container, .=
smallAdsContainer, #ads-header, #whoisRightAdContainerTop, #ad_160x600, .gA=
dMobileTable, .pushdownAd, .ad100x100, #ad120x600container, .four_button_th=
reeone_ad, .WithAds, .slot_integrated_ad, object[width=3D"500"][height=3D"1=
00"], #vidAdRight, .npAdGoogle, .szoAdBox, #iframe_ad_300, #sponsored-foote=
r, .sponsorMaskhead, a[href^=3D"http://clicks.binarypromos.com/"], #long_ad=
vertisement, .ad-displayed, #ads-250, .adTopBk { display: none !important; =
}

#adv_halfpage, .ads-728, .ads-729, .gallery-ad-wrapper, .madison_ad, .remov=
eAdsLink, #grid_ad, #ad-framework-top, #sidebar-ad-boxes, #adv_top, #perm_a=
d, .bot_ads, #banner-advert, .topadtxt428, .js-ad-space-container, .cnnWCAd=
Box, #ad_main_top, .views-field-field-image-ad, .view-id-custom_advertiseme=
nt, .ad-bottomleader, .ad300Wrapper, #oas_Right1, .artAd, #oas_Right2, .big=
-ads, a[href^=3D"http://s5prou7ulr.com/"], .banner_468x60, #dnn_playerAd, a=
[href^=3D"https://landing.brazzersnetwork.com/"], .Advrt_desktop, .desktop_=
only_ad, #ad_topbanner, .c-advertisement--billboard, .cdc-ad, .ads_obrazek,=
 .gridAdRow, #middle_ads, #extraAdsBlock, .ad_adsense_spacer, .vidadtext, .=
G_ads_m, .hidden-ad, #wideskyscraper_160x600_right, .google_adsense1_footer=
, .affiliate-mrec-iframe, #RightColumn125x125AD, #inline_ad, .articleAdsL, =
#advertiserLinks, .wsTopSposoredLinks, #sitead, #extraAd, #ad-btm, .adplace=
, .highlight-news-ad, .left_google_add, .block-boxes-ga_ad, #main-header-ad=
-wrap-home, .leaderboardad, .sponsored_links_title_container_top, .header_a=
d_div, #adv_skin_1_a, .ads_catDivRight, #specialAd_two, #ad2_footer, #media=
-ad, .ad-inserter-widget, .side-ads_sticky-group, #tadsb.c, object[width=3D=
"161"][height=3D"250"], #artist-ad-container, #advertising-728x90, .content=
_column2_ad, .ads-banner-bottom, .homeAd1, .ads__hyperleaderboard--hyperlea=
derboard, .homeAd2, #news_article_ad_mrec_right, .ggl_ads_row, .AdSense_Hea=
der, .adsense_results, object[height=3D"380"][width=3D"190"], .ad-grid-cont=
ainer, div[id^=3D"ads120_600-widget"], #advert_container, #AD_rr_a, .ban728=
, .ad-link-left, #adSlider, .barstool_ad_floater, .topHeaderLeaderADWrap, .=
adsense-top-bar, .advert--mpu--rhs, #ad-f-container, #module-ad-300x250, .s=
ponsored_text, a[href^=3D"http://keep2share.cc/pr/"], object[width=3D"572"]=
[height=3D"106"], #analytics_banner, #yahoo_sponsor_links_title, .homeMainA=
d, .advert-under-hedaer, .srp-grid-speed-ad3, .left-advert, .ng-ad-banner, =
#top_ad_container, .ad-below, .adv-leaderboard, .ad--300x250, .ad_space_rgt=
, #banner-skyscraper, .credited_ad, #adsense_block_350x320, #googlesponsor,=
 .popunder-adv, #AdControl_TowerAd, .googleProfileAd, .HomepageAdsPocket, #=
sideadvert, #keyadvertcontainer, .blog_ad_continue, a[href^=3D"https://evap=
orate.pw/"], .ob_container .item-container-obpd, #gamepage_ad, #adcontainer=
125px, #mrt-node-Col2-1-ComboAd, #bigbox-ad, .rectangle-ad, .rr_skyad, .adB=
orders, .ajdg_bnnrwidgets, #advCarrousel, #adsbysourcewidget-2, #advertisin=
g_holder, #super_ad, .adsShield, .boxAds, .video_ad, .ad_250x200, #skyWrapp=
erAds, .home_offer_adv, .ad-before-header, #ad2-home, #container-ad-content=
-rectangle, .af-block-ad-wrapper, .js-ad-konvento, .tucadtext, #horadslot, =
#adv-title, #ypaAdWrapper-TopAds, #left-ad-skin, .advertiser-links, .yl-lre=
c-wrap, .biz-list-ad, .fnadvert, #advMegaBanner, .fp-right-ad-zone, .redads=
_cont, #header_right_ad, .affiliate_header_ads_container, #ads2_container, =
#adv-box, #ad_bigbox_companion, #adv-google, .player-leaderboard-ad-wrapper=
, .AdZone316, .OcelotAdModule, .footer-ad-section, .iAdserver, .ads_post, .=
adsensemainpage, .linelist-item-ad, #sgAdScGp160x600, .bpcads-bottom-footer=
, #gmi-ResourcePageLowerAd, #adPlaceScripttopBanner, #adv_300_600, #adverti=
sement-728x90, #ad_strip, #adv_videobox, .adsense-ads, #lowerAdvertisementI=
mg, .col-line-ad, #wibiyaAdRotation, .ad-forum, .adMediumRectangle, .ads-to=
p-left, .modulegad, .ad_250x250, .adHed, .ad-size-300x250, #ad_300, #tippyt=
op-ad, .ad_300x240, #northbanner-advert-container, #c_wdt_ads_2, .bb-adv-30=
0x250, .aisoad, #games-mpu-container, #sponsor-sidebar-container, .ad_fille=
r, #adhome, #wrapperAdsTopRight, .news_imgad, .adsleftblock, .wantads, .ad-=
336x280B, #ad-leaderboard-spot, .midarticlead, #container-ad-topright, #ban=
ner_adv, #right-uppder-adverts, #banner_ads, .grev-ad, .eu-miniadvertisment=
, .top-large-google-ad, .right-ad2, #Top468x60AD, .advert-728-90, .as_socia=
l_footer, #dfp-ad-mediumrectangle-wrapper, .csm-strategy-id-ad-placements-d=
ynamic-1, #ad_336, .ad-takeover-homepage, #ads-right-twobottom, .ads_ad_box=
2, #mpu300250, .cross_delete_ads, .ad_special_badge, .otherheader_ad, .head=
erAdWrapper, a[href*=3D"ad2upapp.com/"], #adv_middle_2, .alignads, .wpcnt >=
 .wpa, a[href^=3D"http://dftrck.com/"], #adBannerWrap, .bottomad, #dfp-srp-=
leaderboard, #adunit_article_center_bottom_computer, #adv_center, #national=
_microlink_ads, #branding_ad_comment, .AdsenseDownload, #ad-right-container=
, .mod_ad_top, #rightrail_pos2_ddb_0, .ads-left-side, .right-ads, .right-ad=
v { display: none !important; }

a[href*=3D".smartadserver.com"], #adbannerdiv, .ad-feature-text, .adsensele=
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e_adsense, #adText_container, .beauty_ads, .more-content-and-ads, .hortad, =
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aceholder, #js-wide-ad, #mast_logo_advertisement, .col-ad, .adchoices-link,=
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eader-ads-wrap, #ad-middlethree, a[href^=3D"http://www.linkbucks.com/referr=
al/"], #adzone_content, #wallAd, #stickySkyAd, .WideAdContainer, .div_adv62=
0, #block-dart-dart-tag-ad_top_728x90, .SidebarAdvert, .sponsoredlinkHed, #=
OAS_posRight, .ad_bottomline, #mpuWrapper600, .ads_container_top, .spot-ad,=
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0, .ds-ad-container-ros, #ami_ad_cntnr, .adformobile, .admpu-small, .inline=
Advertisement, #SideBarAdWidget, .box-adv-300-home, .sidebar_ad_580, a[href=
^=3D"http://fusionads.net"], .leftbottomads, #adBlockContent, .leaderboard-=
ad-container, .ads_720x90, .ad-bottom728x90, .ADouter_div, #ap_adtext, #ads=
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rs-article, .GoogleDfpAd, .adsghori, .bannerRightAd, .longAdBox, #medrec_mi=
ddle_ad, #topadbar, .ad-reader, #dfp-tlb, .ads-560-65, #__nq__hh[style=3D"d=
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dth=3D"310"][height=3D"70"], .RightAdvertisement, .hpPublicidadTop, .ads_ri=
ght, .sidebar-text-ad, #ads_absolute_right, .adsinfo, .AdFrameLB, #ad-safe,=
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rginalContentAdvertAddition { display: none !important; }

#ad-2-160x600, .naMediaAd, .advert-title, #squareAds, #top_adsense_cont, .A=
dsLeft_list, .features-advetorial-wrapper, .advertisingLabel, #google_ad_co=
ntainer_right_side_bar, .sponsoredEntry, #adxLeaderboard, #ad-page-sky-300-=
a1, #ad-page-sky-300-a2, .stock-ticker-ad-tag, [onclick*=3D"content.ad/"], =
#adPartnerLinks, .adslisting, .main_wrapper_upper_ad_area, #AdServer, #news=
_right_ad, .block-dfp-ad, .content_ads_index, .cosmo-ads, #SlideShow_adv, .=
wp125ad_1, .wp125ad_2, .admsg__mrec, #pop_ad, .cpmstarHeadline, #buy-sell-a=
ds, .article-footer-ad-container, a[data-redirect^=3D"http://paid.outbrain.=
com/network/redir?"], .region-regions-ad-top-inner, .adv_headerleft, .inhou=
sead, #squareadvert, .footerTextAd, .ad-footer-empty, .zergnetBLock, .stick=
y_ad_wrapper, #adv_01, #inner-deals-ads, #adv_02, .pb-f-ads-ad, #dnn_google=
Adsense_a, .myimg-advert, .adunit-300-250, #gpt-adsene-article-bottom, .c-a=
dunit, .js-ad-static, .ads_container, .ad-script-processed, .videos-ad, #bu=
s-center-ad, .ad-message, .collapse-ad-mob-wrapper, #adv_11, ._bannerAds, #=
footer-advert-area, .advert-728x90, #adTextCustom, .adObj, #ad_banner_728x9=
0, #mainAd1, .ad_box1, .ad_box2, .adv-container, a[href^=3D"http://fileupno=
w.rocks/"], #ads_120x60_block, #ra-taboola-bottom, .sponsored-article-item,=
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ar__ad-label, .MPUTitleWrapperClass, .link_ad, .story-header-ad, #ctl00_ctr=
lAdvert8_iframeAdvert, .adtoggle, a[href^=3D"http://findersocket.com/"], .h=
eaderAdArea, .adsOverPrimary, .shift-ad, #ad-story-right, .ad_300Home, .art=
icle-first-ad, .ad-widget, .side-rail-ad-wrap, #ad_bottom_another, a[href^=
=3D"http://www.brightwheel.info/"], .page-footer-ad, #adv_52, .medium_recta=
ngle_ad_container, #under_content_ad, .widgetAD, .js-dfpAdPosSR, #adv_conte=
nts_tem, .banner1-728x90, #adv_62, #AdvContainerMidCenter, .ib-adv, #adv_65=
, #advertSeparator, .outside_ad, #boxAdContainer, .text-g-sponsored-ads, #a=
dv_70, #ad_medium_rectangular, #adv_73, #adv_71, .js-advert-upsell-popup, .=
col-has-ad, .listings_ad, .adv-inset, #adcontainer2, #adcontainer3, #cnnRR3=
36ad, #adcontainer5, #adid2161, .rtd_ads_text, .SBARightBottom, .hover_300a=
d, #redirect_ad_2_div, .pan-ad-inline1, .pan-ad-inline2, .pan-ad-inline3, .=
double-ad, #midcolumn_ad, .advslideshow, #adv_94, #adv_96, #adv_97, #adv_98=
, .ad_break, .after_post_ad, #banner-ad-container, .leftadd, .sidebar-spons=
ors, a[href^=3D"https://gghf.mobi/"], #dfp-ad-homepage_728x90-wrapper, .blo=
ck_ad_sb_text, embed[width=3D"960"][height=3D"120"], .ad250_250, .ad_space_=
730, .ads_large_ads, #video_reklamy, .adsZoneBlock2, .full_width_ad, .takeO=
verAdLink, .adBlockBottom, #right-advert, .advertising_hibu_lef, .ad300_250=
, .ad-header-pencil, .floatad, a[href^=3D"http://igromir.info/"], a[href^=
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lightAd, .d499d-ads-635x100, .splitter_ad, #sponsoredads, .smallAdvertismen=
ts, .wnIframeAd, .e-advertise, #adsCombo02_2, #adsCombo02_3, #adsCombo02_1,=
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ContainerRectangle, #zag_square_ad, .adOne, .square-advt, #Ad300x600_0_adch=
oice, .leader-ad-728, .widget_advwidget, .Ad_E_Wrapper, .sponsor-text-conta=
iner, .adsLibrary, .wx-adchoices, #topAdWrapper, #publicidadeLREC, .ads-rai=
l, #sticky_adv_container, .ads_frame_wrapper, .widget-advert-728, .ad_horiz=
ontal_marker, .sideads, #bottom_ad_right, .ads_loc_side, .topadrow, .AdModu=
le_Content, .advertThInnBg, .shadvertisment, .ra[width=3D"30%"][align=3D"ri=
ght"] + table[width=3D"70%"][cellpadding=3D"0"], #SE20-ad-container, .block=
_ad_sb_text2, .wahAd, #universalAdContainer, .PERFORMANCE_AD_COMPLETE, #adv=
ertisements_bottom, .sponsored-ad-ob, .ad-300x250-home, .cgs-ad-spot, .play=
Ads1, .playAds2, #adMoveHere, a[href^=3D"http://www.faceporn.net/free?"], .=
vw-header-ads-wrapper, #top_ad_widget_area, #noresultsads, #adsensetopplay,=
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, #fulldown_ads_box, .advertContent, .adv-center, #Adtag300x250Bottom, #pho=
toAdvert, .ad-frame, #adbdiv, .topAdBanner, .section_adarea, #lpAdPanel, #a=
d-right-3, #AdcBB_AdContainer, .adArticleTopText, #horizontalAdvertisement,=
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s-bing-bottom, #article_left_ad01, .AdContainerBottom, a[href^=3D"http://1p=
hads.com/"] { display: none !important; }

.ad-zone-ajax, #adserver_HeaderAd, .__y_outer, #ad-placeholder, .as-admedia=
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Sponsor, .ad768x90, .sType-ad, .ads_300x239, a[href^=3D"http://softexcellen=
ce.com/"], .ad-custom-size, #adsense_item_detail, #lowerAdvertisement, #ad-=
mpu2-spot, #topAdContainer, .mm-ad-sponsored, .top-adsense-banner, .iqadmar=
ker, #rmx-ad-cta-box, #ad_module, .custom-ad-container, .log_ads, .ads_300x=
250, .divider-ad, .advert--mpu, #pswp_advert, .tout-ad-embed, #google_ads_d=
iv_Second_160, .container-adbanner-mobile, #adzone-sidebarSmallPromo1, #adz=
one-sidebarSmallPromo2, #adTableCell, .side_300_ad, #sky-top-ad, #squareAdW=
rap, #dvAd1main, #g_ads_right_top_banner_ads, a[href^=3D"http://www1.clickd=
ownloader.com/"], .adkit-advert, .a-ad, .y7adS, .four-six-eight-ad, .block_=
ads, .l-ad, .mpu-ad-top, a[href^=3D"http://down1oads.com/"], #TopAdDiv, .bl=
ock_adv, #adContentHolder, .cxAdvertisement, #homepageGoogleAds, .adds300x2=
50, .advertorialtitle, #ad_haha_1, #ad_haha_4, .below_player_ad, .adSponsor=
Text, .create_ad, #ScoreboardAd, .adsense-reviews-float, #sidebarTowerAds, =
#widget-adv-12, .adChrome, .double_adsense, #middle_body_advertising, .adve=
rtisementSmall, #adskinright, #ad-region-1, .l-ad-728, .top_ad_336x280, a[h=
ref^=3D"https://secure.bstlnk.com/"], #divBannerTopAds, .widget_adsensem, .=
adserving, div[class^=3D"adpubs-"], .ad_mrect, .darla_ad, .ad_right_col, #t=
op_adblock_fix, .boxsponsor2, .ad-text-blockA01, .lastRowAd, #ad_infoboard_=
box, #menubanner-ad-content, .LazyLoadAd, .postgroup-ads, .Left_Content_Goo=
gle_Ad, .macAd, .advertisement_above_footer, .banner_altervista_300X250, .a=
dBoxHeader, #ad-placard, #adblocktop, #advRectangle1, #sidebar_ads_180, .go=
ogle-ad-content, #downloadAd, #div_side_big_ad, .reklame-right-col, #buysel=
lads, #dAdverts, .tallad, .Ads-slot, #view_ads_bottom_bg, #advertising-bann=
er, .oi-add-block, .right_ad_innercont, object[width=3D"200"][height=3D"150=
"], .adCaptionText, #SIM_ad_728x90_bottom, .MBoxAdRight, #ad-presenter-desk=
top, #sponsored_links, .ad-google, .ajax_ad, .serp_sponsored, .adHplacehold=
er, #ap_adframe, .breakerAd, a[href^=3D"http://record.betsafe.com/"], .adst=
ory, #adspot-149x170, .adColumn, .advertise_sec, .ad--bottom, .adColBgBotto=
m, .rightColumnAd, #ad-popup, #bcaster-ad, .adsd_shift100, #bottomsponad, .=
eb_ad280, #div-ad-r1, #div-ad-coupon_2, #div-ad-coupon_3, #div-ad-coupon_5,=
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p-widget-ad, #div-ad-coupon_1, .topcontentadvertisement, #div-ad-coupon_8, =
#bpcads-top-leaderboard, #md-sidebar-video-companion-ad-loaded, .widget_goo=
gleads, .pane-advertorials-homepage-advertorial-rotator, .rightBoxMidAds, #=
video_ads_overdiv, .ad728x90box, #banner_280_240, .m-dfp-ad-text, #google_a=
d, #widget_advertisement, .header-advertisement, .arcAdsContainer, .mod_r_a=
d1, #advertisement_label, .region-header-ad, .adspace180, #ad-728x90-1, .sp=
onsored-default, #GOOGLEADS_CENTER, #ad_large_rectangular, .ad_section_300x=
250, object[width=3D"200"][height=3D"400"], .ad-bordered, .ad250c, #content=
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bg-custom-ad, #print_ads, #mn #center_col > div > h2.spon:first-child + ol:=
last-child, #adblocktwo, .inline-ad, .rad_container, #adslot300x250ATF, .ad=
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"240"][height=3D"250"], .ad_center, .adstextpad, #adsmegabanner, #content_r=
ight_ad, .firstadsmobile, .billboard_ad, .postads3, .ad_spot_b, .ad_spot_c,=
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#wf_FrontSingleAd, .SecondaryAd, .c300x250-advert, .div_banner468, .r_ad_1,=
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advertising_hibu_mid, .lbadtxt, #more_ad, #AdsRight, #dnn_ctl00_Ad2Pane, #a=
d_120x90, .tl-ad-render, #dfp-global_top, body > #overover[style=3D"positio=
n:fixed;width:100%;height:100%;background:silver;z-index: 2;opacity: 0.1;"]=
, #ad-billboard-bottom, a[href^=3D"https://www.goldenfrog.com/vyprvpn?offer=
_id=3D"][href*=3D"&aff_id=3D"], #movieads, .full_AD, .nSponsoredLcContent, =
#adLeft, .buzz_ad_block, .sponsorsbanner, #mini-panel-two_column_ads, .adsR=
ow, #ad_container_0, #daumAd, #vertAd2, #adsfundo, object[width=3D"880"][he=
ight=3D"80"], #advertsingle, .ads1_250, .c-fragment--container--ad, .post-n=
ativeadcarousel, #inc-ads-bigbox, #BillBoardAdd, #ad_houseslot1_desktop, .g=
AdOne, #ads-block-frame, .branding-ad-wrapper, .adv-phone-hp, #topstuff > #=
tads, #ksperAD, .Banner468X60 { display: none !important; }

#h_ads0, #h_ads1, .bzads-ic-ad-300-250-600, #oas_asponsor, .ad_index02, #st=
atic_textads_1, .doubleGoogleTextAd, #ad_container_side, #bottom_ad_unit, .=
bottomadvert, .ad-728x90, .inlistAd, #adsense-468x60, #premiumsponsorbox, .=
articleFooterAd, .section-front__top-ad, #ContentAdXXL, .sidebar__item-spac=
er--advert-top, #ad_right_main, .sponsored-text-links__ads, #atlasAdDivGame=
, #islandAdPan, .advertising-aside-top, .publicidad_top, #righttop-adverts,=
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20x600-sidebar, #amzn-native-ad-2, #sq_ads, .generic-ad-module, #AD300x250,=
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ad_Middle1, #gAds, .sponsored-ads, .wrb3_x1_adv, .ad-upper_rec, .adBelt, #a=
ds-menu, #event_ads, .section-result[data-result-ad-type], .ad_holder, .adT=
opLink, .nav__adbanner, a[href^=3D"https://spygasm.com/track?"], .adspot200=
x90, #ad_sense, .header_ads_box, a[href^=3D"//5e1fcb75b6d662d.com/"], #adSe=
nseSidebarBottom, .AdContainer-Sidebar, #section-footer-ribbonad, .sponsore=
d-links-right, #bannerAdRight3, #ctl00_ContentRightColumn_RightColumn_Ad2_g=
ooglePublisherAd, .small_ads, .textAdBox, #ad-horizontal-header, #contentad=
-superbanner-1, #contentad-superbanner-2, object[width=3D"720"][height=3D"6=
0"], #rightcolumn_300x250ad, .adplace_center, #right_block_ads, .four_perce=
nt_ad, #textlink_ads_placeholder, .highlightsAd, .adkingprobanner, .rtAdFtr=
, a[href^=3D"http://www.my-dirty-hobby.com/?sub=3D"], .top_sponsor, #ads > =
.dose > .dosesingle, #adv_id, #rt-ad, .adFooterLinks, #headeradcontainer, #=
menuAds, #AdAreaH, .adsense728, .aftContentAdRight, #branding_click, .BoxSp=
onsorBottom, .mgid-wrapper, #td-applet-ads_2_container, #rubicsTextAd, #hea=
dlinesAdBlock, .ad--container, #sidebar_txt_ad_links, .fortune-ad-unit, .co=
ntent-ad-side, .gAdThreeMobile, #header-leader-ad, .r_ad_box, #contextual-a=
ds-block, #homePageBotAd, .tower-ad-wrapper, .plista_widget_retrescoAd_1, .=
goglad, .plista_widget_retrescoAd_2, .advert-banner-holder, #ad-unit-search=
-right-top, .home-sponsored-links, .contains-ad, .ad_center_bottom, .ox-hol=
der, .recent-post-widget-ad, .header-bannerad, .pop-up-ad, #dvCenterAd, .su=
bjects_ad, .cpaAdPosition, .js_contained-ad-container, #tvplayer_main_adwra=
p, div[id^=3D"block-views-topheader-ad-block-"], .header-google-adsense970,=
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.features-advertorial-wrapper, #dartad11, #dartad13, #dartad16, #dartad17, =
#ad_plugs, #dartad19, #adposition, #advert_image1_0, .ads__sidebar--sidebar=
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01, .openx_10, .openx_11, #pushAd, .openx_15, .openx_16, .openx_17, .sgAd, =
.advertising728, #dartad25, .adinsert, #adsense_article_bottom, #dartad28, =
.ad_jnaught, #ctl00_divAdSuper, .poac_ads_text, #adspot-bottom, .block_ad_m=
iddle, .post__ad, #home_ad_sub_spotlight, .sadvert, #hly_ad_side_bar_tower_=
left, .adsoptimal-slot, #headeradvertholder, #mid_ad_title, .topfootad, .fl=
oatads, #foot-ad-1, #bottom-adspot, .macad, a[href^=3D"http://lp.ezdownload=
pro.info/"], #secondBoxAdContainer, .gAdsContainer, a[href^=3D"http://at.at=
wola.com/"], .ad343x290, #nrcAd_Top, #SideMpuAdBar, .ad-box-up, .advertisem=
ent-BottomRight, #ad_middle_bottom, #scroll-ad, .framead, .eu-advertisment1=
, .eu-advertisment2, #nav_ad_728_mid, #block-views-ads-header-top-block-blo=
ck, .topadvertisementsegment, .quigoAdCenter, #advert_561_01, #advert_561_0=
2, #advert_561_03, #advert_561_05, #advert_561_07, .js-ad-unit-bottom, .spo=
nsoredItem, .background-adv, .linkads, .adfeedback, .ads-box-border, #dfp-m=
iddle1, .ad-bline, #box-ad-section, .ad-block-300-widget, .outstream-ad-out=
er-wrapper, #sgAdHeader, #advert_back_300x250_1, #advert_back_300x250_2, .s=
ubmenu_ad, #Content_CA_AD_0_BC, #top-ads, #advert_banner, .AmazonSimpleAdmi=
n_widget, .js-react-simple-ad, .ad--inner, #floatingAds, .ads-square, .widg=
et-adcode, .stripper > a[href*=3D"istripper"] > img, #wp_ads_gpt_widget-4, =
#mrt-node-Col2-1-AdBlockPromo, #wp_ads_gpt_widget-5, .text-ad-links2, #prof=
ileAdHeader, .desktop-aside-ad, .sponsored-products-container, #ad160a, .ad=
-block-bottom, #ads_catDiv, .insideStoryAd, #rockmelt-ad-top, #adshowtop, .=
related-ad, #ads_banner_right1, .home-ad-section, #common_right_player_ad_w=
rapper, .adarticle, .ad-panel__container--styled, .ad-below-images, #google=
ad-sidebar-top, #side_adverts, #dfp-ad-mosad_1, .adblock_primary, .Ad728x90=
, #bottom_player_adv, a[href*=3D".adk2x.com/"], #adslot300x250BTF, .ad-inco=
ntent-ad-plus-middle, .mediaAd, #secondBoxAd { display: none !important; }

.widget_sidebarad_300x250, .gAds, .custom_ad, .featuredadvertising, .ad-wit=
h-us, #brand-box-ad, .fireplaceadtop, object[width=3D"1000"][height=3D"90"]=
, .gpAdBox, .adlnklst, #contentBottomAdLeaderboard, #adbar_ad_4_div, #midad=
vert, .econo-ads1, .SkyScraperAd, .ad_inset, #top-search-ad-wrapper, .Ad-MP=
U, .outermainadtd1, #adsponsored_links_box, #slider_ad, .ad-size-iab-uap-le=
aderboard-728x90, .googleAdsense, .adsense-slot, #adv-right1, .google-ads-r=
ight, .future_dfp-inline_ad, .PencilAd, .adv_medium_rectangle, .adunit-pare=
nt, .blacboard-ads-container, .GAME_Ad160x600, .layer-ad-bottom, #some-more=
-ads, .ad_mrec, .advertisement_flag_sky, .video-ads-wrapper, .AdBorder, .ad=
rectangle, .g-adver, #adtech_728or920_2, .moduleAdvert, #topheader_ads, .hd=
r-ad-text, .full_ad, #adcontrolisland, .otj_adspot, .ads-widget, .home-side=
bar-ad, #mediumAd1, .adsense-module, .thumbs-adv-holder, .tvkidsArticlesBot=
tomAd, #taboola-ad, .ibm_ad_text, #ad-top-right-container, .widget-advert-9=
70, #ir-sidebar-ad, .textAd3, .advertisement-cell, .adspot_728x90, .ad-no-s=
tyle, #zone_c_ads, #adbForum, .publicidadSuperior, .ad_88x31, .adver-text, =
#homeAdLeft, a[href^=3D"https://www.mypornstarcams.com/landing/click/"], .a=
dg-rects, .specials_ads, #onpageads, .ad-diver, .adv_336_280, div[class^=3D=
"ad_position_"], .media-advert, .AdMod, .textAds, .liveads, #header_ad_bloc=
k, .advertisement_main_center_bottom_computer, #cltAd, #popupAd, #top_banne=
r_ads, .ad160x600, .mt-ads, #right-ad1, .searchAdTop, .story_ads_right_spl_=
budget, #sponsor_footer, .js-native-ad, .ds-ad-container-300, #ad_content_t=
op, a[href^=3D"http://abc2.mobile-10.com/"], #column2-145x145-ad, .topadtxt=
, .ad--leaderboard, #microAdDiv, #mordern_adbar_wrap, #header-ad-right, .ad=
-place-holder, .houseAdsStyle, .testAd-holder, #right-ads, .mobileAdWrap, .=
ads300_250, .addarea, object[width=3D"440"][height=3D"100"], #square-sponso=
rs, #frmRightnavAd, .cnIframeAdvertisements, .carbon_ads, .moduletableadver=
t, #pushdown-ad, .pfimgAds, .ad-side, .ad300x250box, .homePageAds, #ad-sla-=
sidebar300x250, .pl_adv1_wr2, #IC2-ad, .ads-right-min, #content_16_pnlAdSlo=
t, #mos-adCarouselContainer, .index_right_ad, .homepage_ads_topspot, #annoy=
ing_ad, .specialAdsContent, #dart_300x250, .ad-flex-center, .advertise_txt,=
 .adlinks-class, #dfp-ad-stamp_3-wrapper, .adsDisclaimer, #googleAdsSml, .a=
d125x125, .ad_report_btn, #BannerAds, #bannerAdvert, a[href^=3D"http://ad.y=
ieldmanager.com/"], .mid-post-ad, .header-menu-horizontal-ads-content, .fg_=
Ad, .ad-w300, .lads[width=3D"100%"][style=3D"background:#FFF8DD"], #advert_=
right1, #netBoard-ad, .adsense-links2, #dfp-ad-content_2-wrapper, #ofie_ad,=
 #Module-From_Advertisers, #sphereAd, .ad-300-250, .advertisement-placehold=
er, .gAdOneMobile, .ad_launchpad, .m-ad-tvguide-box, .adflexi, #HomeBannerA=
d, .ad-width-728, .oas-ad, #SIM_ad_300x250_pos2, #isliveContainer, .SBAMR, =
.ads__leaderboard--header, #ad-leaderboard-1-container, .mapped-ad, #bbccom=
_mpu, .threadAdsHeadlineData, .google-ads-responsive, .dw-sticky-ad-left, .=
site-head-ads, .m-in-content-ad-row--bonus, .widget-pane-section-ad-content=
, #adsd_contentad_r1, #bannerfloat22, #adsd_contentad_r2, #advert_image2_0,=
 #adsd_contentad_r3, .ads--single, .advertise-box, .adsTag, .block-ads-epla=
nning, a[href^=3D"http://www.sex.com/?utm_"], .advert-mini, a[href^=3D"http=
://www.duckcash.eu/"], #innovativeadspan, #ad_tall, .Ad300x250_top, .bb-ad-=
mrec, #gallery-ad-m0, #adskyrightdiv, .widget_adwidget, #left_ad, .Ad_120x6=
00, .sics-component__ad-space, #righttop-adverts-container, #containerMrecA=
d, .rgt-300x250-ad, .adboxTopBanner, .left_ads, .left_adv, #dfp-ad-tower_1,=
 #dfp-ad-tower_2, a[href^=3D"https://go.stripchat.com/"][href*=3D"&campaign=
Id=3D"], .topAdverts, .box-entry-detail--ad, .adBgBottom, #nrAds, .fixed-ad=
-bottom, #docmainad, .bannerAdWrapper300x250, .adspeed, #TopAdTable, .go-ad=
s-widget-ads-wrap, .google-ad-afc-header, #MyAdHeader, #ad_netpromo, #lapho=
-top-ad-1, .bottomgooglead, .banner-paid-ad-label, .adspace-300x600, #webli=
nk_ads_container, #dfp_ad_Thesaurus_728x90, #ad330x240, .ad_bank_wrapper, .=
banners-middle, #adscontainer_banner_new_second_index_1060, #divTopAds, #ad=
spot_300x250, .nw-taboola, #ad_slot_leaderboard, #panoAdBlock, .oasInAds, .=
banner_300_250, #homepage-ad, .ad_viewtop, #btr_horiz_ad, .advert--banner-w=
rap, #tvd-ad-top, .SBAUA, #video-side-adv, .full_ad_box, .pageGoogleAd, #ad=
-teaser, a[href^=3D"http://www.ducksnetwork.com/"], #four_ads, .box-adsense=
, #right_top_gad, .rectAd300 { display: none !important; }

.searchSponsoredResultsList, #turnAD, .GoogleAdWords_container, .ad_column,=
 #b-adw, #side_ad, .td-zergnet, .adSKY, .ajaxads, #feature_adlinks, .advert=
ize_here, #ad-mid, #ad_DisplayAd1, #ad_DisplayAd2, .wall_ad, #googlead1, #a=
ds-300-250, #googlead2, #banneradspace, .footer-advert, #motionAd, #ad_midd=
le_122, #takeoverad, #videopageadblock, .leader-ad, .footerFullAd, .loop_go=
ogle_ad, .ad-space-topbanner, .ad160x600GrayBorder, a[href^=3D"http://landi=
ngpagegenius.com/"], #googleads, .ch_advertisement, .banner300by250, .banne=
rAd_rdr, #header-ad-block, #ad-banner-body-top, .googleAd_728x90, #ads728, =
.RBboxAd, .commercial-unit-mobile-top .jackpot-main-content-container > .Up=
gKEd + .nZZLFc > .vci, #affiliate_ad, .adlabel-vert, #ads-sidebar, .section=
_mpu_wrapper, #ad1-home, .ContentAd2, #side_ad_module, #flash_ads_1, #AdSen=
seMiddleAds, #player-below-advert, .adtextright, #after-header-ads, #ad-sid=
ebar-tall, .joead728, #ad-news-sidebar-300x250-placeholder, .ad_250x250_w, =
#gold_sponsors_sidebar, object[width=3D"150"][height=3D"150"], .ad_section_=
728x90, .ContentAds, #ctl00_LHTowerAd, .tab_ad_area, .sidebar-350ad, #ad_cr=
own_top, #main_left_side_ads, #home-left-ad, .left_adsense, #adtags_left, .=
adv-carousel, #ad-mpu, a[href^=3D"https://track.clickmoi.xyz/"], #article-b=
illboard-ad-1, #moreads, .biz-adtext, .go-ad, .adbladeimg, #site-leaderboar=
d-ads, .ads468x60, .ggl_txt_ads, a[href^=3D"http://www.streamate.com/export=
s/"], .tadsanzeige, #ab_adblock, #li-right-geobooster-oas, .my-ad250x300, .=
ads_topic_after, #relocation_ad_container, .ad_sense_01, .as_ad, .sponsored=
-b, .ads-google, #advgoogle, .ad--object, .adveratising, #vdls-adv, #ads790=
, .openx_ad, .top-ad-slot, #adv_sponsorRowFooter, .TOP-ADS, #ad_overlay_con=
tent, #rightrail_bottom_ddb_0, .portal_searchresultssponsoredlist, .side-ad=
vert, .right-rail-ad, .ad-box-caption, #hl-ad-LDRB2-1, .lgRecAd, a[href^=3D=
"https://www.arthrozene.com/"][href*=3D"?tid=3D"], .taboola_lhs, #catad, .a=
rchive-ads, .incontent_ads, #advertCover, #ad_promotion_wrap, .block-ad300,=
 .dm-ads-125, #googleadsrc, #ads_halfsize, .ad-primary, #right_column_ad_co=
ntainer, .right_ad_common_block, #home-side-ad, #ros_ad, #googleShoppingAds=
Right, .ad-leaderheader, #rectangle_ad_smallgame, a[href^=3D"http://farm.pl=
ista.com/pets"], .ad_gutter_top, .advertisement-layout, .thb_ad_before_head=
er, #ad_300misc, .ad_box_right_120, #dd-ad-head-wrapper, .banner-adverts, .=
sidebar__ad, #sidebarAdSense, .module-zerg, #ad_megabanner, #ad-300-sidebar=
, .square_ads, #adserve-Sky, .adsTopBanner, .leftadtag, #box-ad, #oas_wide_=
skyscraper, .adsTxt, .google-ad-pad, #homepage-adbar, #ADSLOT_SKYSCRAPER, a=
[href^=3D"http://imads.integral-marketing.com/"], .ad-slot-1, .ad-size-medi=
um-rectangle-flex, .kl-ad, .ad-slot-2, .kwd_bloack, .ad_btf_300x250, .ads-o=
uter, .big_ad, .ads_center, #site_bottom_ad_div, .adinjwidget, .spl_ad_plus=
, #banner728x90, #gpt2_ads_widget-10, .ad-unit-wrapper, .rhc-ad-bottom, #Ad=
sContent_SearchShortRecB_UPSSR, #major_ad, .ad-slot-a, .video-ad-content, .=
ad-container-embedded, #uploadMrecAd, a[href^=3D"http://ads.expekt.com/affi=
liates/"], .bonnier-ads, .advert_mpu_body_hdr, #wallpaperAd_right2_1, #Game=
MediumRectangleAD, #adBlockOverlay, .adstrip, #adv-fb-container, .clearerad=
, .webit-ads, .hioxInternalAd, #AdvertisingLeaderboard, .header-taxonomy-im=
age-sponsor, #ob_sponsoredcontent, #adu-sto, #publicidad_button_home, .cont=
ainerAdsense, .AdContainerModule, .mp-ad, .nativeadasideplaceholder, .dvad3=
mov, #content_box_300body_sponsoredoffers, #ad-leader, .adTopBanner_nomobil=
e, .i360ad, #LeftAdF1, #LeftAdF2, .adbckgrnd, .b-adv-mobi, .ad_980x260, .ad=
s__sidebar--sidebar_fourth, .responsiveAdHiding, .adsTopCont, .adspace_2, .=
gt_ad, .ad728x90WithLabel, a[href^=3D"http://ddownload39.club/"], .aarpe-fi=
xed-ad, .rt-ad-leaderboard, .GetRightAds, .ads-728x90, #some-ads-holder, #a=
dv728x90, #txtads, .advertisement-tag, .ad-marketplace-horizontal, .hdr-ads=
, #advert_image3_0, div[id^=3D"tms-ad-dfp-"], .module_single_ads, #submenu-=
ads, .adv_blocker, .adpacks_content, .button-ads, #rightrail-ad, .zRightAdN=
ote, .AdModule_Hdr, #me-adspace-002, .panel-ad-mr, #adtech_leaderboard01, a=
[href^=3D"http://clickandjoinyourgirl.com/"], #ad-unit-search-right-bottom,=
 .side_add_wrap, #footer-im-ad, .ad-no-notice, #AdvertsBottomR, #tgt1-Botto=
m-0-AdBlockPromo-Proxy, #transparentad, #wide_adv, .waterfall-ad-anchor, .g=
ame-ads, a[href*=3D".irtyc.com/"], .ad-in-results, #pageRightAd, .contentTo=
pAd, .marketplace-ad, #adSpot-island, .adResults { display: none !important=
; }

div[class*=3D"_AdInArticle_"], .adPlaceholder_foot, #below_comments_ad_hold=
er, .calendarAd, .adVplaceholder, #adSidebarSq, .ads-stripe, .adssquare2, .=
homepage__ad--middle-leader-board, .ad-container-responsive, a[href^=3D"htt=
ps://ad.atdmt.com/"], #ctl00_AdWords, .post_ads, .ctpl-duplicated-ad, #ad72=
0x90bot, .ads_holder, .qm-ad, .adsense-resposivo-meio, object[width=3D"800"=
][height=3D"128"], .selection-grid-advert, .ad320x250, #pageOwnershipAd_sid=
e, #ad-circfooter, #BannerBox, #ad-new, #bbccom_sponsor_section, .footer-ad=
sense, .custom-ad-one, .top-wide-ad-container, a[href^=3D"https://horny-pus=
sies.com/tds"], #ad-wrap, #header-google, .ads_inside2, .googlead_iframe, .=
absoluteAd_wss, #footer_adspace, #ad-728-90, .sponsoredAd, .cnbcRailAd, .mv=
p-ad-label, #gtm_dfp_leaderboard_top, .container--bannerAd, .proper-ad-unit=
, #divFooterAds, #rightinfoad, .proof_ad, #title-wide-sponsored-by, .block-=
fcc-advertising, .gutter-ad-wrapper, .homepage_ads_secondrow, .ph-ad-medium=
rectangle, .right_picAd, #top-ad-wrapper, #leaderboard-ad-5_iframe, .navi_a=
d300, #ad-lrec, #homepageFooterAd, #y708-ad-partners, .adheader100, .uniAds=
, .adSky, #adMPUHolder, #rightMortgageAd, .pgevoke-fp-bodyad2, #adDivmrec, =
#section-ad-4-160, .ad-statement, #ad_body, #LowerContentAd, #advertismentE=
lementInUniversalbox, #ctl00_ContentPlaceHolder1_ctl00_ContentPlaceHolder1_=
pnlGoogleAdsPanel, #post-content-ad, .undertimyads, .advert_img, .ts-ad, .m=
ember_ad_banner, #rotate_textads_1, .sponsored-title, .ad--panorama, .spons=
ored-links-col, .sponsored-chunk, a[href^=3D"http://reallygoodlink.extremef=
reegames.com/"], .largeUnitAd, #topadblock, #adrectanglea_flex, .ad120x240G=
rayBorder, #td_adunit1_wrapper, .riverAdsLoaded, .advertisement-top, .adver=
tisement_300x250, #ads_header_games, .anchorAd, .abp-homepage-right-ad, .br=
okerad, a[href^=3D"http://45eijvhgj2.com/"], .isocket_ad_row, .wpproadgrid,=
 .Webnegar_Ad_Box, #embedAD, #AdSlot_AF-Right-Multi, #mpu_firstpost, .adTil=
eWrap, .hp-inline-ss-service-ad, .d499d-ads-160x90-left, #ctl00_ContentPlac=
eHolder1_ucAdHomeRightFO_divAdvertisement, .ad960x90, .gridstream_ad, .ad--=
fallback, .ad-246x90, .ds-ad-300, .adv_title, #adposition-REM2, .ad__in-loo=
p--desktop, #main_page_970x250_1_ad, .bottom-leaderboard-adslot, .sweet-dea=
ls-ad, .nw-ad-label, .right-ad-container, .wn-ad, #ads300hp, .wis_adControl=
, #wsAdWrapper, #barraPublicidade, .display-ads-block, .ads_disclaimer, #ad=
-buttons, .main_right_ad, #advert-text, .slideshow-ad-container, .ad-ticker=
, #navi_banner_ad_780, .bannerAdHHP, .ga-ad-split, #ad-zone-default-sidebar=
, #center_col > #taw > #tvcap > .rscontainer, .double_click_widget, .AD_302=
x252, .lbl-advertising, .sponsors_fieldset, #ad_Home_300x250, #adv-midroll,=
 .widget_sponsored_content, .map_media_banner_ad, .SquareAd, .adSub, .HomeA=
d1Label, .ads_300x600, .advertise-inquiry, #banner_pos4_ddb_0, .company-pag=
e__top-ad-container, .ad-masthead-left, #launchpad-ads-2, #adsBox-460_left,=
 #ad_overlay_countdown, .skyCraper_bannerLong, #dsk-box-ad-d, .Publicidade,=
 .rt_ad, #doubleClickAds3, .lastAdvertorial, .keyword-ads-block, #iq-AdSkin=
, .textAdBG, #int-ad, #interstitial_ad_wrapper, .ad-unit-label, .vce_adsens=
e_wrapper, .global_banner_ad, .verysmallads, #topbar_Adc1_AdContainer, .ajd=
g_grpwidgets, #adBrandDev, #adunit-mpu-atf, .businessads, .calloutAd, a[hre=
f^=3D"http://3wr110.net/"], .hbi-ad-advertiser, .bannerandads, .advertiseme=
nt-250, .sbTopadWrapper, #ad_banner_top, a[href^=3D"http://bc.vc/?r=3D"], .=
lg-ads-311x300-up, object[width=3D"750"][height=3D"100"], #dfp_ad_Entry_Ent=
rySetA_300x250, .ad-boxtop, .adContainerSide, .sideBarCubeAd, .ads_rightbar=
_top, .bannervcms, .adGroup, .hp-ad-grp, #adsense-tag, #y708-advertorial-ma=
rketplace, .advertisement-txt, .ad_placement, #adpanel-block, .ad-cluster, =
.rightAdsFix1, object[width=3D"350"][height=3D"115"], #adhzh, .advBottom, .=
blogAd, .ad-top-wrapper, .entry-ads, #advert2area, #bigAd1, #bigAd2, #ad_fo=
oter, #ip-ad-leaderboard, #adzone-top, .goAdverticum, .pixtrack-adcode, #ad=
vertise2, #advertise1, #divWNAdHeader, .adg_table_cell, #movads10, .staticA=
d, a[href^=3D"https://www.popads.net/users/"], #objadscript, .bgr_adv_div, =
.adword-title, .art_aisde_ads, .mpuAdArea, #wide_ad_unit2, embed[height=3D"=
200"][width=3D"100%"], .adkicker, .sponsored-widget, #add_160x600, .ad_336_=
gr_white, .topAdvertistemt, #box_mod_googleadsense, .adSkyOrMpu, .wh_ad, #d=
fp-ad-mosad_1-wrapper, .SideAd, .view_ads_top_bg_middle, #insurance-ad-1-co=
ntainer, .addResources, .g-advertisement-block, .mobile_ad_container, .ad-f=
ullbanner, a[href^=3D"http://adtrack123.pl/"], .referrerDetailAd, .adTab, #=
LeaderTop-ad, .adTag, .region-widget-ad-top-0, .SponsoredLinks { display: n=
one !important; }

.ads_under_fileinfo, #rightAd1, #tgt1-Col2-1-ComboAd-Proxy, .header-ad-slot=
, .m-ad--open, .pane-adv-manager, .wide_grey_ad_box, #middle_mpu, #ad-label=
, .desktop-ad-banner, .pageFooterAd, .sky-ad, #ads_banner, #google_ad_468x6=
0_contnr, .searchSuperTopAds, .under-player-ads, #ad-other, #content_ad_con=
tainer, .sponsored_result, .ad-lock-content, #A9AdsMiddleBoxTop, #rightAds,=
 #search_ad, .home_sidebar_ads, .ad-divider, #glinkswrapper, .bn_textads, #=
ad-leadertop, .magAd, #adv_LdbMastheadPush, #mochila-column-right-ad-300x25=
0, #publicidade_not, a[href^=3D"http://lp.ncdownloader.com/"], .ad-720-affi=
liate, #widgetwidget_adserve2, .main-advert, #ad_footer1, .ad_176_inner, .o=
b_ads_header, .inlineAdNotice, .bvi-ads, .bannerAd300x250, #namecom_ad_host=
ing_main, .search_results_ad, .playerAdv, .ads160x600, .player-ads, .teaser=
-advertisement, .td-a-rec-id-event_bottom_ad, #leftadg, .ad_eyebrow, .listi=
ngs-bottom-ad-w, #khAdSpace, [onclick^=3D"window.open('http://adultfriendfi=
nder.com/search/"], .plista_inimg_box, .hp_w_ad, #adsense-top, #ads2_box, .=
adbox_bottom, .boxyads, .adv-sidelabel, .rightpanelad, .ad-promotion-native=
, .ad-topbanner, .adspot728x90, #adsensehorizontal, .adsbysinodia, #hp-mpu,=
 .homeAdBoxBetweenBlocks, #right_ad_box, .ad--bottommpu, .footerAdModule, .=
top-ads-wrapper, #ad-interstitialBottom, #rightAd160x600two, .adwordListing=
s, .ads-block-panel-tipo-1, .stpro_ads, #top-dfp, #sidead1, #targeted-ads, =
.adFull, .dac__stream-mpu-card, .breakingNewsModuleSponsor, #ad_content_bef=
ore_first_para, .ads300_250-widget, .video-ad-short, #AD_468x60, .view-id-a=
ds_header_top_block, #horizad, #story_top_ddb_0, .sponsoredby, #TOP_ADROW, =
a[href^=3D"http://www.ireel.com/signup?ref"], .AdsenseBox, .home-area3-adv-=
text, .advertisement-position1, .right_col_ad_300_250, #sideads, #adimg, a[=
href^=3D"https://bongacams2.com/track?"], .adb-728x90, .adrule, .block-ads-=
bottom, .advertembed, .AdLeft1, #twogamesAd, .AdLeft2, .AdBox728, .adv-160,=
 .m-advert, .detail-ad, .sidebar-ad-container-1, .pane-tw-ad-master-ad-300x=
600, #content_7_pnlAdSlot, .adpad300spacer, .sidebar-ad-container-2, embed[=
width=3D"680"][height=3D"130"], .wpfp_custom_ad, .adTop, #ad-yahoo-simple, =
.isad_box, .bg-ad-top, #in-article-ad, .ad_240x400, .gAdSky, .sidebar-ad-co=
ntainer-3, #adszed-728x90, .advert-border, .ad-with-background, #adoverlays=
rc, a[href*=3D"5iclx7wa4q.com"], #ad-one, .ads-box-header-pb, .ads320x100, =
#tnt_ad_column, #AD300x600, a[href^=3D"https://fileboom.me/pr/"], #top-adve=
rt, a[href^=3D"https://mk-cdn.net/"], .gridAd, .ads_content, #adPush, .AD30=
0, .AD_MOVIE_ITEM, .adspace-336x280, .skin_ad_638, .ad-sticky-container, #p=
ost-main-banner-ad, .ad-bottomline, .manual-ad, #SearchAd_PlaceHolder, #rel=
ated_ads_box, a[href^=3D"http://liversely.net/"], #banner_slot, #div-social=
-ads, .RightRailAdtext, .cn_ad_placement, .topicDetailsAdRight, .google-ads=
-leaderboard, .advertisement-300, #ads-sidebar-top, .banner_160x600, .b-ads=
728, #banner-300x250, .articleAd, .adinside, .article-sponsor, .home_box_la=
test_ads, .adZone, #bottom-ad-1, #half-page-ad, #google-ad-tower, #adzone, =
.ads-cars-larger, .arcAdsBox, #mid_roll_ad_holder, #google_ads_test, #ad_re=
ctangular, .round_box_advert, #ad_350_200, #ad_message, .adsenseWrapper, #v=
ideo-adv, .post-advertisement-section, .widget_postmedia_layouts_ad, #ad970=
90, #mainPageAds, a[href^=3D"http://www.plus500.com/?id=3D"], #post_adsense=
, .topAdIn, .ads_column, .banner_altervista_728X90, #md_adLoader, .adTwo, .=
p_topad, .advert-lower-right, .small_ad_bg, a[href^=3D"//srv.buysellads.com=
/"], #advertcalc, #commercial-textlinks, .ads-box-header-ws, #gallery_ad, .=
adsitem, .adTxt, #adLink, .advertorial_728x90, .b_ads, #main-ad728x90, .cop=
y-adChoices, .advert_header, #ad_div_bottom, #ads1_block, .ld-ad-inner, .ad=
vertising728_3, #table_ads, .teaserAd, #reklam_buton, .tl-ad-display-3, .he=
avy_ad, #cnt #center_col > #res > #topstuff > .ts, .full-width-ad-container=
, #advman-2, a[href^=3D"https://www.travelzoo.com/oascampaignclick/"], .bel=
ow_game_ad, .base-ad-mpu, .dm-ads-350, .grid-ad, .ads-125-widget, .jam-ad, =
#leftGoogleAds, .ad-sidebar_right_below, .adpost, #ad_leaderboard728x90, .w=
idget_thesun_dfp_ad_widget, #populate_ad_textupper_textlink, #video-advert,=
 .type_adscontainer, #wallpaperAd_left3, .google-ads-rodape, #ad_mpu2, #rel=
ated_ad, .advert-wrap1, .bigad1, .ads_header_bottom, .sidebar_ads, #imPopup=
, .advert-wrap2, .pane-ad-manager-middle, a[href^=3D"http://trk.mdrtrck.com=
/"] { display: none !important; }

.bigad2, .rect_ad, .adBarCenter, #box_ad_middle, .ad_hover_href, .staticad,=
 #sponsored-recommendations, .td-a-rec-id-custom_ad_1, .td-a-rec-id-custom_=
ad_2, .td-a-rec-id-custom_ad_3, .td-a-rec-id-custom_ad_4, a[href^=3D"http:/=
/www.bluehost.com/track/"] > img, .cLeftTextAdUnit, .td-a-rec-id-custom_ad_=
5, .bigads, #adspdl-container, #googleAd, #advert_lrec_format, .affiliate-s=
trip, .adition_Skyscraper, #ctr_adtech_mpu_bot, .adword-structure, .ad728x9=
0-main_wrap, .lp_az_billboard__via_content_header_ad_, .adBanner300x250, #d=
fp-ad-floating, a[href^=3D"http://media.paddypower.com/redirect.aspx?"], .a=
dvert_google_content, #show_ads, .module-advertisement, .leftAd_top_fmt, .b=
anner--ad, .ad-300x, .box_ad_spacer, .featured-sponsors, .ad_sponsor, .ad72=
8_blk, #newstream_first_ad, .AdvertMidPage, .review_ad1, .four-ads, .teaser=
AdHeadline, .side-ad-top, .cnt-half-page-ads, .superscroll-ad, .third-party=
-ad, .tv-ad-aside, .sportsbet_sbad, #adfooter_728x90, .rbFooterSponsors, .w=
pn_ad_content, #cnnTopAd, .mpu-c, .contest_ad, .google-ad-bottom-outer, .pa=
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dvertisement-swimlane, .adword1, .ext-ad, #adspot300x250, .ad-img300X250, .=
mainadbox, .ml-adverts-sidebar-random, .advert-bronze, .dart_tag, #display_=
ads_footer, #ctl00_Footer1_v5footerad, #adSenseModule, .aboveCommentAdsWrap=
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ad, .ms-ads-link, .gallery-ad-container, #bannerAdTop, .shareToolsItemAd, .=
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@media screen and (min-width: 32.5625em) {
  .form-row::after, .form-row::before { content: " "; display: table; }
  .form-row::after { clear: both; }
  .sf-ccnum, .sf-cvv { display: inline-block; vertical-align: top; }
  .sf-ccnum { margin-right: 1em; }
}

a:link, a:visited { color: rgb(246, 93, 34); text-decoration: none; }

a:link.gray-link:focus, a:link.gray-link:hover, a:link:focus, a:link:hover,=
 a:visited.gray-link:focus, a:visited.gray-link:hover, a:visited:focus, a:v=
isited:hover { color: rgb(246, 93, 34); text-decoration: underline; }

a:link.gray-link, a:visited.gray-link { text-decoration: underline; color: =
rgba(64, 64, 64, 0.75); }

a { transition: color 0.2s ease-out 0s; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .social-sharing=
 a span, .interface-controls a .icon, .interface-controls button .icon, .sb=
o-inpage-toc .annotator-wrapper .annotator-modal-wrapper .social-sharing a =
span, .social-sharing a span, .visuallyhidden { border: 0px; clip: rect(0px=
, 0px, 0px, 0px); width: 1px; height: 1px; margin: -1px; overflow: hidden; =
padding: 0px; position: absolute; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .social-sharing=
 a span.focusable:active, #sbo-rt-content .annotator-wrapper .annotator-mod=
al-wrapper .social-sharing a span.focusable:focus, .interface-controls a .f=
ocusable.icon:active, .interface-controls a .focusable.icon:focus, .interfa=
ce-controls button .focusable.icon:active, .interface-controls button .focu=
sable.icon:focus, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapp=
er .social-sharing a span.focusable:active, .sbo-inpage-toc .annotator-wrap=
per .annotator-modal-wrapper .social-sharing a span.focusable:focus, .socia=
l-sharing a span.focusable:active, .social-sharing a span.focusable:focus, =
.visuallyhidden.focusable:active, .visuallyhidden.focusable:focus { clip: a=
uto; height: auto; margin: 0px; overflow: visible; position: static; width:=
 auto; }

.hidden { display: none; }

form input.error, form textarea.error { border: 1px solid rgb(234, 109, 96)=
; background-color: rgb(250, 224, 222); }

.pod { margin: 0px 0px 1.25rem; padding: 1rem; background-color: rgb(255, 2=
55, 255); font-size: 0.875rem; line-height: 1.1875rem; border-radius: 2px; =
}

.pod header h1 { margin-top: 0px; }

.pod header h1.trial { color: rgb(234, 109, 96); }

.pod h3, h3, h4 { color: rgb(119, 119, 119); }

.pod h2 { font-size: 18px; }

h1, h2 { font-weight: 400; color: rgb(64, 64, 64); }

.display-markdown ol, .display-markdown ul { margin: 0px 0px 0px 30px; }

.display-markdown ol li, .display-markdown ul li { list-style-type: disc; m=
argin: 5px 0px !important; }

.display-markdown ol li { list-style-type: lower-alpha; }

.display-markdown blockquote { border-left: 1px solid rgb(233, 131, 0); pad=
ding-left: 10px; margin: 10px; }

p, ul { padding: 0px; }

h1 { font-size: 1.875rem; line-height: 2.375rem; margin: 1.25rem 0px; }

@media screen and (max-width: 30em) {
  .section-header { margin-left: 15px; }
}

h3, p { font-size: 18px; margin: 1.125rem 0px; }

h2 { font-size: 1.5rem; margin: 1.25rem 0px; }

h3 { font-weight: 400; letter-spacing: 1px; font-size: 1.125rem; }

h4 { font-weight: 400; margin: 1.3125rem 0px; }

p { line-height: 1.4em; font-size: 1.125rem; }

small { font-size: 0.875rem; }

.link-to-markdown { padding: 1px 8px; border-radius: 30px; border: 1px soli=
d rgb(187, 187, 187); float: right; }

.bigbutton, .button, .button-primary, a.bigbutton, a.button, a.button-prima=
ry, button, button.button-primary, input[type=3D"reset"], input[type=3D"sub=
mit"] { display: inline-block; padding: 10px 15px; font-weight: 600; font-s=
ize: 14px; line-height: 1.2em; text-transform: uppercase; letter-spacing: 1=
px; cursor: pointer; text-decoration: none; transition: all 0.15s cubic-bez=
ier(0.86, 0, 0.07, 1) 0s; }

.autocomplete-suggestions b, .button-orm, .gen-nav, .gen-nav a, .mknav li a=
, .tooltip { font-weight: 700; }

.bigbutton.disabled, .bigbutton:disabled, .bigbutton:disabled:focus, .bigbu=
tton:disabled:hover, .button-primary.disabled, .button-primary:disabled, .b=
utton-primary:disabled:focus, .button-primary:disabled:hover, .button.disab=
led, .button:disabled, .button:disabled:focus, .button:disabled:hover, a.bi=
gbutton.disabled, a.bigbutton:disabled, a.bigbutton:disabled:focus, a.bigbu=
tton:disabled:hover, a.button-primary.disabled, a.button-primary:disabled, =
a.button-primary:disabled:focus, a.button-primary:disabled:hover, a.button.=
disabled, a.button:disabled, a.button:disabled:focus, a.button:disabled:hov=
er, button.button-primary.disabled, button.button-primary:disabled, button.=
button-primary:disabled:focus, button.button-primary:disabled:hover, button=
.disabled, button:disabled, button:disabled:focus, button:disabled:hover, i=
nput[type=3D"reset"].disabled, input[type=3D"reset"]:disabled, input[type=
=3D"reset"]:disabled:focus, input[type=3D"reset"]:disabled:hover, input[typ=
e=3D"submit"].disabled, input[type=3D"submit"]:disabled, input[type=3D"subm=
it"]:disabled:focus, input[type=3D"submit"]:disabled:hover { cursor: defaul=
t; color: rgb(204, 204, 204) !important; background-color: rgb(245, 245, 24=
5) !important; border-color: rgb(204, 204, 204) !important; }

.button, a.button, button { color: rgb(64, 64, 64); background: rgb(255, 25=
5, 255); border: 1px solid rgb(119, 119, 119); }

.button.active, .button:focus, .button:hover, a.button.active, a.button:foc=
us, a.button:hover, button.active, button:focus, button:hover { color: rgb(=
246, 93, 34); background: rgb(255, 255, 255); border-color: rgb(246, 93, 34=
); text-decoration: none; }

.button-primary, a.button-primary, button.button-primary, input[type=3D"res=
et"], input[type=3D"submit"] { color: rgb(64, 64, 64); background-color: rg=
b(245, 197, 23); border: 1px solid rgb(245, 197, 23); }

.button-primary:focus, .button-primary:hover, a.button-primary:focus, a.but=
ton-primary:hover, button.button-primary:focus, button.button-primary:hover=
, input[type=3D"reset"]:focus, input[type=3D"reset"]:hover, input[type=3D"s=
ubmit"]:focus, input[type=3D"submit"]:hover { color: rgb(64, 64, 64); backg=
round-color: rgb(232, 186, 22); border-color: rgb(232, 186, 22); text-decor=
ation: none; }

.button-orm { padding: 6px 15px; letter-spacing: 1.4px; font-size: 12px; te=
xt-align: center; border: 1px solid rgb(199, 193, 180); background: rgb(255=
, 255, 255); color: rgb(185, 0, 45) !important; }

html.no-touch .button-orm:hover { text-decoration: none; background: rgb(18=
5, 0, 45); border-color: rgb(185, 0, 45); color: rgb(255, 255, 255) !import=
ant; }

input[type=3D"reset"] { min-width: 0px; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .social-sharing=
 li, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .social-sh=
aring li, .social-sharing li { display: inline-block; margin: 0px; list-sty=
le-type: none; text-align: center; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .social-sharing=
 a, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .social-sha=
ring a, .social-sharing a { display: inline-block; padding: 0px; transition=
: all 0.2s ease-in-out 0s; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .social-sharing=
 a.twitter, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .so=
cial-sharing a.twitter, .social-sharing a.twitter { background: url("/stati=
c/images/tweet_gray.c3649492e6d1.png") center center no-repeat; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .social-sharing=
 a.facebook, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .s=
ocial-sharing a.facebook, .social-sharing a.facebook { background: url("/st=
atic/images/fb_gray.3f725069eb2b.png") center center no-repeat; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .social-sharing=
 a.googleplus, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper =
.social-sharing a.googleplus, .social-sharing a.googleplus { background: ur=
l("/static/images/googleplus_gray.1379fcec2ce7.png") center center no-repea=
t; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .social-sharing=
 a.email, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .soci=
al-sharing a.email, .social-sharing a.email { background: url("/static/imag=
es/email_gray.05464fdf00d2.png") center center no-repeat; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotation-car=
d.social-sharing li, #sbo-rt-content .annotator-wrapper .annotator-modal-wr=
apper .button-group.social-sharing li, .annotation-card.social-sharing li, =
.button-group.social-sharing li, .sbo-inpage-toc .annotator-wrapper .annota=
tor-modal-wrapper .annotation-card.social-sharing li, .sbo-inpage-toc .anno=
tator-wrapper .annotator-modal-wrapper .button-group.social-sharing li { ma=
rgin: 10px 10px 0px; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .button-group.s=
ocial-sharing a.share-button, .button-group.social-sharing a.share-button, =
.sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .button-group.s=
ocial-sharing a.share-button { box-shadow: rgb(230, 230, 230) 0px 0px 0px 1=
px; border-radius: 2px; background-clip: padding-box; background-color: rgb=
(255, 255, 255); max-width: 100%; height: 47px; width: 47px; border-top: 1p=
x solid rgba(255, 255, 255, 0.5) !important; border-bottom: 3px solid rgba(=
0, 0, 0, 0.05) !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .button-group.s=
ocial-sharing a.share-button:focus, #sbo-rt-content .annotator-wrapper .ann=
otator-modal-wrapper .button-group.social-sharing a.share-button:hover, .bu=
tton-group.social-sharing a.share-button:focus, .button-group.social-sharin=
g a.share-button:hover { background-color: rgb(245, 245, 245); }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .dropdown-menu.=
social-sharing, #sbo-rt-content .annotator-wrapper .annotator-modal-wrapper=
 .interface-controls .social-sharing, .dropdown-menu.social-sharing, .inter=
face-controls #sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .=
social-sharing, .interface-controls .sbo-inpage-toc .annotator-wrapper .ann=
otator-modal-wrapper .social-sharing, .interface-controls .social-sharing, =
.sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .dropdown-menu.=
social-sharing, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper=
 .interface-controls .social-sharing { display: block; background-color: rg=
b(51, 51, 51); position: absolute; top: 0px; right: 48px; width: 196px; opa=
city: 0; visibility: hidden; transition: opacity 0.2s ease-in-out 0s; borde=
r-radius: 2px 0px 0px 2px; background-clip: padding-box; border-right: 1px =
solid rgb(119, 119, 119); }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .dropdown-menu.=
social-sharing li, #sbo-rt-content .annotator-wrapper .annotator-modal-wrap=
per .interface-controls .social-sharing li, .dropdown-menu.social-sharing l=
i, .interface-controls #sbo-rt-content .annotator-wrapper .annotator-modal-=
wrapper .social-sharing li, .interface-controls .sbo-inpage-toc .annotator-=
wrapper .annotator-modal-wrapper .social-sharing li, .interface-controls .s=
ocial-sharing li, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapp=
er .dropdown-menu.social-sharing li, .sbo-inpage-toc .annotator-wrapper .an=
notator-modal-wrapper .interface-controls .social-sharing li { display: blo=
ck; float: left; background: 0px 0px; border-left: 1px solid rgb(119, 119, =
119); }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .dropdown-menu.=
social-sharing li:first-child, #sbo-rt-content .annotator-wrapper .annotato=
r-modal-wrapper .interface-controls .social-sharing li:first-child, .dropdo=
wn-menu.social-sharing li:first-child, .interface-controls #sbo-rt-content =
.annotator-wrapper .annotator-modal-wrapper .social-sharing li:first-child,=
 .interface-controls .sbo-inpage-toc .annotator-wrapper .annotator-modal-wr=
apper .social-sharing li:first-child, .interface-controls .social-sharing l=
i:first-child, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper =
.dropdown-menu.social-sharing li:first-child, .sbo-inpage-toc .annotator-wr=
apper .annotator-modal-wrapper .interface-controls .social-sharing li:first=
-child { border-left: none; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .dropdown-menu.=
social-sharing a.twitter, #sbo-rt-content .annotator-wrapper .annotator-mod=
al-wrapper .interface-controls .social-sharing a.twitter, .dropdown-menu.so=
cial-sharing a.twitter, .interface-controls #sbo-rt-content .annotator-wrap=
per .annotator-modal-wrapper .social-sharing a.twitter, .interface-controls=
 .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .social-sharin=
g a.twitter, .interface-controls .social-sharing a.twitter, .sbo-inpage-toc=
 .annotator-wrapper .annotator-modal-wrapper .dropdown-menu.social-sharing =
a.twitter, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .int=
erface-controls .social-sharing a.twitter { background-image: url("/static/=
images/tweet.a62814fba328.png"); }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .dropdown-menu.=
social-sharing a.facebook, #sbo-rt-content .annotator-wrapper .annotator-mo=
dal-wrapper .interface-controls .social-sharing a.facebook, .dropdown-menu.=
social-sharing a.facebook, .interface-controls #sbo-rt-content .annotator-w=
rapper .annotator-modal-wrapper .social-sharing a.facebook, .interface-cont=
rols .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .social-sh=
aring a.facebook, .interface-controls .social-sharing a.facebook, .sbo-inpa=
ge-toc .annotator-wrapper .annotator-modal-wrapper .dropdown-menu.social-sh=
aring a.facebook, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapp=
er .interface-controls .social-sharing a.facebook { background-image: url("=
/static/images/fb.249a5073b401.png"); }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .dropdown-menu.=
social-sharing a.googleplus, #sbo-rt-content .annotator-wrapper .annotator-=
modal-wrapper .interface-controls .social-sharing a.googleplus, .dropdown-m=
enu.social-sharing a.googleplus, .interface-controls #sbo-rt-content .annot=
ator-wrapper .annotator-modal-wrapper .social-sharing a.googleplus, .interf=
ace-controls .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .s=
ocial-sharing a.googleplus, .interface-controls .social-sharing a.googleplu=
s, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .dropdown-me=
nu.social-sharing a.googleplus, .sbo-inpage-toc .annotator-wrapper .annotat=
or-modal-wrapper .interface-controls .social-sharing a.googleplus { backgro=
und-image: url("/static/images/googleplus.84ff91fb93fb.png"); }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .dropdown-menu.=
social-sharing a.email, #sbo-rt-content .annotator-wrapper .annotator-modal=
-wrapper .interface-controls .social-sharing a.email, .dropdown-menu.social=
-sharing a.email, .interface-controls #sbo-rt-content .annotator-wrapper .a=
nnotator-modal-wrapper .social-sharing a.email, .interface-controls .sbo-in=
page-toc .annotator-wrapper .annotator-modal-wrapper .social-sharing a.emai=
l, .interface-controls .social-sharing a.email, .sbo-inpage-toc .annotator-=
wrapper .annotator-modal-wrapper .dropdown-menu.social-sharing a.email, .sb=
o-inpage-toc .annotator-wrapper .annotator-modal-wrapper .interface-control=
s .social-sharing a.email { background-image: url("/static/images/email.60e=
a89b93003.png"); }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .active .dropdo=
wn-menu.social-sharing, #sbo-rt-content .annotator-wrapper .annotator-modal=
-wrapper .active .interface-controls .social-sharing, .active #sbo-rt-conte=
nt .annotator-wrapper .annotator-modal-wrapper .dropdown-menu.social-sharin=
g, .active .dropdown-menu.social-sharing, .active .interface-controls #sbo-=
rt-content .annotator-wrapper .annotator-modal-wrapper .social-sharing, .ac=
tive .interface-controls .sbo-inpage-toc .annotator-wrapper .annotator-moda=
l-wrapper .social-sharing, .active .interface-controls .social-sharing, .ac=
tive .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .dropdown-=
menu.social-sharing, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wr=
apper .active .dropdown-menu.social-sharing, .sbo-inpage-toc .annotator-wra=
pper .annotator-modal-wrapper .active .interface-controls .social-sharing {=
 opacity: 1; visibility: visible; }

@media screen and (max-width: 26.25em) {
  #sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .dropdown-men=
u.social-sharing, #sbo-rt-content .annotator-wrapper .annotator-modal-wrapp=
er .interface-controls .social-sharing, .dropdown-menu.social-sharing, .int=
erface-controls #sbo-rt-content .annotator-wrapper .annotator-modal-wrapper=
 .social-sharing, .interface-controls .sbo-inpage-toc .annotator-wrapper .a=
nnotator-modal-wrapper .social-sharing, .interface-controls .social-sharing=
, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .dropdown-men=
u.social-sharing, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapp=
er .interface-controls .social-sharing { left: 48px; right: 0px; border-rad=
ius: 0px 2px 2px 0px; background-clip: padding-box; border-right: none; bor=
der-left: 1px solid rgb(119, 119, 119); }
}

.addone { float: right; }

@media screen and (max-width: 32.5em) {
  .addone { float: left; margin-top: 0.25rem; }
}

@media screen and (min-height: 33.6875em) and (min-width: 32.5625em) {
  body { padding-top: 26px; }
  body.sidenav { padding-left: 55px; }
}

.topbar { background-color: rgb(230, 230, 230); }

a.skip { display: block; position: absolute; top: -1000px; left: -1000px; w=
idth: 1px; height: 1px; overflow: hidden; transition: all 0.2s ease-in-out =
0s; }

a.skip:active, a.skip:focus, a.skip:hover { padding: 0.625rem; position: fi=
xed; z-index: 5000; left: 0px; top: 0px; width: 100%; height: auto; overflo=
w: visible; background-color: rgb(246, 93, 34); color: rgb(255, 255, 255); =
text-align: center; text-decoration: none; font-size: 12px; }

.touch .shortcuts { display: none; }

@media screen and (min-width: 32.5em), screen and (max-height: 33.75em) {
  .topnav .l0 { overflow: hidden; max-width: 190px; }
  .nav-collapsed .topnav .l0 { max-width: 55px; }
}

.topnav { position: relative; }

.topnav::after, .topnav::before { content: " "; display: table; }

.topnav > li { float: left; }

.dropdown.usermenu, .searchbox { float: right; }

.topnav > li a { transition: all 0.15s ease-in-out 0s; }

.topnav .flyout-parent .flyout .l2, .topnav > li a { transition: all 0.15s =
ease-in-out 0s; }

.topnav > li a:focus, .topnav > li a:hover { color: rgb(64, 64, 64); backgr=
ound-color: rgb(216, 216, 216); text-decoration: none; }

.topnav .flyout-parent .flyout .l2 { display: block; opacity: 0; transition=
: all 0.15s ease-in-out 0s; height: 0px; width: 0px; padding: 0px; position=
: relative; left: -999999px; }

.topnav .flyout-parent:hover .flyout .l2 { height: 50px; width: 190px; padd=
ing: 18px 18px 19px; opacity: 1; left: 0px; }

.topnav .flyout-parent:hover a.l1 { background-color: rgb(245, 245, 245); }

.topnav .flyout { display: block; position: absolute; left: 190px; margin-t=
op: -50px; }

.topnav .flyout li a { display: inline-block; width: 190px; background-colo=
r: rgb(230, 230, 230); padding: 18px 18px 19px; }

.topnav .flyout li a:hover { background-color: rgb(216, 216, 216); }

@media screen and (max-width: 32.5em), screen and (max-height: 33.75em) {
  .topnav .flyout-parent .flyout .l2 { opacity: 1; height: 50px; width: 190=
px; padding: 18px 18px 19px; left: 43px; }
  .topnav .flyout-parent:hover .flyout .l2 { left: 43px; }
  .topnav .flyout-parent:hover a.l1 { background-color: transparent !import=
ant; }
  .topnav .flyout { position: relative; left: 0px; margin-top: 0px; }
  .topnav .flyout li a { background-color: transparent; padding: 18px 18px =
19px 56px; width: 100%; }
  .topnav .flyout li a:hover { background-color: rgb(153, 153, 153); }
}

@media screen and (min-width: 32.5625em) {
  .topnav .l2 { display: none; }
}

@media screen and (max-height: 33.75em) {
  .topnav .l2 { display: block; }
}

.l2 { padding: 0px 10px; display: inline-block; }

a.l0, a.l1, a.l2 { display: block; color: rgb(64, 64, 64); font-size: 0.812=
5rem; line-height: 1em; }

.l0.active, .l1.active { background: rgb(245, 245, 245); }

.nav-dropdown { position: absolute; right: 0px; top: 0px; }

.drop-content { max-height: 0px; overflow: hidden; transition: max-height 0=
.3s ease-in-out 0s; }

.dropdown.active .l0, .dropdown.active .l0:hover { color: rgb(255, 255, 255=
); background-color: rgb(153, 153, 153); }

.dropdown .l0 svg { transform: rotate(180deg); transition: all 0.15s cubic-=
bezier(0.86, 0, 0.07, 1) 0s; }

.dropdown.active .l0 svg { fill: rgb(255, 255, 255); transform: rotate(0deg=
); }

.reading .dropdown.searchbox, .reading li.search { display: none; }

.dropdown.usermenu .drop-content { position: absolute; background-color: rg=
b(153, 153, 153); z-index: 30; right: 0px; top: 61px; width: 200px; }

.tooltip.bottom-right .tooltip-arrow, .tooltip.top-right .tooltip-arrow { r=
ight: 5px; }

@media screen and (max-width: 32.5em), screen and (max-height: 33.75em) {
  .l0 { height: 62px; line-height: 1.75em !important; }
  .wrap-search-form.active .drop-content { overflow: initial; }
  .dropdown.active .drop-content { max-height: 900px; padding-bottom: 5px; =
}
  .dropdown.active .drop-content a { color: rgb(255, 255, 255); }
  .dropdown.active .drop-content a:focus, .dropdown.active .drop-content a:=
hover { background-color: rgb(136, 136, 136) !important; }
  .dropdown.active .drop-content a.active { background-color: rgb(119, 119,=
 119); color: rgb(68, 68, 68); }
  .dropdown.active .drop-content #js-shortcuts-info { display: none; }
  .dropdown.active .drop-content ul.profile { border-top: 1px solid rgb(153=
, 153, 153); padding: 0px 0px 0px 0.375rem; display: none; }
  .dropdown.active .drop-content ul.profile li { margin: 0.625rem 0px; }
  .dropdown.active .drop-content ul.profile li a:focus, .dropdown.active .d=
rop-content ul.profile li a:hover { background-color: transparent; }
  .dropdown.active .drop-content ul.profile li .active { background-color: =
transparent; color: rgb(255, 255, 255); }
  .dropdown.active .drop-content ul.profile li #nav-nag { color: rgb(179, 1=
79, 179); }
  .dropdown.active .drop-content ul.profile li #nav-nag a { text-decoration=
: none; color: rgb(179, 179, 179); }
  .dropdown.active .drop-content ul.profile li #nav-nag a:focus, .dropdown.=
active .drop-content ul.profile li #nav-nag a:hover { color: rgb(255, 255, =
255); }
}

.autocomplete-suggestions { text-align: left; background-color: rgb(255, 25=
5, 255); box-shadow: rgb(213, 213, 213) 1px 2px 3px; border: 1px solid rgb(=
213, 213, 213); color: rgb(102, 102, 102); position: absolute; width: 100%;=
 z-index: 9999; display: block; }

.autocomplete-suggestions:empty { border: none; box-shadow: transparent 0px=
 0px 0px; }

.autocomplete-suggestions .autocomplete-suggestion { padding: 0.5rem 0px 0.=
5rem 1.25rem; line-height: 1.25em; }

.autocomplete-suggestions .autocomplete-suggestion.autocomplete-selected, .=
autocomplete-suggestions .autocomplete-suggestion:focus, .autocomplete-sugg=
estions .autocomplete-suggestion:hover { background-color: rgba(199, 194, 1=
86, 0.15); color: rgb(246, 93, 34); cursor: pointer; }

.searchbox, .wrap-search-form { margin: 0.75rem 1.25rem 0px; position: rela=
tive; z-index: 8; }

.searchbox .search-form, .wrap-search-form .search-form { border-radius: 2p=
x; background-clip: padding-box; z-index: 8; position: relative; display: i=
nline-block; border: 1px solid rgb(213, 213, 213); background-color: rgb(25=
5, 255, 255); margin: 0px; }

.searchbox .search-form.active, .searchbox .search-form:active, .searchbox =
.search-form:focus, .searchbox .search-form:hover, .wrap-search-form .searc=
h-form.active, .wrap-search-form .search-form:active, .wrap-search-form .se=
arch-form:focus, .wrap-search-form .search-form:hover { border: 1px solid r=
gb(246, 93, 34); }

.searchbox .nav-search-in, .wrap-search-form .nav-search-in { border-radius=
: 2px 0px 0px 2px; background-clip: padding-box; display: inline-block; bac=
kground-color: rgb(255, 255, 255); }

.searchbox .search-query, .searchbox select.search-params, .wrap-search-for=
m .search-query, .wrap-search-form select.search-params { display: inline-b=
lock; vertical-align: middle; border: none; outline: 0px; -webkit-appearanc=
e: none; }

.searchbox select.search-params, .wrap-search-form select.search-params { w=
idth: 107px; margin: 0px 10px 0px 0px; padding: 5px 5px 5px 10px; -webkit-a=
ppearance: none; background: url("/static/images/down_arrow_icon.183ac2d274=
57.svg") right 60% no-repeat; color: rgb(119, 119, 119); cursor: pointer; }

.searchbox select.search-params:active, .searchbox select.search-params:foc=
us, .searchbox select.search-params:hover, .wrap-search-form select.search-=
params:active, .wrap-search-form select.search-params:focus, .wrap-search-f=
orm select.search-params:hover { color: rgb(64, 64, 64); }

.ie8 .searchbox select.search-params, .ie8 .wrap-search-form select.search-=
params { background: 0px 0px; }

.searchbox .search-query, .wrap-search-form .search-query { width: 250px; h=
eight: 28px; padding: 3px 0px; background-color: rgb(255, 255, 255); color:=
 rgb(51, 51, 51); white-space: nowrap; text-overflow: ellipsis; outline: 0p=
x; }

.searchbox .search-query:focus::-webkit-input-placeholder, .wrap-search-for=
m .search-query:focus::-webkit-input-placeholder { transition: opacity 0.35=
s ease 0.35s; opacity: 0; }

.searchbox .search-button, .wrap-search-form .search-button { width: 28px; =
height: 28px; padding: 0px; color: rgb(199, 194, 186); vertical-align: midd=
le; border: none; }

.searchbox .search-button span, .wrap-search-form .search-button span { dis=
play: none; }

.searchbox .search-button svg, .wrap-search-form .search-button svg { displ=
ay: block; height: 17px; width: 28px; fill: rgb(199, 194, 186); }

.no-touch .searchbox .search-button:focus svg, .no-touch .searchbox .search=
-button:hover svg, .no-touch .wrap-search-form .search-button:focus svg, .n=
o-touch .wrap-search-form .search-button:hover svg, .searchbox .search-butt=
on:active svg, .searchbox .search-button:focus svg, .searchbox .search-butt=
on:hover svg, .wrap-search-form .search-button:active svg, .wrap-search-for=
m .search-button:focus svg, .wrap-search-form .search-button:hover svg { fi=
ll: rgb(64, 64, 64); }

@media screen and (max-width: 32.5em), screen and (max-height: 33.75em) {
  .searchbox, .wrap-search-form { width: 100%; background-color: rgb(153, 1=
53, 153); margin: -5px 0px 0px !important; }
  .searchbox .search-form, .wrap-search-form .search-form { margin: 12px 15=
px 5px; width: calc(100% - 30px); }
  .searchbox .search-query, .wrap-search-form .search-query { width: calc(1=
00% - 153px); }
}

.nav-collapse { display: none; }

@media screen and (min-height: 33.6875em) and (min-width: 32.5625em) {
  .searchbox .drop-content, .wrap-search-form .drop-content { max-height: 9=
99px; overflow: visible; }
  body.nav-collapsed .topbar { width: 55px; box-shadow: none; }
  .topbar { width: 190px; position: fixed; left: 0px; top: 26px; height: 10=
0%; z-index: 31; transition: width 0.1s ease-in-out 0s; box-shadow: rgba(0,=
 0, 0, 0.1) 0px 0px 4px; }
  .topbar a::before { top: 4px; font-size: 21px; }
  .topbar [class*=3D"ss-"].l0 span { display: inline; }
  .topbar .l0 { width: 100%; }
  .topbar ul > li { width: auto; display: block; }
  .topbar ul > li.search { display: none; }
  .reading .topbar { top: 0px; }
  .topnav .dropdown .drop-content { display: block; position: static; backg=
round-color: transparent; max-height: 999px; width: 100%; transition: none =
0s ease 0s; }
  .page-head, .page-head::after { width: 100%; display: inline-block; }
  .last-item { margin-bottom: 10px; }
  .l2 { padding-top: 5px; padding-bottom: 5px; }
  .l2:focus, .l2:hover { background-color: transparent; color: rgb(246, 93,=
 34); }
  .page-head { padding: 0px; background-color: rgb(255, 255, 255); z-index:=
 999; text-align: justify; box-shadow: rgba(0, 0, 0, 0.2) 0px 3px 4px -4px;=
 height: 55px; }
  .page-head::after { content: ""; }
  .nav-collapse, .page-head h1 { display: block; text-align: left; }
  .page-head h1 { font-size: 18px; line-height: 1.4em; margin: 0px 20px; pa=
dding: 10px 150px 0px 0px; vertical-align: top; position: relative; top: 3p=
x; color: rgb(119, 119, 119); }
  .nav-collapse { background-color: transparent; position: absolute; bottom=
: 0px; left: 0px; padding: 20px 0px 15px; width: 100%; transition: all 0.2s=
 ease-in-out 0s; box-shadow: none; border-radius: 0px; background-clip: pad=
ding-box; border: none; line-height: 1; color: rgb(155, 155, 155); text-dec=
oration: none; text-indent: 20px; cursor: pointer; }
  .nav-collapse::before { font-size: 15px; }
  .nav-collapse:focus, .nav-collapse:hover { background-color: rgb(218, 218=
, 218) !important; }
  .nav-collapse:active { top: auto; }
}

.tooltip.top .tooltip-arrow, .tooltip.top-left .tooltip-arrow, .tooltip.top=
-right .tooltip-arrow { bottom: 0px; border-top-color: rgb(119, 119, 119); =
border-width: 5px 5px 0px; }

.gen-nav { background-color: rgb(7, 7, 7); width: 100%; min-width: 230px; }

.mknav, .tooltip.active .tooltip-inner { background-color: rgb(246, 93, 34)=
; }

.gen-nav::after, .gen-nav::before { content: " "; display: table; }

.gen-nav a { color: rgb(255, 255, 255); padding: 0px 16px; display: block; =
text-decoration: none; }

.gen-nav .login, .gen-nav h1 { font-size: 16px; line-height: 50px; }

.gen-nav h1 { display: inline; margin: 0px; float: left; }

.gen-nav .login { float: right; color: rgb(246, 93, 34); }

.mknav { color: rgb(7, 7, 7); font-size: 16px; padding: 16px; }

.mknav li { display: inline; padding-right: 0.4em; }

.mknav li::before { padding-right: 0.4em; content: "/"; }

.mknav li:first-child::before { padding-right: 0px; content: ""; }

.mknav li a { color: rgb(255, 255, 255); text-decoration: none; }

.mknav li a:focus, .mknav li a:hover { text-decoration: underline; }

.tooltip { position: absolute; z-index: 1030; display: block; font-size: 14=
px; line-height: 1.4; opacity: 0; visibility: visible; white-space: nowrap;=
 }

.tooltip.in { opacity: 0.9; }

.tooltip.top { padding: 5px 0px; margin-top: -3px; }

.tooltip.top .tooltip-arrow { left: 50%; margin-left: -5px; }

.tooltip.top-left .tooltip-arrow { left: 5px; }

.tooltip.right { padding: 0px 5px; margin-left: 3px; }

.tooltip.right .tooltip-arrow { top: 50%; left: 0px; margin-top: -5px; bord=
er-right-color: rgb(119, 119, 119); border-width: 5px 5px 5px 0px; }

.tooltip.bottom .tooltip-arrow, .tooltip.bottom-left .tooltip-arrow, .toolt=
ip.bottom-right .tooltip-arrow { top: 0px; border-bottom-color: rgb(119, 11=
9, 119); border-width: 0px 5px 5px; }

.tooltip.active.right .tooltip-arrow { border-right-color: rgb(246, 93, 34)=
; }

.tooltip.bottom { padding: 5px 0px; margin-top: 3px; }

.tooltip.bottom .tooltip-arrow { left: 50%; margin-left: -5px; }

.tooltip.bottom-left .tooltip-arrow { left: 5px; }

.tooltip.left { padding: 0px 5px; margin-left: -3px; }

.tooltip.left .tooltip-arrow { top: 50%; right: 0px; margin-top: -5px; bord=
er-left-color: rgb(119, 119, 119); border-width: 5px 0px 5px 5px; }

.tooltip-inner { max-width: 300px; padding: 5px 12px; color: rgb(255, 255, =
255); text-align: center; text-decoration: none; background-color: rgb(119,=
 119, 119); border-radius: 2px; background-clip: padding-box; }

.tooltip-arrow { position: absolute; width: 0px; height: 0px; border-color:=
 transparent; border-style: solid; }

.fade { opacity: 0; transition: opacity 0.25s linear 0s; }

.fade.in { opacity: 1; }

.l1.no-icon { padding: 16px 15px 16px 55px; white-space: nowrap; }

a.nav-icn { padding: 15px 17px; white-space: nowrap; }

a.nav-icn svg { width: 20px; height: 20px; margin: 0px; }

a.nav-icn.l0 svg { margin: 7px 0px 0px 2px; }

a.nav-icn.l0 span { display: none; }

a.nav-icn.l1 svg { margin: 0px 18px 0px 2px; vertical-align: middle; }

a.nav-icn.l1 span { display: inline-block; vertical-align: middle; }

.usermenu { float: right; }

.usermenu .trigger { padding: 16px 15px 19px 17px; }

.usermenu .trigger:hover { color: rgb(64, 64, 64); background-color: rgb(21=
6, 216, 216); text-decoration: none; }

.usermenu .trigger.active { color: rgb(255, 255, 255); background-color: rg=
b(153, 153, 153); }

.topnav a svg * { fill: rgb(74, 59, 48); }

.topnav .usermenu a.l1 svg { fill: rgb(255, 255, 255); }

@media screen and (min-height: 33.6875em) and (min-width: 32.5625em) {
  .dropdown.usermenu, .topnav > li { float: none; }
  a.nav-icn.l0 { width: auto; }
  a.nav-icn.l0 svg, a.nav-icn.l1 svg { margin: 0px 18px 0px 2px; vertical-a=
lign: middle; }
  a.nav-icn.l0.safari-home svg { margin: 0px 16px 0px 4px; }
  a.nav-icn.l0 span, a.nav-icn.l1 span { display: inline-block; vertical-al=
ign: middle; }
  a.nav-icn.safari-home { padding: 22px 15px; }
  a.nav-icn.safari-home span { padding-top: 4px; }
  .dropdown .trigger { display: none; }
  .topnav .usermenu a.l1 svg * { fill: rgb(74, 59, 48); }
}

.articlelist { max-width: 1600px; margin: 0px auto 15px; }

.selected-card { outline-style: solid; outline-color: rgba(0, 134, 202, 0.2=
5); box-shadow: rgba(0, 134, 202, 0.35) 0px 0px 0px 3px; }

.articlelist > li { width: 100%; height: 100%; min-height: 200px; backgroun=
d-color: rgb(255, 255, 255); display: inline-block; position: relative; mar=
gin-bottom: 20px; vertical-align: top; border: 1px solid rgb(213, 213, 213)=
; border-radius: 2px; background-clip: padding-box; transition: width 0.15s=
 ease-in-out 0s; }

.articlelist > li .position-link { text-decoration: none; float: right; fon=
t-size: 0.75rem; letter-spacing: 1px; position: relative; z-index: 1; }

.articlelist > li .topic-display { clear: left; }

.articlelist > li.js-last-viewed span.expired { display: none; }

.articlelist > li.js-related .feedback.text { font-size: 24px; }

.articlelist > li.js-related .feedback::before { top: 35px; }

@media screen and (max-width: 767px) {
  .articlelist > li { width: 100%; }
}

@media screen and (max-width: 1279px) and (min-width: 768px) {
  .articlelist > li { width: 48.7207%; margin-right: 1.95313%; }
  .articlelist > li:nth-child(2n+2) { color: rgb(255, 255, 255); margin-rig=
ht: 0px; }
}

@media only screen and (max-width: 1600px) and (min-width: 1280px) {
  .articlelist > li { width: 31.5234%; margin-right: 2.34375%; }
  .articlelist > li:nth-child(3n+3) { margin-right: 0px; }
}

@media only screen and (min-width: 1601px) {
  .articlelist > li { width: 23.375%; margin-right: 1.875%; }
  .articlelist > li:nth-child(4n+4) { margin-right: 0px; }
}

.articlelist > li.more-container { display: block; width: 100%; margin: 0px=
 auto; border: none; background-color: transparent; text-align: center; }

.news-block .articlelist > li { background: rgb(255, 255, 255); }

.news-block .articlelist > li p { font-size: 14px; }

.feedback { position: absolute; top: 0px; left: 0px; width: 100%; height: 1=
00%; background-color: rgba(255, 255, 255, 0.9); text-align: center; z-inde=
x: 99; }

.feedback .text { font-size: 1.75rem; position: relative; top: 50%; line-he=
ight: 1.1em; color: rgba(64, 64, 64, 0.75); font-weight: 300; font-style: n=
ormal; display: inline-block; width: 95%; }

.feedback .canceled, .feedback .expired { display: block; color: rgba(64, 6=
4, 64, 0.75); font-size: 18px; margin-top: 8px; line-height: 1.25em; }

.feedback::before { font-size: 36px; left: 50%; margin-left: -21px; top: 50=
%; margin-top: -50px; position: absolute; }

.feedback.added::before { color: rgb(246, 93, 34); }

.feedback.canceled::before, .feedback.error::before, .feedback.expired::bef=
ore, .feedback.removed::before { color: rgb(178, 180, 179); }

.detail-book .feedback .text, .detail-video .feedback .text { font-size: 2r=
em; margin-top: 20px; }

@media screen and (max-width: 32.5em) {
  .detail-book .feedback .text, .detail-video .feedback .text { font-size: =
1.625rem; }
}

.articlelist > li .info { text-align: left; }

.articlelist > li .info h2 { margin: 0px; padding: 15px 10px 10px; display:=
 inline-block; color: rgb(0, 183, 152); }

.articlelist > li .info .main { padding: 0px 0.9375rem 0.9375rem; color: rg=
ba(64, 64, 64, 0.75); }

.articlelist > li .info .main::after, .articlelist > li .info .main::before=
 { content: " "; display: table; }

.articlelist > li .info .main::after { clear: both; }

@media screen and (min-width: 650px) {
  .articlelist > li .info { width: 100%; right: 0px; bottom: 0px; }
}

@media screen and (min-width: 1250px) {
  .articlelist > li .info .main { padding: 0px 0.625rem 0.625rem; }
}

.title-block { display: block; text-decoration: none; font-size: 1.125rem; =
margin-bottom: 0.1875rem; line-height: 1.25rem; }

.book-title { margin-bottom: 0.3125rem; line-height: 1.125rem; font-size: 0=
.8125rem; }

.book-title .issued { display: block; font-style: italic; }

.last-access { font-size: 12px; color: rgb(119, 119, 119); margin-bottom: 1=
0px; }

.articlelist > li .controls { min-height: 45px; user-select: none; border-b=
ottom: 1px solid rgb(213, 213, 213); font-size: 0.1px; line-height: 0.1px; =
text-align: right; margin-bottom: 10px; position: relative; }

.articlelist > li .controls .format-title { font-size: 10px; display: block=
; color: rgba(64, 64, 64, 0.75); position: absolute; left: 15px; top: 50%; =
}

.articlelist > li .controls .format-title::before { font-family: SSFlow; fo=
nt-size: 11px; padding-right: 3px; color: rgb(199, 194, 186); position: rel=
ative; top: 2px; }

@media screen and (min-width: 1250px) {
  .articlelist > li .controls .format-title { left: 10px; }
}

.format-book .format-title::before { content: "=F0=9F=93=95"; }

.format-video .format-title::before { content: "=F0=9F=93=B9"; }

.articlelist .rec-delete, .articlelist .rec-fav { padding: 10px 12px; margi=
n: 3px; }

.rec-delete, .rec-fav { text-shadow: none; transition: all 0.15s ease-in-ou=
t 0s; text-transform: lowercase; cursor: pointer; display: inline-block; te=
xt-align: center; border-radius: 0px; background-clip: padding-box; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .uppercase, .ca=
rd-annotation .note, .progress, .sbo-inpage-toc .annotator-wrapper .annotat=
or-modal-wrapper .uppercase { text-transform: uppercase; }

.rec-delete.invalid, .rec-delete:disabled, .rec-fav.invalid, .rec-fav:disab=
led { background-color: transparent; color: rgba(64, 64, 64, 0.75); }

.rec-delete::before, .rec-fav::before { vertical-align: middle; font-size: =
0.875rem; }

.rec-fav.active, .rec-fav.active::before { color: rgb(246, 93, 34); }

.no-touch button.rec-fav:focus { color: rgb(153, 153, 153); }

.no-touch button.rec-delete:focus, .no-touch button.rec-delete:hover { colo=
r: rgb(234, 109, 96); }

@media screen and (max-width: 1250px) {
  .no-touch .articlelist button.rec-delete:hover, .no-touch .articlelist bu=
tton.rec-fav:hover { background-color: rgb(238, 238, 238); }
}

.progress .gridtc { display: table-cell; white-space: nowrap; }

.progress { font-size: 0.75rem; display: block; margin: 0px; color: rgba(64=
, 64, 64, 0.65); letter-spacing: 1px; }

.progress .bar, .progress .prog-text { vertical-align: middle; display: tab=
le-cell; }

.progress .bar { width: 100%; }

.progress .prog-text { white-space: nowrap; padding-left: 10px; }

.progress .per, .progress .per .time { background-clip: padding-box; displa=
y: block; height: 8px; }

.progress .per { border-radius: 2px; background-color: rgb(213, 213, 213); =
padding: 0px; }

.progress .per .time { margin: 0px; border-radius: 2px; background-color: r=
gb(153, 144, 130); }

.sort-box { font-size: 20px; line-height: 1.3em; margin-bottom: 1em; text-a=
lign: right; color: rgb(119, 119, 119); font-weight: 300; }

.recommended-reason .book-title, .recommended-reason .book-title .topic-dis=
play li { font-size: 14px; }

@media screen and (min-width: 40.625em) {
  .sort-box { max-width: 650px; }
}

@media screen and (min-width: 96.125em) {
  .sort-box { max-width: 1315px; }
}

@media screen and (min-width: 137.5625em) {
  .sort-box { max-width: 1975px; }
}

@media screen and (min-width: 179em) {
  .sort-box { max-width: 2635px; }
}

@media screen and (min-width: 220.4375em) {
  .sort-box { max-width: 100%; }
}

.recommended-reason { padding: 5px 15px; background-color: rgb(247, 247, 24=
7); border-top: 1px solid rgb(213, 213, 213); color: rgb(153, 153, 153); }

.recommended-reason .book-title a { color: rgba(64, 64, 64, 0.75); text-dec=
oration: underline; }

.chat-wrapper a, .chat-wrapper a:hover, .chat-wrapper input.sales-chat-btn:=
focus, .chat-wrapper input.sales-chat-btn:hover { text-decoration: none; }

.recommended-reason .book-title a:focus, .recommended-reason .book-title a:=
hover { color: rgb(246, 93, 34); }

.topic-display li { display: inline-block; font-size: 0.75rem; color: rgb(1=
19, 119, 119); }

.topic-display li .topic { color: rgb(246, 93, 34); }

.topic-display li::after { color: rgb(204, 204, 204); content: " / "; }

.topic-display li:last-child::after, [class*=3D"hex-"] .topic-display li::a=
fter { content: ""; }

.trial-banner { background-color: rgb(255, 255, 255); margin: 0px 20px 20px=
; border-radius: 2px; background-clip: padding-box; text-align: center; pad=
ding: 15px; border: 1px solid rgba(0, 0, 0, 0.2); box-shadow: rgb(204, 204,=
 204) 0px 0px 10px; }

.trial-banner h1 { font-size: 2.375rem; font-weight: 400; margin-bottom: 0p=
x; line-height: 1.15em; }

@media screen and (max-width: 53.125em) {
  .trial-banner h1 { font-size: 2.1875rem; }
}

.trial-banner p { font-size: 1.5rem; font-weight: 300; color: rgb(153, 153,=
 153); margin-bottom: 1em; line-height: 1.1em; }

.trial-banner.trial-expired { padding: 15px 0px; }

.trial-banner.trial-expired h1 { font-size: 1.625rem; }

@media screen and (max-width: 32.5625em) {
  .trial-banner.trial-expired h1 { font-size: 1.3125rem; }
}

.trial-banner .red-banner { background-color: rgb(234, 109, 96); color: rgb=
(255, 255, 255); padding: 15px 10% 25px; font-weight: 300; margin-bottom: 2=
0px; }

.js-disable-shortcuts label { display: inline-block; margin: 0px 0px 0px 10=
px; }

.keyboard-shortcuts-pane { overflow: hidden; clear: both; font-family: "sou=
rce sans pro", Helvetica, Arial, sans-serif !important; }

.keyboard-shortcuts-pane .inner .headline { border-bottom: 1px solid rgb(20=
4, 204, 204); padding: 0.375rem 0px; border-radius: 2px 2px 0px 0px; backgr=
ound-clip: padding-box; height: 50px; }

.keyboard-shortcuts-pane .inner .headline h2 { margin: 0px; color: rgb(119,=
 119, 119); font-size: 1.3125rem; padding: 0.625rem; line-height: 1em; floa=
t: left !important; }

.keyboard-shortcuts-pane .inner .headline .js-close { width: 20px; height: =
20px; display: block; float: right; font-size: 1.3125rem; margin: 0.6875rem=
 0.9375rem 0px; color: rgb(153, 153, 153); text-decoration: none; line-heig=
ht: 1em; }

.keyboard-shortcuts-pane .inner .headline .js-close:focus, .keyboard-shortc=
uts-pane .inner .headline .js-close:hover { color: rgb(102, 102, 102); }

.keyboard-shortcuts-pane .inner .headline .js-close span { display: block; =
text-indent: -99999px; }

.keyboard-shortcuts-pane .inner h4 { margin: 0px; font-size: 1.125rem; colo=
r: rgb(119, 119, 119); }

.keyboard-shortcuts-pane .inner .disable-shortcuts { clear: both; padding: =
0px 0px 0.625rem 1.25rem; font-size: smaller; }

.keyboard-shortcuts-pane .inner.popup { color: rgb(119, 119, 119); top: 100=
px; min-height: 250px; transition: height 0.15s ease-in-out 0s; border: 1px=
 solid rgb(179, 179, 179) !important; }

@media screen and (max-width: 620px) {
  .keyboard-shortcuts-pane .inner { display: none; }
}

.keyboard-shortcuts-pane .inner .tooltip-inner { width: 100%; max-width: 10=
0% !important; }

.keyboard-shortcuts-pane .inner .column { width: 50%; }

.keyboard-shortcuts-pane .inner .column.right { float: right; padding: 0.62=
5rem 2.5rem 1.25rem 0px; }

.keyboard-shortcuts-pane .inner .column.left { padding: 0.625rem 0px 1.25re=
m 2.5rem; float: left; }

.keyboard-shortcuts-pane .inner .key { padding: 0.3125rem 0.375rem; color: =
rgb(119, 119, 119); font-family: Monaco, "Liberation Mono", Courier, monosp=
ace; line-height: 1; display: inline-block; font-size: 0.75rem; border-radi=
us: 2px; background: linear-gradient(rgb(216, 216, 216) 0px, rgb(242, 242, =
242) 100%); box-shadow: rgb(255, 255, 255) 0px 1px 0px inset, rgb(204, 204,=
 204) 0px 1px 0px; border: 1px solid rgb(204, 204, 204); }

.keyboard-shortcuts-pane .inner td, .keyboard-shortcuts-pane .inner th { di=
splay: table-cell; }

.keyboard-shortcuts-pane .inner tr { display: table-row; vertical-align: in=
herit; border-color: inherit; }

.keyboard-shortcuts-pane .inner th { text-align: left; color: rgb(0, 183, 1=
38); font-weight: 700; padding: 0.625rem 0px; }

.keyboard-shortcuts-pane .inner td { padding: 0.1875rem 0px; vertical-align=
: top; line-height: 1.25rem; font-size: 1rem; }

.keyboard-shortcuts-pane .inner td.keys { text-align: right; padding-right:=
 10px; white-space: nowrap; }

.chat-wrapper { position: fixed; z-index: 1000; color: rgb(255, 255, 255); =
font-size: 1rem; }

.chat-wrapper input.sales-chat-btn { border-radius: 2px 0px 0px 2px; backgr=
ound-clip: padding-box; cursor: pointer; white-space: normal; display: bloc=
k !important; }

.chat-wrapper input:focus { box-shadow: none; border: none; }

.subscribe-nag .chat-wrapper { visibility: hidden; }

@media screen and (min-width: 450px) {
  .chat-wrapper { right: 0px; margin-bottom: -107px; display: block; bottom=
: 50% !important; }
  .chat-wrapper.slideUp { visibility: visible !important; }
  .chat-wrapper input.sales-chat-btn { background: url("/static/images/sale=
s-chat.b34d45f2713c.svg") 25px 158px / 40px no-repeat rgb(246, 93, 34); wid=
th: 90px; height: 215px; padding: 12px 9px 81px; font: 400 1.05em/1.38 "Sou=
rce Sans Pro"; }
  .expanded .live-agent { width: 188px; margin: 0px auto; display: block; p=
osition: relative; }
  .expanded .live-agent::before { content: url("/static/images/sales-chat.b=
34d45f2713c.svg"); position: absolute; left: 8px; top: 13px; z-index: 10; }
  .expanded .live-agent input { white-space: normal; background:  0% 0% / 3=
6px no-repeat rgb(246, 93, 34); padding-left: 60px; text-align: left; line-=
height: 1em; }
  .expanded .live-agent input:focus, .expanded .live-agent input:hover { ba=
ckground: linear-gradient(rgb(245, 197, 23) 0px, rgb(246, 93, 34) 100%) 0% =
0% / 100% rgb(246, 93, 34); text-decoration: none !important; }
}

@media screen and (max-width: 449px) {
  .chat-wrapper { bottom: 0px; left: 50%; padding: 0px; margin-left: -25.5%=
; width: 50%; position: fixed; }
  .chat-wrapper input.sales-chat-btn { background: url("/static/images/sale=
s-chat.b34d45f2713c.svg") 9px 15px / 25px no-repeat padding-box rgb(246, 93=
, 34); border-radius: 2px 2px 0px 0px; margin-left: 5px; font: 400 0.95em/1=
.1 "Source Sans Pro"; text-align: left; padding: 0.0125rem 0.65rem 0px 2.75=
rem; height: 60px; }
  .chat-wrapper.slideUp { bottom: -70px !important; visibility: visible !im=
portant; }
  .register .chat-wrapper { display: none; }
  .subscribe-nag .expanded .live-agent { width: 172px; margin: 0px auto; di=
splay: block; }
  .subscribe-nag .expanded .live-agent input { white-space: normal; backgro=
und: url("/static/images/sales-chat.b34d45f2713c.svg") 9px 12px / 36px no-r=
epeat rgb(246, 93, 34); padding: 10px 9px 10px 55px; text-align: left; line=
-height: 1em; margin: 0.25rem 0px 0.625rem !important; }
  .subscribe-nag .chat-wrapper { bottom: -300%; position: absolute; left: 0=
px; margin: 0px; }
}

.legal-agreement-details { color: rgb(0, 0, 0); margin: 15px 0px; }

.cover { display: inline-block; }

.cover a, .cover img, .cover span { display: block; }

.cover a { position: relative; max-width: 100%; }

.cover img { max-width: 100%; height: auto; box-shadow: rgba(0, 0, 0, 0.2) =
2px 0px 6px 0px; }

.detail-video .cover a::before, .format-case-study .cover a::before, .forma=
t-learning-path .cover a::before, .format-video .cover a::before { content:=
 ""; background: url("/static/images/icon__cover-image__media-type--video.a=
76cad93c7f6.svg") center center no-repeat; position: absolute; height: 40px=
; width: 40px; line-height: 50px; margin-top: -20px; margin-left: -20px; to=
p: 50%; left: 50%; text-align: center; text-indent: 3px; text-decoration: n=
one; z-index: 1; }

.detail-video .cover a::before { height: 50px; width: 50px; margin: -25px 0=
px 0px -25px; background-size: 100%; }

.format-case-study .cover a::before { height: 17px; width: 17px; margin: 15=
px 0px 0px 15px; background-size: 100%; }

.results-list .cover { float: left; margin-left: -75px; }

.results-list .cover img { max-width: 60px; }

@media (min-width: 450px) {
  .results-list .cover { margin-left: -90px; }
  .results-list .cover img { max-width: 73px; width: 73px; }
}

.articlelist > li.format-video .cover { max-width: 7.625rem; height: 70px; =
overflow: hidden; }

.display-modal-view, .modal-view { display: none; overflow: scroll; positio=
n: absolute; z-index: 99; }

.articlelist > li.format-video .cover a { max-height: 70px; }

.articlelist > li .cover { float: left; width: 100%; max-width: 4.0625rem; =
margin: 0.125rem 0.9375rem 0.3125rem 0px; }

.articlelist > li .cover a { border: 1px solid transparent; }

.articlelist > li .cover a:focus { border: 1px solid rgb(246, 93, 34); }

@font-face { font-family: "Stag Sans"; src: url("/static/fonts/StagSans-Lig=
ht-Web.dc285b98d7a4.woff") format("opentype"); font-weight: 100; font-style=
: normal; }

@font-face { font-family: "Stag Sans"; src: url("/static/fonts/StagSans-Boo=
k-Web.31c8d367698b.woff") format("opentype"); font-weight: 400; font-style:=
 normal; }

@font-face { font-family: "Stag Sans"; src: url("/static/fonts/StagSans-Bol=
d-Web.8db395cead3c.woff") format("opentype"); font-weight: 700; font-style:=
 normal; }

@font-face { font-family: "Stag Web"; src: url("/static/fonts/Stag-Light-We=
b.fbb273737603.woff") format("opentype"); font-weight: 100; font-style: nor=
mal; }

@font-face { font-family: "Stag Web"; src: url("/static/fonts/Stag-Book-Web=
.53c49737b233.woff") format("opentype"); font-weight: 400; font-style: norm=
al; }

@font-face { font-family: "Stag Web"; src: url("/static/fonts/Stag-Bold-Web=
.5522801745aa.woff") format("opentype"); font-weight: 700; font-style: norm=
al; }

.display-modal-view { text-align: center; background: padding-box rgb(255, =
255, 255); border: 1px solid rgb(213, 214, 210); border-radius: 2px; width:=
 650px; top: 10%; left: 50%; margin-left: -325px; font-family: "source sans=
 pro", sans-serif; }

@media screen and (max-width: 620px) {
  .display-modal-view { width: 95%; margin: 0px 2.5% !important; left: 0px =
!important; }
}

.display-modal-view button.close-display-modal { position: absolute; top: 0=
px; right: 0px; padding: 10px; border: none; }

.display-modal-view button.close-display-modal::before { font-family: SSFlo=
w; font-size: 14px; content: "=E2=90=A1"; color: rgb(119, 119, 119); }

.display-modal-view button.close-display-modal:hover { text-decoration: non=
e; }

.display-modal-view h2.modal__title { font-size: 2.25rem; padding: 1rem; fo=
nt-weight: 300; line-height: 1.3; margin: 0px; color: rgb(64, 64, 64); }

.display-modal-view p.modal__body, .display-modal-view p.modal__document, .=
modal-view h2.modal__title { padding: 1rem; font-weight: 300; line-height: =
1.3; color: rgb(119, 119, 119); }

.display-modal-view p.modal__body { font-size: 1.5rem; margin: 0px; }

.display-modal-view p.modal__document { font-size: 1rem; margin: 0px; }

.display-modal-view p.modal__document cite { font-style: italic; }

.display-modal-view div.modal__controls { margin-bottom: 1rem; }

.modal-view { text-align: left; background: padding-box rgb(255, 255, 255);=
 border: 1px solid rgb(213, 214, 210); border-radius: 2px; width: 650px; to=
p: 30%; left: 50%; margin-left: -325px; }

#sbo-rt-content .annotator-wrapper .annotator-hide, .annotator-notice, .sbo=
-inpage-toc .annotator-wrapper .annotator-hide { display: none !important; =
}

@media screen and (max-width: 620px) {
  .modal-view { width: 95%; margin: 0px 2.5% !important; left: 0px !importa=
nt; }
}

.modal-view h2.modal__title { font-size: 1.5rem; border-bottom: 1px solid r=
gb(213, 213, 213); margin: 0px; }

.modal-view .modal__content form fieldset { padding: 0px 1rem 1rem; }

.modal-view .modal__content form fieldset label { font-size: 1rem; }

.modal-view .modal__content form fieldset input { width: 100%; max-width: 1=
00%; }

.modal-view .modal__controls { float: right; }

.pdf #sbo-rt-content .annotator-wrapper .annotator-hl { opacity: 0.65; }

#sbo-rt-content, .sbo-inpage-toc { transform: none; position: static !impor=
tant; }

#sbo-rt-content .annotator-wrapper, .sbo-inpage-toc .annotator-wrapper { ma=
rgin: 0px; }

#sbo-rt-content .annotator-wrapper .annotator-hl, .sbo-inpage-toc .annotato=
r-wrapper .annotator-hl { background-color: rgb(255, 227, 79); }

#sbo-rt-content .annotator-wrapper .annotator-hl-has-note, .sbo-inpage-toc =
.annotator-wrapper .annotator-hl-has-note { position: relative; }

#sbo-rt-content .annotator-wrapper .annotator-hl-has-note::before, .sbo-inp=
age-toc .annotator-wrapper .annotator-hl-has-note::before { content: "=E2=
=80=A2"; font-size: 40px; position: absolute; left: -8px; top: 0px; line-he=
ight: 0; color: rgb(246, 93, 34); box-shadow: rgba(0, 0, 0, 0.8) 1px 3px 6p=
x 1px; }

#sbo-rt-content .annotator-wrapper .annotator-item, .sbo-inpage-toc .annota=
tor-wrapper .annotator-item { list-style-type: none; margin-left: 0px; clea=
r: both; }

#sbo-rt-content .annotator-wrapper .annotator-item input.disabled, #sbo-rt-=
content .annotator-wrapper .annotator-item label.disabled, .sbo-inpage-toc =
.annotator-wrapper .annotator-item input.disabled, .sbo-inpage-toc .annotat=
or-wrapper .annotator-item label.disabled { opacity: 0.25; }

#sbo-rt-content .annotator-wrapper .animateIn, .sbo-inpage-toc .annotator-w=
rapper .animateIn { animation-name: animateIn; animation-duration: 0.15s; a=
nimation-timing-function: ease-in-out; visibility: visible; }

#sbo-rt-content .annotator-wrapper .stretchRight, .sbo-inpage-toc .annotato=
r-wrapper .stretchRight { animation-name: stretchRight; animation-duration:=
 0.3s; animation-timing-function: ease-out; transform-origin: 0px 0px; }

#sbo-rt-content .annotator-wrapper .expandUp, .sbo-inpage-toc .annotator-wr=
apper .expandUp { animation-name: expandUp; animation-duration: 0.2s; anima=
tion-timing-function: ease; visibility: visible !important; }

#sbo-rt-content .annotator-wrapper .annotator-touch-controls, #sbo-rt-conte=
nt .annotator-wrapper .annotator-viewer.viewer, .sbo-inpage-toc .annotator-=
wrapper .annotator-touch-controls, .sbo-inpage-toc .annotator-wrapper .anno=
tator-viewer.viewer { position: absolute; margin: 0px; padding: 0px; backgr=
ound-color: transparent; }

.js-playlist-icon, .js-playlist-icon:disabled, .js-playlist-icon:disabled:f=
ocus, .js-playlist-icon:disabled:hover { background-color: transparent !imp=
ortant; }

#sbo-rt-content .annotator-wrapper .annotator-touch-controls div, #sbo-rt-c=
ontent .annotator-wrapper .annotator-viewer.viewer div, .sbo-inpage-toc .an=
notator-wrapper .annotator-touch-controls div, .sbo-inpage-toc .annotator-w=
rapper .annotator-viewer.viewer div { display: none; }

#sbo-rt-content .annotator-wrapper .annotator-touch-controls .annotator-wid=
get, #sbo-rt-content .annotator-wrapper .annotator-viewer.viewer .annotator=
-widget, .sbo-inpage-toc .annotator-wrapper .annotator-touch-controls .anno=
tator-widget, .sbo-inpage-toc .annotator-wrapper .annotator-viewer.viewer .=
annotator-widget { margin-top: 0px !important; }

#sbo-rt-content .annotator-wrapper .toggle_public ul, .sbo-inpage-toc .anno=
tator-wrapper .toggle_public ul { margin: 0px; padding: 0px; }

#sbo-rt-content .annotator-wrapper .toggle_public ul li, .sbo-inpage-toc .a=
nnotator-wrapper .toggle_public ul li { font-family: "Source Sans Pro", ari=
al, sans-serif; list-style-type: none; float: left; color: rgb(64, 64, 64);=
 font-size: 0.9em !important; margin: 0px 10px 0px 0px !important; }

#sbo-rt-content .annotator-wrapper .toggle_public ul li input + span, .sbo-=
inpage-toc .annotator-wrapper .toggle_public ul li input + span { opacity: =
0.75; font-size: 15px; margin-left: 5px; }

#sbo-rt-content .annotator-wrapper .toggle_public ul li input:checked + spa=
n, .sbo-inpage-toc .annotator-wrapper .toggle_public ul li input:checked + =
span { opacity: 1; }

#sbo-rt-content .annotator-wrapper .toggle_public ul li label.disabled, .sb=
o-inpage-toc .annotator-wrapper .toggle_public ul li label.disabled { opaci=
ty: 0.25; }

#sbo-rt-content .annotator-wrapper .editor_section, .sbo-inpage-toc .annota=
tor-wrapper .editor_section { font-family: "Source Sans Pro", arial, sans-s=
erif; padding-top: 10px; border-top: 1px solid rgb(204, 204, 204); font-siz=
e: 0.9em !important; margin-top: 40px !important; }

#sbo-rt-content .annotator-wrapper .editor_section label, .sbo-inpage-toc .=
annotator-wrapper .editor_section label { display: inline-block; margin-lef=
t: 10px; }

#sbo-rt-content .annotator-wrapper small.error, .sbo-inpage-toc .annotator-=
wrapper small.error { color: red !important; }

#sbo-rt-content .annotator-wrapper .annotator-view-click, .sbo-inpage-toc .=
annotator-wrapper .annotator-view-click { margin: 0px !important; }

#sbo-rt-content .annotator-wrapper .annotator-listing, .sbo-inpage-toc .ann=
otator-wrapper .annotator-listing { padding-left: 0px !important; }

#sbo-rt-content .annotator-wrapper .annotator-adder, #sbo-rt-content .annot=
ator-wrapper .annotator-view-clicker, .sbo-inpage-toc .annotator-wrapper .a=
nnotator-adder, .sbo-inpage-toc .annotator-wrapper .annotator-view-clicker =
{ height: auto; width: 100%; padding: 0px; margin: 0px; position: absolute =
!important; background-color: transparent !important; }

#sbo-rt-content .annotator-wrapper .annotator-adder ul, #sbo-rt-content .an=
notator-wrapper .annotator-view-clicker ul, .sbo-inpage-toc .annotator-wrap=
per .annotator-adder ul, .sbo-inpage-toc .annotator-wrapper .annotator-view=
-clicker ul { background-color: rgb(255, 255, 255); border-radius: 2px; bac=
kground-clip: padding-box; box-shadow: rgba(0, 0, 0, 0.2) 0px 2px 5px 2px; =
border: 1px solid rgb(204, 204, 204); float: left; margin: 0px !important; =
padding: 3px 5px !important; }

#sbo-rt-content .annotator-wrapper .annotator-adder ul li, #sbo-rt-content =
.annotator-wrapper .annotator-view-clicker ul li, .sbo-inpage-toc .annotato=
r-wrapper .annotator-adder ul li, .sbo-inpage-toc .annotator-wrapper .annot=
ator-view-clicker ul li { list-style-type: none; list-style-image: none; fl=
oat: left; margin: 0px !important; }

#sbo-rt-content .annotator-wrapper .annotator-adder ul li:last-child a, #sb=
o-rt-content .annotator-wrapper .annotator-view-clicker ul li:last-child a,=
 .sbo-inpage-toc .annotator-wrapper .annotator-adder ul li:last-child a, .s=
bo-inpage-toc .annotator-wrapper .annotator-view-clicker ul li:last-child a=
 { border-right: none; }

#sbo-rt-content .annotator-wrapper .annotator-adder ul li a, #sbo-rt-conten=
t .annotator-wrapper .annotator-view-clicker ul li a, .sbo-inpage-toc .anno=
tator-wrapper .annotator-adder ul li a, .sbo-inpage-toc .annotator-wrapper =
.annotator-view-clicker ul li a { border: none; padding: 5px 10px; color: r=
gb(37, 101, 149); font-family: "Source Sans Pro", arial, sans-serif; font-s=
ize: 15px; font-weight: 600; }

#sbo-rt-content .annotator-wrapper .annotator-adder ul li a:hover, #sbo-rt-=
content .annotator-wrapper .annotator-view-clicker ul li a:hover, .sbo-inpa=
ge-toc .annotator-wrapper .annotator-adder ul li a:hover, .sbo-inpage-toc .=
annotator-wrapper .annotator-view-clicker ul li a:hover { color: rgb(0, 39,=
 118) !important; text-decoration: underline !important; }

#sbo-rt-content .annotator-wrapper .annotator-viewer, .sbo-inpage-toc .anno=
tator-wrapper .annotator-viewer { width: 100%; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper, .sbo-inpage-to=
c .annotator-wrapper .annotator-modal-wrapper { position: absolute; z-index=
: 29; width: 100%; max-width: 650px; transition: height 0.15s ease-in-out 0=
s; background-image: url("/static/images/loading.6b1710a5f2bc.gif"); backgr=
ound-position: center center; background-size: initial; background-repeat: =
no-repeat; background-attachment: initial; background-origin: initial; disp=
lay: none; top: 130px; box-shadow: rgb(230, 230, 230) 0px 3px 0px; border-r=
adius: 2px; background-clip: padding-box; background-color: rgb(255, 255, 2=
55) !important; margin-left: -322px !important; left: 50% !important; color=
: rgb(64, 64, 64) !important; right: auto !important; height: auto !importa=
nt; border: 1px solid rgb(179, 179, 179) !important; font-size: 100% !impor=
tant; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper code, #sbo-rt-c=
ontent .annotator-wrapper .annotator-modal-wrapper li, #sbo-rt-content .ann=
otator-wrapper .annotator-modal-wrapper p, .sbo-inpage-toc .annotator-wrapp=
er .annotator-modal-wrapper code, .sbo-inpage-toc .annotator-wrapper .annot=
ator-modal-wrapper li, .sbo-inpage-toc .annotator-wrapper .annotator-modal-=
wrapper p { color: rgb(64, 64, 64) !important; background-color: rgb(255, 2=
55, 255) !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper div, .sbo-inpag=
e-toc .annotator-wrapper .annotator-modal-wrapper div { margin: 0px !import=
ant; background-color: rgb(255, 255, 255) !important; }

@media screen and (max-width: 53.125em) and (min-width: 45.0625em) {
  #sbo-rt-content .annotator-wrapper .annotator-modal-wrapper, .sbo-inpage-=
toc .annotator-wrapper .annotator-modal-wrapper { max-width: 80% !important=
; margin-left: 0px !important; left: 10% !important; }
}

@media screen and (max-width: 45em) {
  #sbo-rt-content .annotator-wrapper .annotator-modal-wrapper, .sbo-inpage-=
toc .annotator-wrapper .annotator-modal-wrapper { padding-bottom: 10px; pos=
ition: absolute !important; max-width: 100% !important; left: 0px !importan=
t; margin-left: 0px !important; }
  #sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .editor, .sbo=
-inpage-toc .annotator-wrapper .annotator-modal-wrapper .editor { float: le=
ft; height: 100%; position: static !important; top: 0px !important; }
}

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .left, #sbo-rt-=
content .annotator-wrapper .annotator-modal-wrapper .right, .sbo-inpage-toc=
 .annotator-wrapper .annotator-modal-wrapper .left, .sbo-inpage-toc .annota=
tor-wrapper .annotator-modal-wrapper .right { margin: 0px !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .annotator-=
widget { background-color: rgb(255, 255, 255) !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .social-media .=
left, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .social-m=
edia .left { line-height: 1.3em; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .social-media .=
left a, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .social=
-media .left a { margin-top: 10px; display: block; font-size: 0.8em; line-h=
eight: 1.3em; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-oute=
r > .title, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .an=
notator-outer > .title { font: 500 1.5em/1.38 "Source Sans Pro"; padding: 0=
px 15px 10px !important; margin: 10px 0px 0px !important; border-bottom: 1p=
x solid rgb(221, 221, 221) !important; color: rgb(119, 119, 119) !important=
; background-color: rgb(255, 255, 255) !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .row, .sbo-inpa=
ge-toc .annotator-wrapper .annotator-modal-wrapper .row { padding: 8px 0px;=
 display: block; float: left; width: 100%; border-top: 1px solid rgb(221, 2=
21, 221) !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .row.delete-hig=
hlight, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .row.de=
lete-highlight { padding: 18px 0px 8px; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .indent, .sbo-i=
npage-toc .annotator-wrapper .annotator-modal-wrapper .indent { padding: 0p=
x 20px; margin-bottom: 15px; }

@media screen and (max-width: 32.5625em) {
  #sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .indent, .sbo=
-inpage-toc .annotator-wrapper .annotator-modal-wrapper .indent { padding: =
0px; }
}

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper h4, #sbo-rt-con=
tent .annotator-wrapper .annotator-modal-wrapper small, .sbo-inpage-toc .an=
notator-wrapper .annotator-modal-wrapper h4, .sbo-inpage-toc .annotator-wra=
pper .annotator-modal-wrapper small { font: 500 0.8em/1.2 "Source Sans Pro"=
; color: rgb(119, 119, 119) !important; margin-top: 5px !important; backgro=
und-color: rgb(255, 255, 255) !important; }

@media screen and (min-width: 45.0625em) {
  #sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .left, .sbo-i=
npage-toc .annotator-wrapper .annotator-modal-wrapper .left { float: left; =
width: 50%; }
}

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .right, .sbo-in=
page-toc .annotator-wrapper .annotator-modal-wrapper .right { float: right;=
 }

@media screen and (min-width: 45.0625em) {
  #sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .right, .sbo-=
inpage-toc .annotator-wrapper .annotator-modal-wrapper .right { width: 50%;=
 }
}

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .sans, .sbo-inp=
age-toc .annotator-wrapper .annotator-modal-wrapper .sans { font: 500 0.9em=
/1.2 "Source Sans Pro"; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper a, .sbo-inpage-=
toc .annotator-wrapper .annotator-modal-wrapper a { white-space: initial; c=
olor: rgb(246, 93, 34); border-bottom: none !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper a:focus, #sbo-r=
t-content .annotator-wrapper .annotator-modal-wrapper a:hover, .sbo-inpage-=
toc .annotator-wrapper .annotator-modal-wrapper a:focus, .sbo-inpage-toc .a=
nnotator-wrapper .annotator-modal-wrapper a:hover { text-shadow: transparen=
t 0px 0px 0px; text-decoration: underline; background: no-repeat; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper a.edit-highligh=
t, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper a.edit-highl=
ight { color: rgb(64, 64, 64); top: 0px; right: 20px; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper a.button, .sbo-=
inpage-toc .annotator-wrapper .annotator-modal-wrapper a.button { padding: =
10px 25px; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-dele=
te, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .annotator-=
delete { width: auto; color: rgb(255, 255, 255); }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-dele=
te:hover, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .anno=
tator-delete:hover { background: linear-gradient(rgb(245, 197, 23) 0px, rgb=
(246, 93, 34) 100%) rgb(246, 93, 34); text-decoration: none; color: rgb(255=
, 255, 255) !important; text-shadow: transparent 0px 0px 0px !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .grey-btn, .sbo=
-inpage-toc .annotator-wrapper .annotator-modal-wrapper .grey-btn { width: =
auto; position: relative; top: 10px; background: no-repeat rgb(199, 194, 18=
6) !important; color: rgb(255, 255, 255) !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .grey-btn:hover=
, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .grey-btn:hov=
er { text-decoration: none; color: rgb(7, 7, 7) !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .close, .sbo-in=
page-toc .annotator-wrapper .annotator-modal-wrapper .close { width: 20px; =
height: 20px; background: url("/static/images/close.862fc3a7237a.png") no-r=
epeat; display: block; text-indent: -99999px; position: absolute; right: 20=
px; top: 16px; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .close:focus, #=
sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .close:hover, .s=
bo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .close:focus, .sb=
o-inpage-toc .annotator-wrapper .annotator-modal-wrapper .close:hover { opa=
city: 0.8; background: url("/static/images/close.862fc3a7237a.png") no-repe=
at; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .social-sharing=
, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .social-shari=
ng { float: right; text-align: right; margin: 15px 0px 0px !important; padd=
ing: 0px !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .social-sharing=
 li, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .social-sh=
aring li { margin: 0px 0px 0px 10px !important; }

@media screen and (max-width: 32.5625em) {
  #sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .social-shari=
ng, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .social-sha=
ring { float: none; text-align: center; padding: 0px !important; }
}

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .annotator-=
widget { width: 100%; left: auto; bottom: auto; position: relative; float: =
left; margin: 0px; padding: 10px 25px; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et .delete-confirm, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wra=
pper .annotator-widget .delete-confirm { text-align: center; padding: 15px =
35px 25px; color: rgb(119, 119, 119); font: 400 0.9em/1.3 "Source Sans Pro"=
, arial, sans-serif !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et .annotator-controls .link-to-markdown, .sbo-inpage-toc .annotator-wrappe=
r .annotator-modal-wrapper .annotator-widget .annotator-controls .link-to-m=
arkdown { margin-top: -14px; line-height: 22px; padding: 0px 8px; position:=
 absolute; right: 25px; color: rgb(246, 93, 34); font-size: 14px; border: 1=
px solid rgb(187, 187, 187) !important; }

@media screen and (max-width: 32.5625em) {
  #sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-wi=
dget, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .annotato=
r-widget { padding: 10px 15px; }
}

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et .comment, #sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .a=
nnotator-widget .selected, .sbo-inpage-toc .annotator-wrapper .annotator-mo=
dal-wrapper .annotator-widget .comment, .sbo-inpage-toc .annotator-wrapper =
.annotator-modal-wrapper .annotator-widget .selected { padding: 0px; color:=
 rgb(119, 119, 119); overflow: hidden; font: 400 0.9em/1.3 "Source Sans Pro=
", arial, sans-serif !important; background-color: rgb(255, 255, 255) !impo=
rtant; }

@media screen and (max-width: 32.5625em) {
  #sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-wi=
dget .comment, #sbo-rt-content .annotator-wrapper .annotator-modal-wrapper =
.annotator-widget .selected, .sbo-inpage-toc .annotator-wrapper .annotator-=
modal-wrapper .annotator-widget .comment, .sbo-inpage-toc .annotator-wrappe=
r .annotator-modal-wrapper .annotator-widget .selected { padding: 0px 0px 1=
2px !important; }
}

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et .comment, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .a=
nnotator-widget .comment { padding: 8px 0px; font: 200 1em/1.3 "Source Sans=
 Pro", arial, sans-serif !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et .annotator-listing, .sbo-inpage-toc .annotator-wrapper .annotator-modal-=
wrapper .annotator-widget .annotator-listing { padding: 0px !important; mar=
gin: 0px !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et .annotator-listing .annotator-item, .sbo-inpage-toc .annotator-wrapper .=
annotator-modal-wrapper .annotator-widget .annotator-listing .annotator-ite=
m { list-style-type: none; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et textarea, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .a=
nnotator-widget textarea { clear: both; max-width: 100%; color: rgb(153, 15=
3, 153); padding: 10px; font: 400 0.875em/1.3 "Source Sans Pro", arial, san=
s-serif; }

@media screen and (max-width: 32.5625em) {
  #sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-wi=
dget textarea, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper =
.annotator-widget textarea { background-color: rgb(238, 238, 238); }
  #sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-wi=
dget textarea:focus, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wr=
apper .annotator-widget textarea:focus { background-color: rgb(246, 246, 24=
6); }
}

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et .annotator-controls, .sbo-inpage-toc .annotator-wrapper .annotator-modal=
-wrapper .annotator-widget .annotator-controls { text-align: center; paddin=
g: 0px; margin: 0px !important; background-color: rgb(255, 255, 255) !impor=
tant; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et .annotator-controls ul, .sbo-inpage-toc .annotator-wrapper .annotator-mo=
dal-wrapper .annotator-widget .annotator-controls ul { width: 100%; display=
: block; margin: 10px 0px 0px; float: left; padding: 0px !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et .annotator-controls ul li, .sbo-inpage-toc .annotator-wrapper .annotator=
-modal-wrapper .annotator-widget .annotator-controls ul li { display: inlin=
e-block; text-decoration: none; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et .annotator-controls ul li.delete, .sbo-inpage-toc .annotator-wrapper .an=
notator-modal-wrapper .annotator-widget .annotator-controls ul li.delete { =
float: left; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et .annotator-controls ul li.delete a, .sbo-inpage-toc .annotator-wrapper .=
annotator-modal-wrapper .annotator-widget .annotator-controls ul li.delete =
a { margin-left: 0px; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et .annotator-controls ul li.cancel, #sbo-rt-content .annotator-wrapper .an=
notator-modal-wrapper .annotator-widget .annotator-controls ul li.save, .sb=
o-inpage-toc .annotator-wrapper .annotator-modal-wrapper .annotator-widget =
.annotator-controls ul li.cancel, .sbo-inpage-toc .annotator-wrapper .annot=
ator-modal-wrapper .annotator-widget .annotator-controls ul li.save { float=
: right; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et .annotator-controls p, .sbo-inpage-toc .annotator-wrapper .annotator-mod=
al-wrapper .annotator-widget .annotator-controls p { background-color: rgb(=
255, 255, 255) !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et .annotator-controls a, .sbo-inpage-toc .annotator-wrapper .annotator-mod=
al-wrapper .annotator-widget .annotator-controls a { display: inline-block;=
 padding: 5px 25px; color: rgb(255, 255, 255); transition: all 0.2s ease-in=
-out 0s; -webkit-appearance: none !important; font-family: "Source Sans Pro=
" !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et .annotator-controls a.annotator-cancel, .sbo-inpage-toc .annotator-wrapp=
er .annotator-modal-wrapper .annotator-widget .annotator-controls a.annotat=
or-cancel { background: no-repeat rgb(199, 194, 186) !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et .annotator-controls a.positive, .sbo-inpage-toc .annotator-wrapper .anno=
tator-modal-wrapper .annotator-widget .annotator-controls a.positive { -web=
kit-appearance: none; color: rgb(255, 255, 255); margin-left: 12px; border:=
 none; background: rgb(246, 93, 34); text-shadow: rgba(0, 0, 0, 0.4) 0px 1p=
x 6px !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et .annotator-controls a.positive:focus, #sbo-rt-content .annotator-wrapper=
 .annotator-modal-wrapper .annotator-widget .annotator-controls a.positive:=
hover, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wrapper .annotat=
or-widget .annotator-controls a.positive:focus, .sbo-inpage-toc .annotator-=
wrapper .annotator-modal-wrapper .annotator-widget .annotator-controls a.po=
sitive:hover { background: linear-gradient(rgb(245, 197, 23) 0px, rgb(246, =
93, 34) 100%) rgb(246, 93, 34); color: rgb(255, 255, 255) !important; text-=
shadow: transparent 0px 0px 0px !important; }

#sbo-rt-content .annotator-wrapper .annotator-modal-wrapper .annotator-widg=
et .annotator-controls a:focus, #sbo-rt-content .annotator-wrapper .annotat=
or-modal-wrapper .annotator-widget .annotator-controls a:hover, .sbo-inpage=
-toc .annotator-wrapper .annotator-modal-wrapper .annotator-widget .annotat=
or-controls a:focus, .sbo-inpage-toc .annotator-wrapper .annotator-modal-wr=
apper .annotator-widget .annotator-controls a:hover { background-color: rgb=
(199, 194, 186) !important; text-decoration: none !important; color: rgb(64=
, 64, 64) !important; }

@media screen and (min-width: 45em) {
  .touch .annotator-modal-wrapper { position: absolute !important; margin-t=
op: 200px !important; }
}

.annotator-touch-controls { width: 100%; text-align: center; min-width: aut=
o; z-index: 9999; }

.annotator-touch-controls .animateIn { animation-name: animateIn; animation=
-duration: 0.35s; animation-timing-function: ease-in-out; visibility: visib=
le; }

.annotator-touch-controls .annotator-edit { background-color: rgb(245, 245,=
 245); position: absolute; right: -25px; border-radius: 2px 0px 0px 2px; ba=
ckground-clip: padding-box; }

.annotator-touch-controls.annotator-touch-hide { right: -9999em; opacity: 0=
; }

.annotator-touch-controls .annotator-add { padding: 0.5rem; border-radius: =
2px; background-clip: padding-box; background-color: rgb(119, 119, 119); co=
lor: rgb(255, 255, 255); position: absolute; margin-left: -20px; left: 50%;=
 width: 48px; height: 45px; cursor: pointer; border-bottom: none; box-shado=
w: rgb(205, 205, 205) 0px 0px 1px; display: block; text-align: center; }

.annotator-touch-controls .annotator-add::after, .annotator-touch-controls =
.annotator-add::before { width: 0px; height: 0px; border-width: 0.65em; bor=
der-style: solid; border-image: initial; border-color: rgb(119, 119, 119) r=
gb(119, 119, 119) transparent transparent; transform: rotate(-45deg); conte=
nt: ""; left: 14px; top: -10px; position: absolute; }

.annotator-touch-controls .annotator-add::before { top: -11px; border-color=
: rgb(205, 205, 205) rgb(205, 205, 205) transparent transparent; }

.annotator-touch-controls .annotator-add span { display: block; }

.annotator-touch-controls .annotator-add span::before { font-family: SSFlow=
; content: "=EF=9C=87"; height: 48px; width: 49px; font-size: 1.625rem; top=
: 5px; position: relative; color: rgb(255, 255, 255); }

.card-annotation { color: rgba(64, 64, 64, 0.65); }

.card-annotation .wrap-pod { max-width: 800px; margin: 0px auto; }

.card-annotation .pod { float: left; padding: 1.25rem 1.25rem 1.875rem; }

@media screen and (max-width: 32.5625em) {
  .card-annotation .pod { margin: 0px 0px 1.25rem; }
}

.card-annotation .pod h2 { margin: 5px 0px 20px; font-size: 21px; color: rg=
ba(74, 60, 49, 0.75); }

.card-annotation form textarea { display: block; max-width: 100%; width: 10=
0%; }

.card-annotation form [type=3D"submit"] { margin-left: 0.9375rem; }

.card-annotation form ul.delete-option { margin-top: 20px; }

.card-annotation form ul.delete-option input { margin: 0px; font-size: 14px=
; }

.card-annotation form ul.buttons { margin-top: 15px; }

.card-annotation form ul#id_privacy_option li { margin-left: 0.625rem; }

.card-annotation form ul.privacy-options li label { font-size: 1rem; }

.card-annotation form ul li { display: inline-block; }

.card-annotation form ul li input { margin: 0px 5px; }

.card-annotation .popup { overflow: hidden; color: rgb(119, 119, 119); back=
ground-color: rgb(255, 255, 255); border-radius: 2px; background-clip: padd=
ing-box; clear: both; width: 600px; position: fixed; z-index: 9999; transit=
ion: opacity 0.15s ease-in-out 0s; border: 1px solid rgb(204, 204, 204); bo=
x-shadow: rgb(230, 230, 230) 0px 3px 0px; top: 200px; left: 50%; margin-lef=
t: -300px; font-family: "source sans pro", Helvetica, Arial, sans-serif !im=
portant; }

.card-annotation .popup h1 { margin: 0px; color: rgb(119, 119, 119); font-s=
ize: 1.625rem; padding: 0.9375rem; line-height: 1em; font-weight: 500; floa=
t: left !important; }

.card-annotation .popup .headline { width: 100%; float: left; border-bottom=
: 1px solid rgb(204, 204, 204); }

@media screen and (max-width: 40.625em) {
  .card-annotation .popup { max-width: 95%; margin: 0px 2.5%; left: 0px; }
}

.card-annotation .popup .inner { padding: 0px 20px 20px; float: left; width=
: 100%; }

.card-annotation .popup ul { float: right; }

.card-annotation .popup ul li { display: inline-block; margin-left: 15px; }

.card-annotation .media-thumbnail { float: left; margin: 0px 0.9375rem 0.62=
5rem 0px; }

.card-annotation .annotation-note { margin: 0px 0px 0.65em; word-break: bre=
ak-all; }

.card-annotation .clear { clear: both; }

.card-annotation .left { float: left; margin: 0px; }

@media screen and (min-width: 32.5625em) {
  .card-annotation .left { width: 50%; }
}

.card-annotation .right { float: right; margin: 0px; }

@media screen and (max-width: 32.5625em) {
  .card-annotation .right { float: none; text-align: center; }
}

.card-annotation .row { border-top: 1px solid rgb(221, 221, 221); display: =
block; padding-top: 0.625rem; margin: 0px 0px 0.625rem; float: left; width:=
 100%; }

.card-annotation .note.quote, .card-annotation .row.border { margin-bottom:=
 0px; }

.card-annotation div.quote { padding-bottom: 0.9375rem; }

.card-annotation .note { color: rgb(136, 136, 136); padding-bottom: 0.5rem;=
 display: inline-block; }

.card-annotation .social-sharing { text-align: center; margin-top: 0.9375re=
m; }

.card-annotation .social-sharing li { margin: 0.625rem 0.625rem 0px; }

.card-annotation .sign-up { text-align: center; padding: 0px 7.5rem; }

.card-annotation .sign-up h1 { padding-bottom: 0px; margin-bottom: 0px; }

.card-annotation .sign-up > p { margin-top: 10px; }

@media screen and (max-width: 51.3125em) {
  .card-annotation .sign-up { padding: 0px; }
}

.card-annotation .annotation-quote { color: rgba(64, 64, 64, 0.75); font-fa=
mily: Georgia, serif; margin: 0px; }

.card-annotation .annotation-quote::before { content: "=E2=80=9C"; float: l=
eft; font-size: 50px; }

.card-annotation .annotation-quote::after { content: "=E2=80=9D"; float: ri=
ght; font-size: 50px; }

.ios-app-teaser { position: relative; height: 40px; margin: 0px 1.25rem -5p=
x; }

@media only screen and (max-width: 520px) {
  .ios-app-teaser { margin: 0px 1.25rem -5px; }
}

.ios-app-teaser ul { background: rgb(64, 64, 64); }

.ios-app-teaser ul::after, .ios-app-teaser ul::before { content: " "; displ=
ay: table; }

.ios-app-teaser ul::after { clear: both; }

.ios-app-teaser ul li { list-style: none; float: left; width: 50%; text-ali=
gn: center; font-size: 16px; vertical-align: middle; }

.ios-app-teaser ul li:active, .ios-app-teaser ul li:focus, .ios-app-teaser =
ul li:hover { background: rgb(27, 26, 26); transition: background 0.7s ease=
 0s; }

.ios-app-teaser ul li a { display: block; color: rgb(255, 255, 255); font-w=
eight: 300; padding: 10px 0px; }

.ios-app-teaser ul li a:active, .ios-app-teaser ul li a:focus, .ios-app-tea=
ser ul li a:hover { text-decoration: none; color: rgb(255, 255, 255); }

.sbo-toc .ios-app-teaser { display: none; margin: 0px; }

.sbo-toc.has-ios-app-teaser .ios-app-teaser { display: block; }

.sbo-toc.has-ios-app-teaser .close { top: 40px; }

body.night-mode .sbo-toc .ios-app-teaser ul { background: rgb(34, 34, 34); =
border-bottom: 1px solid rgb(68, 68, 68); }

body.night-mode .sbo-toc .ios-app-teaser ul li:active, body.night-mode .sbo=
-toc .ios-app-teaser ul li:focus, body.night-mode .sbo-toc .ios-app-teaser =
ul li:hover { background: rgb(7, 7, 7); }

.pagefoot { font-family: "source sans pro", sans-serif; font-size: 0.875rem=
; color: rgb(119, 119, 119); line-height: 1.25em; }

.pagefoot .copyright { display: block; margin: 0.3em 0px; }

@media screen and (min-width: 32.5625em) {
  .pagefoot .copyright { display: inline; }
}

.pagefoot a { color: rgb(64, 64, 64); }

.pagefoot a:active, .pagefoot a:focus, .pagefoot a:hover, .pagefoot li a { =
color: rgb(246, 93, 34); }

.pagefoot li { display: inline-block; line-height: 1.5em; }

.pagefoot li::after { content: " / "; }

.pagefoot li:last-child::after, .subscribe-nag .promotion strike::before { =
content: ""; }

.user-anon .pagefoot { margin-top: 1em; }

.user-anon .pagefoot a { color: rgb(119, 119, 119); }

.user-anon .pagefoot li a { color: rgb(214, 67, 9); }

.pagefoot .icon-up { display: block; padding: 10px; position: fixed; right:=
 20px; bottom: 20px; z-index: 99999; text-transform: lowercase; border: 1px=
 solid rgb(204, 204, 204); border-radius: 2px; background-clip: padding-box=
; background-color: rgb(213, 213, 213); text-decoration: none; }

.course-nag .close, .course-nag .message, .pagination-label, h1.video-toc-t=
itle { text-transform: uppercase; }

.pagefoot .icon-up span { display: none; }

.pagefoot .icon-up::before { font-size: 19px; content: "=E2=AC=86"; font-fa=
mily: SSFlow; display: inline-block; vertical-align: middle; color: rgb(119=
, 119, 119); }

.subscribe-panel .pagefoot .icon-up { bottom: 80px; }

.user-anon .pagefoot #legal, .user-anon .pagefoot nav { margin: 0.3125rem 0=
px 0.3125rem 3.4375rem; line-height: 1.15em; }

.user-anon .pagefoot nav a { text-decoration: none; }

.user-anon .pagefoot div#legal a { color: rgb(119, 119, 119); text-decorati=
on: none; }

.full-support, .pagefoot .full-support { display: none; }

@media screen and (min-width: 48.0625em) {
  .full-support, .pagefoot .full-support { display: inline-block; }
  .mobile-support, .pagefoot .mobile-support { display: none; }
}

.subscribe-nag.collapsed .expanded, .subscribe-nag.promotion-included .page=
foot { display: none; }

#js-subscribe-panel-filler { float: left; width: 100%; }

.subscribe-nag { position: fixed; width: 100%; max-width: 100%; padding: 0p=
x 10px; bottom: -300%; max-height: 50%; left: 0px; z-index: 99999; margin: =
0px; background-color: rgb(255, 255, 255); box-shadow: rgba(0, 0, 0, 0.2) 0=
px 0px 20px 0px; border-top: 1px solid rgb(204, 204, 204); text-align: cent=
er; }

.subscribe-nag .cta-group { padding-bottom: 15px; }

.subscribe-nag.expired-panel, .subscribe-nag.trial-panel { max-height: 350p=
x; }

.subscribe-nag.promotion-included { max-height: 515px; color: rgb(255, 255,=
 255); }

.subscribe-nag.collapsed p { margin: 12px 0px; }

.subscribe-nag h2, .subscribe-nag h3 { line-height: 1.1em; color: rgb(64, 6=
4, 64); font-size: 2.25rem; font-weight: 300; margin: 1.25rem 3rem; }

.subscribe-nag p { color: rgb(74, 60, 49); }

.subscribe-nag h3 { font-size: 1.5rem; }

.subscribe-nag .green { color: rgb(246, 93, 34); }

.subscribe-nag .js-toggle-nag { position: absolute; text-align: center; lin=
e-height: 1.3em; right: 0px; top: 0px; color: rgb(136, 136, 136); font-size=
: 1.125rem; text-decoration: none; z-index: 10; padding: 0.9375rem 0.9375re=
m 0.75rem; }

.subscribe-nag .js-toggle-nag:focus, .subscribe-nag .js-toggle-nag:hover { =
background-color: rgb(246, 93, 34); color: rgb(255, 255, 255); text-decorat=
ion: none; }

.subscribe-nag.expanded { position: absolute; }

.subscribe-nag.collapsed .sample-message { padding: 0px; }

.subscribe-nag.collapsed h2 { font-size: 1.5rem; margin: 0.625rem 3rem 0.93=
75rem; }

.subscribe-nag.slideUp { animation-name: slideUp; animation-duration: 0.5s;=
 animation-timing-function: ease; bottom: 0px !important; visibility: visib=
le !important; }

.subscribe-nag a { text-decoration: none; }

.subscribe-nag .promotion { background-color: rgb(0, 0, 0); padding: 20px 1=
0px; margin-bottom: 20px; position: relative; }

.subscribe-nag .promotion strike { position: relative; text-decoration: non=
e; }

.subscribe-nag .promotion strike::before { border-bottom: 4px solid rgb(252=
, 71, 71); position: absolute; width: 115%; top: 46%; transform: rotate(-14=
deg); left: -6%; }

.subscribe-nag .promotion h1 { color: rgb(245, 197, 23); font-family: "Stag=
 Web", georgia, serif; font-weight: 400; font-style: normal; font-stretch: =
normal; font-size: 2.5em; }

.subscribe-nag .promotion h2 { color: rgb(255, 255, 255); margin-top: 10px;=
 }

.subscribe-nag .promotion b { font-weight: 700; }

.subscribe-nag .promotion .button { background: no-repeat rgb(255, 255, 255=
); text-shadow: none; border-radius: 0px; color: rgb(51, 51, 51); padding: =
10px 20px; }

.subscribe-nag .promotion .callout { position: absolute; right: 0px; top: 0=
px; }

.subscribe-nag .promotion .callout img { width: 30%; float: right; }

.subscribe-nag .promotion .callout .accessible-text { position: relative; t=
ext-indent: -9999px; display: block; }

@media screen and (max-width: 56.25em) {
  .subscribe-nag .promotion h1, .subscribe-nag .promotion h2, .subscribe-na=
g .promotion h3 { font-size: 2em; }
}

@media screen and (max-width: 48em) {
  .subscribe-nag .promotion h1, .subscribe-nag .promotion h2, .subscribe-na=
g .promotion h3 { font-size: 1.5em; }
}

.subscribe-nag .help { font-size: smaller; text-decoration: none; }

.subscribe-nag .trending-topics { margin: 0px; }

.subscribe-nag .old-price { text-decoration: line-through; }

.course-nag .close:hover, .subscribe-nag .sample-message .cta-group .signin=
 a { text-decoration: none; }

.subscribe-nag .bigbutton.loading, .subscribe-nag .bigbutton.loading:hover =
{ background-color: rgb(178, 180, 179); background-image: none; }

.subscribe-nag .bigbutton.loading .spinner, .subscribe-nag .bigbutton.loadi=
ng:hover .spinner { background: url("/static/images/loading.6b1710a5f2bc.gi=
f") center center / 16px no-repeat; width: 16px; display: inline-block; tex=
t-indent: -9999px; float: right; }

.subscribe-nag .bigbutton .spinner { display: none; }

.subscribe-nag .pagefoot #legal a.copyright, .subscribe-nag .pagefoot nav a=
.copyright { color: rgb(119, 119, 119); }

.subscribe-nag.anon-panel h2, .subscribe-nag.anon-panel h3 { margin: 0.625r=
em 0.75rem; }

@media screen and (max-width: 48em) {
  .subscribe-nag.anon-panel .doc-title { display: none; }
  .subscribe-nag.anon-panel .doc-type { white-space: nowrap; }
}

.subscribe-nag .sample-message { margin: 0px auto; padding: 0.3125rem 1.25r=
em 0px; border-radius: 0px; background-clip: padding-box; box-shadow: trans=
parent 0px 0px 0px; border: none; max-width: 56.25rem; position: relative; =
color: rgb(74, 60, 49); }

.subscribe-nag .sample-message .cta-group .bigbutton { display: inline-bloc=
k; }

.subscribe-nag .sample-message .cta-group .signin { display: inline-block; =
font-size: smaller; }

.subscribe-nag .sample-message .text-links { display: inline-block; margin:=
 0px 0px 0px 10px; vertical-align: middle; }

.subscribe-nag .sample-message p { max-width: 34.375rem; font-size: 1.125re=
m; line-height: 1.5rem; margin: 10px auto 15px; font-weight: 500; }

.subscribe-nag .sample-message footer { text-align: left; margin: 0.9375rem=
 0px 0.625rem; padding: 0px; }

.subscribe-nag .sample-message footer object { display: none; }

.subscribe-nag .sample-message footer #logo { background: url("/static/imag=
es/sunshine_flag.0e1a4eec8506.svg") right -10px / 45px 66px no-repeat; widt=
h: 45px; height: 42px; margin-top: -12px; margin-right: 10px; text-indent: =
-9999px; display: block; float: left; padding-bottom: 3.75rem; }

@media screen and (max-width: 32.5em) {
  .subscribe-nag .sample-message footer #logo { display: none; }
}

.subscribe-nag .sample-message.nag-a, .subscribe-nag .sample-message.nag-b =
{ max-width: 85rem; padding: 0px; transition: all 0.5s ease-in-out 0s; }

.subscribe-nag .sample-message.nag-a h2, .subscribe-nag .sample-message.nag=
-b h2 { text-align: left; margin-left: 0px; }

.subscribe-nag .sample-message.nag-a .doc-title, .subscribe-nag .sample-mes=
sage.nag-b .doc-title { display: none; }

.subscribe-nag .sample-message.nag-a .cta-group, .subscribe-nag .sample-mes=
sage.nag-b .cta-group { display: inline-block; }

.subscribe-nag .sample-message.nag-a .cta-group .bigbutton, .subscribe-nag =
.sample-message.nag-b .cta-group .bigbutton { width: 45%; padding: 10px; fo=
nt-size: 1rem; font-weight: 400; float: left; }

.subscribe-nag .sample-message.nag-a .cta-group .bigbutton.team-btn, .subsc=
ribe-nag .sample-message.nag-b .cta-group .bigbutton.team-btn { width: 45%;=
 margin-right: 0px; }

.subscribe-nag .sample-message.nag-a .cta-group div.bigbutton, .subscribe-n=
ag .sample-message.nag-b .cta-group div.bigbutton { display: none; }

.subscribe-nag .sample-message.nag-a .cta-group .signin, .subscribe-nag .sa=
mple-message.nag-b .cta-group .signin { width: 100%; margin: 5px 0px; }

.subscribe-nag .sample-message.nag-a .registration-form, .subscribe-nag .sa=
mple-message.nag-b .registration-form { float: left; text-align: left; }

.subscribe-nag .sample-message.nag-a .registration-form li, .subscribe-nag =
.sample-message.nag-b .registration-form li { display: inline-block; width:=
 31.5%; margin-right: 2%; vertical-align: top; }

.subscribe-nag .sample-message.nag-a .registration-form li.password, .subsc=
ribe-nag .sample-message.nag-b .registration-form li.password { margin-righ=
t: 0px; }

.subscribe-nag .sample-message.nag-a .registration-form li input, .subscrib=
e-nag .sample-message.nag-b .registration-form li input { max-width: 100%; =
min-width: 100%; }

.subscribe-nag .sample-message.nag-a .registration-form li.error input, .su=
bscribe-nag .sample-message.nag-b .registration-form li.error input { margi=
n-bottom: 0px; }

.subscribe-nag .sample-message.nag-a .registration-form .terms-conditions, =
.subscribe-nag .sample-message.nag-b .registration-form .terms-conditions {=
 display: none; width: 100% !important; }

.subscribe-nag .sample-message.nag-a .registration-form .terms-conditions i=
nput, .subscribe-nag .sample-message.nag-a .registration-form .terms-condit=
ions label, .subscribe-nag .sample-message.nag-b .registration-form .terms-=
conditions input, .subscribe-nag .sample-message.nag-b .registration-form .=
terms-conditions label { margin: 0px 10px 10px 0px; display: inline-block !=
important; }

.subscribe-nag .sample-message.nag-a .registration-form .terms-conditions .=
error, .subscribe-nag .sample-message.nag-b .registration-form .terms-condi=
tions .error { display: block; }

.subscribe-nag .sample-message.nag-a.active .terms-conditions, .subscribe-n=
ag .sample-message.nag-b.active .terms-conditions { display: block; float: =
left; }

.subscribe-nag .sample-message.nag-a.active .terms-conditions label, .subsc=
ribe-nag .sample-message.nag-b.active .terms-conditions label { width: 90%;=
 }

.subscribe-nag .sample-message.nag-a.active .terms-conditions #id_legal, .s=
ubscribe-nag .sample-message.nag-b.active .terms-conditions #id_legal { ver=
tical-align: top; margin: 3px 10px 0px 0px; }

.subscribe-nag .sample-message.nag-a.active .doc-title, .subscribe-nag .sam=
ple-message.nag-b.active .doc-title { display: inline-block; }

.subscribe-nag .sample-message.nag-a.active .team-btn, .subscribe-nag .samp=
le-message.nag-b .cta-group button, .subscribe-nag .sample-message.nag-b.ac=
tive .team-btn { display: none; }

.subscribe-nag .sample-message.nag-a.active .bigbutton, .subscribe-nag .sam=
ple-message.nag-b.active .bigbutton { width: 100%; }

.subscribe-nag .sample-message.nag-a .registration-form { width: 69%; }

.subscribe-nag .sample-message.nag-a .cta-group { width: 30%; float: right;=
 }

.subscribe-nag .sample-message.nag-a .cta-group .bigbutton, .subscribe-nag =
.sample-message.nag-a .cta-group .team-btn { width: 100%; line-height: init=
ial; }

.subscribe-nag .sample-message.nag-b .registration-form { width: 85%; displ=
ay: none; }

.subscribe-nag .sample-message.nag-b h2 { margin: 1rem 0px 1rem 7%; float: =
left; width: 50%; }

.subscribe-nag .sample-message.nag-b form { width: 75%; margin: 1rem auto; =
}

.subscribe-nag .sample-message.nag-b .cta-group { width: 35%; float: right;=
 margin: 0.5rem 0px 1rem 2%; }

.subscribe-nag .sample-message.nag-b .cta-group div.bigbutton { display: bl=
ock; width: 100%; margin: 0px 0px 10px; }

.subscribe-nag .sample-message.nag-b .cta-group div.bigbutton.mobile { disp=
lay: none; }

.subscribe-nag .sample-message.nag-b.active h2 { width: 73%; margin: 1rem a=
uto; float: none; }

.subscribe-nag .sample-message.nag-b.active form { margin: 0px auto; }

.subscribe-nag .sample-message.nag-b.active .registration-form { display: b=
lock; width: 100%; }

.subscribe-nag .sample-message.nag-b.active .registration-form li { width: =
50%; margin-right: 0px; float: left; padding: 0px 1%; }

.subscribe-nag .sample-message.nag-b.active .registration-form_item.email {=
 width: 100%; display: block; }

.subscribe-nag .sample-message.nag-b.active .cta-group button { display: bl=
ock; }

.subscribe-nag .sample-message.nag-b.active .cta-group div.bigbutton { disp=
lay: none; }

@media screen and (max-width: 50em) {
  .subscribe-nag .sample-message.nag-a, .subscribe-nag .sample-message.nag-=
b { padding: 0px 10%; }
  .subscribe-nag .sample-message.nag-a h2, .subscribe-nag .sample-message.n=
ag-b h2 { display: none; }
  .subscribe-nag .sample-message.nag-a .registration-form, .subscribe-nag .=
sample-message.nag-b .registration-form { display: none; float: none; paddi=
ng: 1.5rem 16.5% 0.5rem; width: 100%; }
  .subscribe-nag .sample-message.nag-a .registration-form li, .subscribe-na=
g .sample-message.nag-b .registration-form li { display: block; width: 100%=
; }
  .subscribe-nag .sample-message.nag-a form, .subscribe-nag .sample-message=
.nag-b form { margin-bottom: 0.75rem; }
  .subscribe-nag .sample-message.nag-a .cta-group, .subscribe-nag .sample-m=
essage.nag-b .cta-group { width: 100%; padding: 1.5rem 16.5% 0px; margin: 0=
px; }
  .subscribe-nag .sample-message.nag-a .cta-group div.bigbutton, .subscribe=
-nag .sample-message.nag-b .cta-group div.bigbutton { display: block; margi=
n: 0px 0px 10px; }
  .subscribe-nag .sample-message.nag-a .cta-group button, .subscribe-nag .s=
ample-message.nag-b .cta-group button { display: none; font-family: "source=
 sans pro", sans-serif; margin: 0px; }
  .subscribe-nag .sample-message.nag-a.active h2, .subscribe-nag .sample-me=
ssage.nag-b.active h2 { display: block; padding: 1.5rem 16.5% 0px; margin: =
0px; }
  .subscribe-nag .sample-message.nag-a.active .registration-form, .subscrib=
e-nag .sample-message.nag-b.active .registration-form { display: block; }
  .subscribe-nag .sample-message.nag-a.active .doc-title, .subscribe-nag .s=
ample-message.nag-b.active .doc-title { display: none; }
  .subscribe-nag .sample-message.nag-a.active .terms-conditions input, .sub=
scribe-nag .sample-message.nag-b.active .terms-conditions input { margin: 4=
px 10px 0px 0px; vertical-align: top; }
  .subscribe-nag .sample-message.nag-a.active .terms-conditions label, .sub=
scribe-nag .sample-message.nag-b.active .terms-conditions label { width: 90=
%; }
  .subscribe-nag .sample-message.nag-b form, .subscribe-nag .sample-message=
.nag-b.active h2 { width: 100%; }
  .subscribe-nag .sample-message.nag-a.active .cta-group, .subscribe-nag .s=
ample-message.nag-b.active .cta-group { padding: 0px 16.5%; }
  .subscribe-nag .sample-message.nag-a.active .cta-group button, .subscribe=
-nag .sample-message.nag-b.active .cta-group button { display: block; }
  .subscribe-nag .sample-message.nag-a.active .cta-group div.bigbutton, .su=
bscribe-nag .sample-message.nag-b.active .cta-group div.bigbutton { display=
: none; }
  .subscribe-nag .sample-message.nag-b .cta-group { padding: 0px; margin: 0=
px 0px 10px; }
  .subscribe-nag .sample-message.nag-b .cta-group div.bigbutton.mobile { di=
splay: inline-block; float: none; }
  .subscribe-nag .sample-message.nag-b .cta-group div.bigbutton, .subscribe=
-nag .sample-message.nag-b.active .cta-group div.bigbutton.mobile { display=
: none; }
  .subscribe-nag .sample-message.nag-b .cta-group .signin { margin: 0px; wi=
dth: 100%; }
  .subscribe-nag .sample-message.nag-b.active .registration-form li { width=
: 100% !important; }
  .subscribe-nag .sample-message.nag-b.active .cta-group { padding: 0px 17%=
; }
  .subscribe-nag .sample-message .text-links { display: block; margin: 10px=
 0px 0px; }
}

.subscribe-nag p.welcome { font-size: 1.5rem; margin: 1.5rem 0px; font-weig=
ht: 300; }

.subscribe-nag .registration-form__minimize::before { content: "=E2=90=A1";=
 font-family: SSFlow; position: absolute; }

.subscribe-nag .registration-form__minimize, .subscribe-nag .registration-f=
orm__minimize__title { display: none; }

.subscribe-nag .registration-form__minimize.active { position: absolute; di=
splay: block; width: 20px; height: 20px; right: 20px; top: 5px; z-index: 10=
; cursor: pointer; }

@media screen and (max-width: 32.5625em), screen and (max-height: 25.0625em=
) {
  .subscribe-nag.collapsed .header { margin: 10px 0px; }
  .subscribe-nag.collapsed footer { margin-top: 5px !important; }
  .subscribe-nag h2 { font-size: 1.5rem; }
  .subscribe-nag h3 { font-size: 1.125rem; }
  .subscribe-nag .sample-message .signin { position: relative; right: auto;=
 margin: 0px 0px 0.9375rem; font-size: small; }
  .subscribe-nag .sample-message p { font-size: 1rem; }
  .subscribe-nag .sample-message p.usage-data { padding: 0px 3.125rem; line=
-height: 1.3em; }
  .subscribe-nag .sample-message .bigbutton { margin: 0px 0px 0.625rem; }
  .subscribe-nag .sample-message .comment { margin: -10px auto 0px !importa=
nt; }
  .subscribe-nag footer { text-align: center !important; }
  .subscribe-nag footer #logo { float: none !important; margin: 0px 0px 12p=
x !important; padding: 0px !important; }
  .subscribe-nag footer ul { padding: 0px; margin-top: 5px; font-size: smal=
ler; line-height: 1em; }
}

.cover-position-right { max-width: 100%; max-height: 100%; height: auto; di=
splay: inline-block; }

.academic-text { text-align: left; }

.course-nag, .servererror .pod { text-align: center; }

.academic-text h1 { color: rgb(119, 119, 119); font-family: "source sans pr=
o", sans-serif; font-size: 2.5rem; }

.academic-text h2 { font-size: 1.25rem; }

.academic-text ol li { font-size: 1.125rem; }

#academic-text-bold { font-weight: 700; }

.support-text { margin-top: 20px; }

.support-text p { font-size: 0.875rem; margin: 0px; }

@media screen and (min-width: 1024px) and (orientation: landscape) {
  .cover-position-right { float: right; }
  .academic-text { float: left; }
  .academics-topics { clear: left; }
}

.academic-mailto-link { margin-top: 20px; }

.course-nag { width: 140px; padding: 20px 10px 10px; position: fixed; z-ind=
ex: 9999999; background: rgb(255, 255, 255); top: 15%; right: 0px; box-shad=
ow: rgba(0, 0, 0, 0.1) 0px 0px 15px 4px; font-size: 14px; line-height: 1.3;=
 font-family: "source sans pro", arial, sans-serif; }

.course-nag .close { padding: 1px 7px; position: absolute; top: 0px; right:=
 0px; font-size: 12px; font-weight: 600; color: rgb(255, 255, 255); backgro=
und: rgb(0, 0, 0); }

.course-nag .background { width: 100%; position: absolute; top: 0px; left: =
0px; z-index: -1; }

.course-nag .avatar { margin-bottom: 5px; }

.course-nag .avatar img { width: 100px; height: 100px; border: 2px solid rg=
b(255, 255, 255); border-radius: 50%; }

.course-nag .time { font-weight: 600; }

.course-nag .button { display: block; margin-top: 10px; padding: 7px 4px; f=
ont-size: 13px; }

.course-nag .button.is-streaming-now { color: rgb(0, 133, 66); }

.no-touch .rec-delete:focus, .no-touch .rec-delete:hover, .no-touch .rec-fa=
v:focus, .no-touch .rec-fav:hover, .rec-delete, .rec-fav { background: 0px =
0px; color: rgb(204, 204, 204); }

.rec-delete, .rec-fav { box-shadow: none; line-height: 1; margin: 0px; padd=
ing: 0px; border: none; font-weight: 400; }

.rec-delete:active, .rec-fav:active { top: 0px; }

.django-messages { margin: 1rem 0px; font-family: "source sans pro", sans-s=
erif; }

.django-messages > li { position: relative; padding: 1rem; border-radius: 2=
px; background-clip: padding-box; color: rgb(255, 255, 255); }

@media screen and (max-width: 30em) {
  .django-messages > li { margin: 1rem 0.9375rem; }
}

.django-messages .fixed-position { position: fixed; width: 92%; z-index: 99=
; }

.django-messages .info, .django-messages .success { background: rgb(246, 93=
, 34); font-weight: 400; }

.django-messages .info a, .django-messages .success a { color: rgb(255, 255=
, 255); text-decoration: underline; }

.django-messages .info a.close, .django-messages .success a.close { text-de=
coration: none; }

.django-messages .info::before, .django-messages .success::before { speak: =
none; content: "=E2=9C=93"; position: relative; top: 3px; font-size: 21px; =
padding-right: 1rem; color: rgb(255, 255, 255); font-family: SSFlow; }

.django-messages .success { background: rgb(0, 133, 66); }

.django-messages .warning { background: rgb(129, 92, 0); }

.django-messages .error { background: maroon; }

.django-messages .welcome-banner { background-color: rgb(255, 255, 255); co=
lor: rgb(51, 51, 51); padding: 0.125rem 1rem; }

.django-messages .welcome-banner h2 { margin-bottom: 0px; line-height: 1.15=
em; }

.django-messages .welcome-banner p { margin-top: 10px; }

.django-messages .alert { background-color: rgb(232, 186, 22); color: rgb(2=
55, 255, 255); }

.django-messages .alert::before { content: ""; background: url("/static/ima=
ges/alert.a1ddd023edd3.png") 0% 0% / 25px no-repeat; width: 25px; height: 2=
1px; display: block; margin-top: -3px; }

.django-messages .alert a { color: rgb(255, 255, 255); text-decoration: und=
erline; }

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body.cloudy-mode .search-in-archive.active .search-controls::before { backg=
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body.cloudy-mode .sbo-book-meta, body.cloudy-mode .search-in-archive .searc=
h-archive-bar, body.cloudy-mode .search-in-archive .search-archive-results =
li, body.cloudy-mode .search-in-archive .search-archive-results li.paginati=
on a, body.cloudy-mode .search-in-archive .search-archive-results li.search=
-whole-site a, body.cloudy-mode .search-in-archive .search-archive-results =
ul, body.cloudy-mode .toc-contents, body.cloudy-mode .tocList li { backgrou=
nd-color: rgb(245, 238, 224); }

body.cloudy-mode .search-in-archive .search-archive-results li { border-col=
or: rgb(199, 193, 180); color: rgb(64, 64, 64); }

body.cloudy-mode .search-in-archive .search-archive-results li .description=
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body.cloudy-mode .search-in-archive .search-archive-results li a.title { co=
lor: rgb(64, 64, 64); background-color: rgb(245, 238, 224); }

@media screen and (min-width: 49.4375em) {
  body.cloudy-mode .interface-controls #font-controls, body.cloudy-mode .in=
terface-controls .search-in-archive, body.cloudy-mode .interface-controls b=
utton { border-bottom: 1px solid rgb(199, 193, 180); }
  body.cloudy-mode .interface-control-btns { border: 1px solid rgb(199, 193=
, 180); }
}

body.cloudy-mode .toc-contents { border: 10px solid rgb(199, 193, 180); }

body.cloudy-mode .sbo-book-meta { border-bottom: 1px solid rgb(199, 193, 18=
0); }

body.cloudy-mode .tocList li.currently-reading, body.cloudy-mode .tocList l=
i.currently-reading a { background-color: rgb(234, 231, 219); }

body.cloudy-mode .nav-link, body.cloudy-mode .sbo-menu-top { background-col=
or: rgb(245, 238, 224); }

body.cloudy-mode .sbo-prev .nav-link { border-top: none; border-left: none;=
 border-image: initial; border-right: 1px solid rgb(199, 193, 180); border-=
bottom: 1px solid rgb(199, 193, 180); }

body.cloudy-mode .sbo-menu-top, body.cloudy-mode .sbo-next .nav-link { bord=
er-bottom: 1px solid rgb(199, 193, 180); }

body.cloudy-mode .sbo-menu-top { border-right: 1px solid rgb(199, 193, 180)=
; border-left: 1px solid rgb(199, 193, 180); }

body.cloudy-mode .sbo-next.sbo-nav-bottom, body.cloudy-mode .sbo-prev.sbo-n=
av-bottom { border-top: 1px solid rgb(199, 193, 180); }

body.cloudy-mode .topbar { background-color: rgb(224, 217, 203) !important;=
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body.cloudy-mode .topbar .topnav > li a:hover { background-color: rgb(245, =
238, 224); }

@media screen and (max-width: 32.5625em), (max-height: 26.25em) {
  body.cloudy-mode .sbo-next .nav-link { border-top: none; }
}

body.cloudy-mode #sbo-rt-content { background-color: rgb(245, 238, 224) !im=
portant; }

body.cloudy-mode #sbo-rt-content div, body.cloudy-mode #sbo-rt-content tabl=
e, body.cloudy-mode #sbo-rt-content table th, body.cloudy-mode #sbo-rt-cont=
ent table thead, body.cloudy-mode #sbo-rt-content table tr { background-col=
or: rgb(245, 238, 224) !important; border: none !important; }

body.cloudy-mode #sbo-rt-content .box_title, body.cloudy-mode #sbo-rt-conte=
nt .chaptertitle, body.cloudy-mode #sbo-rt-content .cn-chapter-number, body=
.cloudy-mode #sbo-rt-content .figure-title, body.cloudy-mode #sbo-rt-conten=
t .fm_title_document, body.cloudy-mode #sbo-rt-content .h1, body.cloudy-mod=
e #sbo-rt-content .heading-1, body.cloudy-mode #sbo-rt-content .heading-3, =
body.cloudy-mode #sbo-rt-content .paragraph-head, body.cloudy-mode #sbo-rt-=
content .title, body.cloudy-mode #sbo-rt-content .title_document, body.clou=
dy-mode #sbo-rt-content h1, body.cloudy-mode #sbo-rt-content h2, body.cloud=
y-mode #sbo-rt-content h3, body.cloudy-mode #sbo-rt-content h4, body.cloudy=
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mode #sbo-rt-content hr { background-color: rgb(245, 238, 224); color: rgb(=
64, 64, 64) !important; }

body.cloudy-mode #sbo-rt-content .pre, body.cloudy-mode #sbo-rt-content .pr=
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ent .pre_w, body.cloudy-mode #sbo-rt-content p.pre, body.cloudy-mode #sbo-r=
t-content pre { background-color: rgb(245, 238, 224) !important; color: rgb=
(64, 64, 64) !important; border: none !important; }

body.cloudy-mode #sbo-rt-content a, body.cloudy-mode #sbo-rt-content dt, bo=
dy.cloudy-mode #sbo-rt-content li, body.cloudy-mode #sbo-rt-content p, body=
.cloudy-mode #sbo-rt-content strong { color: rgb(64, 64, 64); box-shadow: n=
one !important; }

body.cloudy-mode #sbo-rt-content div { color: inherit !important; }

body.cloudy-mode #sbo-rt-content div.bgbox dd, body.cloudy-mode #sbo-rt-con=
tent div.bgbox dt, body.cloudy-mode #sbo-rt-content div.bgbox li, body.clou=
dy-mode #sbo-rt-content div.bgbox p, body.cloudy-mode #sbo-rt-content div.b=
oxg dt, body.cloudy-mode #sbo-rt-content div.boxg li, body.cloudy-mode #sbo=
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dy.cloudy-mode #sbo-rt-content div.feature dt, body.cloudy-mode #sbo-rt-con=
tent div.note dd, body.cloudy-mode #sbo-rt-content div.note dt, body.cloudy=
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e p, body.cloudy-mode #sbo-rt-content div.sidebar dd, body.cloudy-mode #sbo=
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, body.cloudy-mode #sbo-rt-content div.sidebar p, body.cloudy-mode #sbo-rt-=
content div.sidebar1 dd, body.cloudy-mode #sbo-rt-content div.sidebar1 dt, =
body.cloudy-mode #sbo-rt-content div.sidebar1 li, body.cloudy-mode #sbo-rt-=
content div.sidebar1 p, body.cloudy-mode #sbo-rt-content div.tip dd, body.c=
loudy-mode #sbo-rt-content div.tip dt, body.cloudy-mode #sbo-rt-content div=
.tip li, body.cloudy-mode #sbo-rt-content div.tip p, body.cloudy-mode #sbo-=
rt-content div.warning dd, body.cloudy-mode #sbo-rt-content div.warning dt,=
 body.cloudy-mode #sbo-rt-content div.warning li, body.cloudy-mode #sbo-rt-=
content div.warning p, body.cloudy-mode #sbo-rt-content p.note, body.cloudy=
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body.cloudy-mode #sbo-rt-content div.bgbox p a, body.cloudy-mode #sbo-rt-co=
ntent div.boxg p a, body.cloudy-mode #sbo-rt-content div.note a, body.cloud=
y-mode #sbo-rt-content div.note p a, body.cloudy-mode #sbo-rt-content div.s=
idebar p a, body.cloudy-mode #sbo-rt-content div.sidebar1 p a, body.cloudy-=
mode #sbo-rt-content div.tip p a, body.cloudy-mode #sbo-rt-content div.warn=
ing p a, body.cloudy-mode #sbo-rt-content p.note a, body.cloudy-mode #sbo-r=
t-content p.pre-ex a { color: rgb(64, 64, 64); text-decoration: none; }

body.cloudy-mode #sbo-rt-content div.note h3, body.cloudy-mode #sbo-rt-cont=
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.cloudy-mode #sbo-rt-content div.sidebar p.title, body.cloudy-mode #sbo-rt-=
content div.sidebar-title, body.cloudy-mode #sbo-rt-content div.tip h3, bod=
y.cloudy-mode #sbo-rt-content div.warning h3, body.cloudy-mode #sbo-rt-cont=
ent p.box_title { background-color: transparent; color: rgb(64, 64, 64) !im=
portant; }

body.cloudy-mode #sbo-rt-content .boxbg, body.cloudy-mode #sbo-rt-content .=
note, body.cloudy-mode #sbo-rt-content .note1, body.cloudy-mode #sbo-rt-con=
tent .sidebar1, body.cloudy-mode #sbo-rt-content .tip, body.cloudy-mode #sb=
o-rt-content .warning, body.cloudy-mode #sbo-rt-content div.note, body.clou=
dy-mode #sbo-rt-content div.sidebar, body.cloudy-mode #sbo-rt-content div.t=
ip, body.cloudy-mode #sbo-rt-content div.warning { box-shadow: none; color:=
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body.cloudy-mode #sbo-rt-content td, body.cloudy-mode #sbo-rt-content td a,=
 body.cloudy-mode #sbo-rt-content td li, body.cloudy-mode #sbo-rt-content t=
d p, body.cloudy-mode #sbo-rt-content td p a, body.cloudy-mode #sbo-rt-cont=
ent th, body.cloudy-mode #sbo-rt-content th p { color: rgb(64, 64, 64); }

body.cloudy-mode #sbo-rt-content span.annotator-hl { background-color: rgb(=
221, 221, 221); color: rgb(0, 0, 0); }

.scale-right-to-left-appear { transform: scale(0); transform-origin: right =
top; transition: all 0.3s cubic-bezier(0.19, 1, 0.22, 1) 0s; }

.scale-right-to-left-appear-active { transform: scale(1); }

.fade-in-appear { opacity: 0.01; }

.fade-in-appear-active { opacity: 1; transition: opacity 0.5s ease-in 0s; }

.right { float: right; }

.modal-active { overflow: hidden; }

.no-touch .modal-active .title-cards .title-hover { visibility: visible; op=
acity: 1; display: block; }

button.fetching { background-size: 30px; padding-right: 35px !important; }

.modal-underlay { position: fixed; width: 100%; height: 100%; background-co=
lor: rgba(255, 255, 255, 0.7); left: 0px; top: 0px; z-index: 999; transitio=
n: opacity 0.25s ease-in-out 0s; }

.modal-underlay-appear { opacity: 0.01; }

.modal-underlay-appear-active { opacity: 1; transition: opacity 0.5s ease-i=
n 0s; }

.modal-menu { height: 140px; overflow-y: auto; }

.modal-wrapper .dropdown-item a, .modal-wrapper .dropdown-item a .item-titl=
e { overflow: hidden; text-overflow: ellipsis; max-width: 420px; }

.modal-wrapper { width: 480px; z-index: 9999; background-color: rgb(255, 25=
5, 255); position: fixed; left: 50%; margin-left: -240px; top: 100px; borde=
r: 1px solid rgb(237, 237, 237); box-shadow: rgba(0, 0, 0, 0.1) 0px 1px 3px=
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.modal-wrapper h1 { margin: 0px 0px 20px; font-size: 24px; font-weight: 400=
; }

.modal-wrapper h4 { color: rgb(7, 7, 7); font-size: 16px; font-weight: 700;=
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.modal-wrapper input[type=3D"search"] { width: 100%; padding: 8px; border: =
1px solid rgb(221, 221, 221); font-size: larger; margin: 0px; -webkit-appea=
rance: none; }

.modal-wrapper .wrap-search { position: relative; }

.modal-wrapper .wrap-search svg { position: absolute; right: 5px; top: 5px;=
 }

.modal-wrapper .modal-menu .does-exist-in-collection { background-color: rg=
b(245, 245, 245); }

.modal-wrapper .modal-menu li { height: 35px; }

.modal-wrapper .modal-menu li a { color: rgb(7, 7, 7); padding: 0px 0.5em; =
width: 100%; display: block; font-size: 16px; line-height: 35px; }

.modal-wrapper .modal-menu li a:hover { background-color: rgb(237, 237, 237=
); text-decoration: none; }

.modal-wrapper .dropdown-item a { white-space: nowrap; position: relative; =
padding-right: 40px !important; }

.modal-wrapper .error-message { background-color: rgb(239, 154, 154); margi=
n-bottom: 30px; margin-top: 10px; max-width: 920px; padding: 10px 20px; wid=
th: 100%; }

.modal-wrapper .error-message p { font-size: 1em; margin: 0px; }

@media (max-width: 768px) {
  .modal-wrapper { width: 100%; margin-left: 0px; left: 0px; top: 0px; heig=
ht: 100%; }
}

.modal-wrapper .modal-close { position: absolute; top: 0px; right: 0px; pad=
ding: 0.6em; max-width: 40px; max-height: 40px; background: rgb(255, 255, 2=
55); transition: all 0.5s cubic-bezier(0.23, 1, 0.32, 1) 0s; border-radius:=
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.modal-wrapper .modal-close svg { fill: rgb(103, 103, 103); height: 24px; p=
ointer-events: none; width: 24px; vertical-align: top; }

.modal-close:hover { background-color: rgb(221, 221, 221); }

.modal-close:focus { background-color: rgb(170, 170, 170); }

.modal-wrapper .modal-menu li.list-slide-leave { height: 35px; opacity: 1; =
}

.modal-wrapper .modal-menu li.list-slide-leave-active { height: 0px; opacit=
y: 0.01; transition: all 0.3s ease-in 0s; }

.modal-wrapper .modal-menu li.list-slide-enter { height: 0px; opacity: 0.01=
; }

.modal-wrapper .modal-menu li.list-slide-enter-active { height: 35px; opaci=
ty: 1; transition: all 0.3s ease-in 0s; }

.modal-wrapper .dropdown-item a .is-fetching-gif, .modal-wrapper .dropdown-=
item a svg, .modal-wrapper .dropdown-item a.error svg { position: absolute;=
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.modal-create-collection.modal-wrapper { padding: 1em 2em 6em; }

.modal-create-collection .create-collection-container input[type=3D"text"],=
 .modal-create-collection .create-collection-container textarea { border-to=
p: none; border-right: none; border-left: none; border-image: initial; bord=
er-bottom: 2px solid rgb(64, 64, 64); background-color: transparent; width:=
 100%; max-width: 100%; border-radius: 0px; outline: 0px; padding: 6px 0px;=
 }

.modal-create-collection .create-collection-container input[type=3D"text"] =
{ font-size: 20px; }

.modal-create-collection .create-collection-container textarea { margin-top=
: 0.35em; resize: none; }

.modal-create-collection .create-collection-container label { line-height: =
1.3em; margin-top: 0px; color: rgb(153, 153, 153); }

.modal-create-collection .create-collection-container input[type=3D"text"].=
error { border-top: none; border-right: none; border-left: none; border-ima=
ge: initial; border-bottom: 2px solid rgb(185, 0, 45); background-color: tr=
ansparent; }

.modal-create-collection .create-collection-container input[type=3D"text"].=
success { border-top: none; border-right: none; border-left: none; border-i=
mage: initial; border-bottom: 2px solid green; background-color: transparen=
t; }

.modal-create-collection .create-collection-container label.error, .modal-c=
reate-collection .create-collection-container label.success { font-weight: =
700; color: rgb(68, 68, 68); }

.modal-create-collection .create-collection-container label.success a { cur=
sor: pointer; color: rgb(246, 93, 34); }

.modal-create-collection .create-collection-container .actions { position: =
absolute; right: 28px; bottom: 30px; display: block; }

.modal-create-collection .create-collection-container .actions .cancel { co=
lor: rgb(51, 51, 51); }

.modal-create-collection .create-collection-container .actions li { display=
: inline-block; margin-left: 15px; }

#sbo-rt-content nav[hidden], .js-playlist-addto-label, .modal-wrapper .crea=
te-collection-container .wrap-textarea h2, .modal-wrapper .wrap-collection-=
name-input .wrap-svg { display: none; }

.modal-wrapper .wrap-collection-name-input { padding-right: 0px; }

.modal-wrapper .wrap-collection-name-input .actions { position: absolute; t=
op: 300px; left: auto; right: 30px; }

@media screen and (max-width: 51.25em) {
  .modal-wrapper .create-collection-container { margin-top: 0px; }
}

.modal-wrapper .create-collection-container .wrap-collection-name-input, .m=
odal-wrapper .create-collection-container .wrap-textarea { margin-top: 0px;=
 }

@media screen and (max-width: 320px) {
  .modal-wrapper .create-collection-container .actions { left: 0px; }
  .modal-wrapper .create-collection-container .actions li { width: 100%; }
  .modal-wrapper .create-collection-container .actions li button { width: 1=
00%; margin-bottom: 5px; }
}

.modal-pair-devices { text-align: center; padding-top: 30px; }

.modal-pair-devices p { font-size: 14px; color: rgb(170, 170, 170); }

.modal-pair-devices .button-primary, .modal-pair-devices .button-secondary,=
 .modal-pair-devices button { padding: 10px 40px; margin-top: 15px; }

.modal-wrapper.expiring-pair-code-modal-nag h1, .modal-wrapper.modal-pair-d=
evices h1 { padding-right: 30px; line-height: 1.25em; margin-top: 15px; }

.modal-wrapper.expiring-pair-code-modal-nag, .modal-wrapper.modal-pair-devi=
ces { text-align: center; }

.modal-wrapper.expiring-pair-code-modal-nag p, .modal-wrapper.modal-pair-de=
vices p { color: rgb(153, 153, 153); }

@media (max-width: 540px) {
  .modal-wrapper.expiring-pair-code-modal-nag .button-primary, .modal-wrapp=
er.expiring-pair-code-modal-nag .button-secondary, .modal-wrapper.expiring-=
pair-code-modal-nag button, .modal-wrapper.modal-pair-devices .button-prima=
ry, .modal-wrapper.modal-pair-devices .button-secondary, .modal-wrapper.mod=
al-pair-devices button { width: 100%; margin: 10px 0px; text-align: center;=
 }
}

.title-cards .card-hover-actions .card-button { min-width: fit-content; }

.title-cards .card-hover-actions .title-add-to-queue { position: absolute; =
right: 10px; }

.js-transform-playlist-titles .title-hover .js-playlist-icon { left: 30px; =
position: inherit; top: 8px; }

.js-transform-playlist-titles .title-hover .js-playlist-icon svg { right: 0=
px; position: inherit; }

@media screen and (max-width: 580px) {
  .js-transform-playlist-titles .title-hover .js-playlist-icon { top: 10px;=
 left: 25px; position: inherit; }
  .js-transform-playlist-titles .title-hover .js-playlist-icon svg { top: -=
3px; left: 3px; position: relative; }
}

.js-playlist-icon { position: relative; top: 1px; left: 2px; width: 18px; h=
eight: 16px; overflow: visible; border: none !important; outline: 0px !impo=
rtant; }

.menu-dropdown-region li a, .sbo-title { white-space: nowrap; text-overflow=
: ellipsis; overflow: hidden; }

.sbo-inpage-toc-inner .js-playlist-icon { left: 20px; position: initial; }

.js-playlists-menu { position: relative; bottom: -2px; right: 2px; }

.icon-add-to-playlist-sml, .icon-added-to-playlist-sml { width: 16px; heigh=
t: 14px; position: initial; bottom: 2px; right: 1px; }

.queue-control .icon-add-to-playlist-sml, .queue-control .icon-added-to-pla=
ylist-sml { width: auto; height: auto; bottom: 15px; right: 15px; }

.interface-controls .collections-dropdown .menu-control .tooltip.top-right.=
playlist-tooltip { top: 40px !important; right: 16px !important; }

.js-playlists-menu .icon-add-to-playlist-sml g g { fill: rgb(179, 179, 179)=
; }

.js-playlists-menu .icon-added-to-playlist-sml g g, .js-playlists-menu:hove=
r .icon-add-to-playlist-sml g g { fill: rgb(246, 93, 34); }

.top-right.playlist-tooltip { top: 32px !important; right: -5px !important;=
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.top-left.playlist-tooltip { left: 4px !important; }

* { box-sizing: border-box; -webkit-tap-highlight-color: transparent; -webk=
it-font-smoothing: antialiased; }

#sbo-rt-content { position: relative; z-index: 10; }

#sbo-rt-content img { height: auto; max-width: 100%; }

#sbo-rt-content .sbo-vid-wrapper { background-color: rgb(0, 0, 0); width: 1=
00%; position: relative; padding-bottom: 75%; }

#sbo-rt-content .sbo-vid-wrapper.arriving { background: center center no-re=
peat rgb(0, 0, 0); }

#sbo-rt-content .sbo-vid-wrapper iframe, #sbo-rt-content .sbo-vid-wrapper o=
bject { position: absolute; top: 0px; bottom: 0px; left: 0px; right: 0px; }

#sbo-rt-content .sbo-vid-wrapper.kaltura-player { padding-bottom: 60.1%; }

@media screen and (max-width: 78.125em) {
  #sbo-rt-content .sbo-vid-wrapper.kaltura-player { padding-bottom: 61%; }
}

@media screen and (max-width: 50em) {
  #sbo-rt-content .sbo-vid-wrapper.kaltura-player { padding-bottom: 62%; }
}

@media screen and (max-width: 43.75em) {
  #sbo-rt-content .sbo-vid-wrapper.kaltura-player { padding-bottom: 63%; }
}

@media screen and (max-width: 40.625em) {
  #sbo-rt-content .sbo-vid-wrapper.kaltura-player { padding-bottom: 64%; }
}

@media screen and (max-width: 34.375em) {
  #sbo-rt-content .sbo-vid-wrapper.kaltura-player { padding-bottom: 64.5%; =
}
}

@media screen and (max-width: 30em) {
  #sbo-rt-content .sbo-vid-wrapper.kaltura-player { padding-bottom: 66%; }
}

@media screen and (max-width: 26.25em) {
  #sbo-rt-content .sbo-vid-wrapper.kaltura-player { padding-bottom: 67%; }
}

@media screen and (max-width: 23.75em) {
  #sbo-rt-content .sbo-vid-wrapper.kaltura-player { padding-bottom: 68%; }
}

body { margin: 0px; }

body.reading { background-color: rgb(255, 255, 255); padding-top: 62px; }

@media screen and (max-width: 32.5em), screen and (max-height: 26.25em) {
  body.reading { padding-top: 0px; }
}

body.reading.video { padding-top: 0px; }

.practice-exam-float { margin: 0px; display: flex; flex-direction: column; =
justify-content: center; align-items: center; position: fixed; bottom: 24px=
; right: 80px; width: 280px; height: 124px; background-color: rgb(247, 250,=
 252); color: rgb(61, 59, 73); z-index: 100001; }

.practice-exam-float p { margin: 0px 0px 8px; font-size: 20px; font-weight:=
 600; line-height: 24px; }

.practice-exam-float a { color: rgb(211, 0, 45); font-size: 16px; }

.practice-exam-float a:hover { color: rgb(211, 0, 45); }

.practice-exam-float .bar { position: absolute; top: 16px; left: 11px; widt=
h: 11px; height: 92px; background-color: rgb(211, 0, 45); }

.practice-exam-float svg { position: relative; top: 3px; left: 0px; }

.practice-exam-float svg * { fill: rgb(211, 0, 45); }

.practice-exam-control { display: flex; align-items: center; justify-conten=
t: center; border-top: 1px solid rgb(204, 204, 204); }

.practice-exam-control a:hover svg * { fill: rgb(246, 93, 34); }

.is-fetching-gif { max-width: 18px; float: right; }

.menu-caret .is-fetching-gif { max-width: 12px; }

.menu-dropdown-region { position: absolute; left: -305px; top: -1px; width:=
 300px; text-align: left; background-color: rgb(246, 246, 246); z-index: 99=
; border-radius: 5px 0px 0px 5px; background-clip: padding-box; box-shadow:=
 rgb(170, 170, 170) 0px 2px 5px; border: 1px solid rgb(238, 238, 238); }

.menu-dropdown-region li { float: left; background-color: transparent !impo=
rtant; }

.interface-controls .collections-dropdown .caret .is-fetching-gif, .modal-w=
rapper .modal-menu li.dropdown-item { float: none; }

.menu-dropdown-region li.is-fetching { background-color: rgb(245, 245, 245)=
; }

.menu-dropdown-region li.is-fetching a { opacity: 0.65; }

.menu-dropdown-region li a { display: inline-block; max-width: 300px; heigh=
t: auto; font-size: inherit; padding: 10px 30px 10px 10px; width: 100%; tex=
t-align: left; font-family: "Source Sans Pro", arial, sans-serif; color: rg=
b(29, 34, 37); }

.nav-link, .sbo-prev-next, .sbo-reading-menu { font-family: "source sans pr=
o", sans-serif; }

.menu-dropdown-region li a:focus, .menu-dropdown-region li a:hover { backgr=
ound-color: rgb(238, 238, 238); color: rgb(29, 34, 37); text-decoration: no=
ne !important; }

.menu-dropdown-region li img, .menu-dropdown-region li svg { position: abso=
lute; top: 9px; right: 10px; }

@media screen and (max-width: 49.375em) {
  .menu-dropdown-region { left: -150px; top: 40px; }
  .menu-dropdown-region li { float: none; width: 100%; }
}

.modal-active .sbo-reading-menu { display: none; }

.modal-wrapper input { margin: 0px 0px 0.5em; }

.modal-wrapper .modal-close { margin: 5px; }

.modal-wrapper .dropdown-item a { text-align: left; }

.modal-wrapper .actions a, .modal-wrapper .actions button { width: auto; he=
ight: auto; font-size: 15px; color: rgb(64, 64, 64); }

.interface-controls .modal-wrapper a { width: auto; height: auto; font-size=
: 13px; cursor: pointer; }

.interface-controls .queue-control .collections-dropdown .rec-fav::before {=
 left: -5px; }

.interface-controls .collections-dropdown .caret { position: absolute; top:=
 10px; width: 10px; left: 35px; background-color: transparent; }

.interface-controls .collections-dropdown .caret .menu-caret { padding: 0px=
; width: auto; height: auto; border: none; text-align: left; outline: 0px; =
}

.interface-controls .collections-dropdown .caret .menu-caret svg { transfor=
m: rotate(0deg); }

.interface-controls .collections-dropdown .caret .menu-caret.opened svg { t=
ransform: rotate(180deg); }

.interface-controls .collections-dropdown .caret a { height: 20px; }

.interface-controls .collections-dropdown .dropdown-item.border-top { borde=
r-top: 1px solid rgb(209, 209, 209); }

.interface-controls .collections-dropdown .menu-control { border-bottom: 1p=
x solid rgb(204, 204, 204); height: 50px; }

.interface-controls .collections-dropdown .menu-control svg { width: 19px !=
important; height: 25px !important; }

@media screen and (max-width: 49.4375em) {
  .interface-controls .collections-dropdown .menu-control { border-bottom: =
0px; }
}

@media screen and (max-height: 26.25em) {
  .interface-controls .collections-dropdown .menu-control { border-bottom: =
0px; }
}

.interface-controls .collections-dropdown .menu-control .tooltip { position=
: absolute; right: 0px; top: 45px; color: rgb(255, 255, 255); opacity: 1; }

.interface-controls .collections-dropdown .menu-control .tooltip.queue-tool=
tip { right: 20px; }

.interface-controls .collections-dropdown .queue-spinner { width: 30px; pos=
ition: relative; top: 8px; right: 5px; }

.interface-controls .collections-dropdown .rec-fav { border-bottom: none; }

.interface-controls .collections-dropdown .rec-fav:hover { color: rgb(246, =
93, 34); }

.sbo-inpage-toc .collections-dropdown { width: 80px; height: 40px; position=
: absolute; right: 10px; top: 0px; max-width: 10%; }

.sbo-inpage-toc .queue-spinner { width: 20px; position: absolute; right: 12=
px; top: 10px; }

.sbo-inpage-toc .collections-dropdown .menu-caret { position: relative; wid=
th: 15px; height: 20px; top: -1px; left: 70px; border: none; background-col=
or: transparent; outline: 0px; padding: 0px !important; margin: 0px !import=
ant; }

.sbo-inpage-toc .collections-dropdown .menu-caret svg { transform: rotate(0=
deg); width: 6px; height: 4px; }

.sbo-inpage-toc .collections-dropdown .menu-caret.opened svg { transform: r=
otate(180deg); }

.sbo-inpage-toc .collections-dropdown .menu-caret a:hover { text-decoration=
: none; }

.sbo-inpage-toc .collections-dropdown .menu-caret .is-fetching-gif { positi=
on: absolute; right: 0px; top: 1px; }

.sbo-inpage-toc .collections-dropdown .menu-caret::before { margin-left: 0p=
x !important; }

.sbo-inpage-toc .collections-dropdown .menu-dropdown-region { left: -255px;=
 }

.sbo-inpage-toc .collections-dropdown .menu-dropdown-region .dropdown-item =
{ width: 100%; padding: 0px; }

.sbo-inpage-toc .collections-dropdown .menu-dropdown-region .dropdown-item.=
border-top { border-top: 1px solid rgb(209, 209, 209); }

.sbo-inpage-toc .collections-dropdown .menu-dropdown-region .dropdown-item =
a { padding: 6px 15px 6px 10px; border: none; }

@media screen and (max-width: 28.125em) {
  .sbo-inpage-toc .collections-dropdown .menu-dropdown-region { left: -170p=
x; }
}

.sbo-inpage-toc .collections-dropdown .menu-control .tooltip { position: ab=
solute; right: 10px; top: 35px; color: rgb(255, 255, 255); opacity: 1; }

.sbo-inpage-toc .collections-dropdown .menu-control .tooltip.queue-tooltip =
{ right: 13px; }

.sbo-inpage-toc .collections-dropdown .menu-control .tooltip.collections-to=
oltip { right: -10px; }

.tooltip.top-right .tooltip-arrow { top: -5px; transform: rotate(180deg); }

.reading .mfp-bg { background-color: rgb(0, 0, 0); }

.reading .mfp-content { margin: 0.625rem; }

@media screen and (max-width: 32.625em) {
  .reading .mfp-content { margin: 0px; }
}

.reading .mfp-content img { background-color: rgb(255, 255, 255); padding: =
0px; }

.reading .mfp-content .mfp-figure { background-color: rgb(0, 0, 0); padding=
: 1.5625rem 0.625rem 0px; border: 1px solid rgb(85, 85, 85); border-radius:=
 2px; background-clip: padding-box; }

.reading .mfp-content .mfp-figure button { color: rgb(155, 155, 155); font-=
weight: 700; font-size: 1.5625rem; padding: 0px; right: 5px; top: -8px; }

@media screen and (max-width: 32.5em) {
  .reading .mfp-content .mfp-figure { padding: 2.5rem 0px; }
}

.reading .mfp-content .mfp-figure .mfp-title { color: rgba(64, 64, 64, 0.75=
); }

.reading .mfp-content .mfp-figure::after { position: relative; }

.reading .mfp-content .mfp-figure .mfp-bottom-bar { position: relative; mar=
gin: 20px 0px 0px; }

@media screen and (max-width: 32.625em) {
  .reading .mfp-content .mfp-figure .mfp-bottom-bar { margin: 20px 0px 0px =
10px; }
}

#sbo-rt-content img.js-totri-lightbox { transition: border 200ms linear 0s;=
 cursor: zoom-in; border: 2px solid rgb(64, 64, 64) !important; }

#sbo-rt-content a.totri-footnote { padding: 0.5rem 0.375rem 0.375rem; displ=
ay: inline-block; border: none !important; }

#sbo-rt-content a.totri-footnote:hover { text-decoration: underline; }

#sbo-rt-content sup { position: relative; top: -8px; z-index: 2; }

.topnav .search { display: none; }

@media screen and (max-width: 32.5625em) {
  .topnav .search { display: inline-block; }
}

.clearfix::after, .clearfix::before { content: " "; display: table; }

.clearfix::after { clear: both; }

.sbo-prev-next { background: rgb(255, 255, 255); }

.sbo-nav-bottom { position: relative; z-index: 20; }

.sbo-nav-top { position: relative; z-index: 1; }

.nav-link { text-overflow: ellipsis; }

.nav-link, .pagination-label, .pagination-label::after, .pagination-label::=
before { transition: color 0.2s ease-out 0s; }

.nav-link, .pagination-label, .pagination-label::after, .pagination-label::=
before, .ss-list::before { transition: color 0.2s ease-out 0s; }

.sbo-reading-menu { background-color: rgb(247, 247, 247); position: relativ=
e; }

.sbo-reading-menu a { text-decoration: none; }

.ss-list::before { transition: color 0.2s ease-out 0s; color: rgb(119, 119,=
 119); font-size: 13px; margin-right: 5px; vertical-align: middle; }

.sbo-toc-thumb { z-index: 29; padding: 0.75rem; text-align: center; width: =
100%; display: inline-block; border: none; box-shadow: transparent 0px 0px =
0px; text-shadow: transparent 0px 0px 0px; }

@media screen and (max-width: 32.5625em) {
  .sbo-toc-thumb { padding: 1.375rem 0px 0px; }
}

.sbo-toc-thumb:active, .sbo-toc-thumb:focus, .sbo-toc-thumb:hover { backgro=
und-color: transparent; }

.sbo-toc-thumb.close:hover { background-color: transparent; }

.sbo-title { display: inline-block; width: 87%; position: relative; }

@media screen and (min-width: 32.625em) {
  .sbo-title { top: 5px; }
}

.sbo-title h1 { display: inline; }

.touch .pdfdoc #font-controls, body.video #font-controls, body.video .searc=
h-controls { display: none; }

.sbo-menu-top { margin-right: 55px; z-index: 30; }

.sbo-menu-bottom .sbo-toc-thumb, .sbo-menu-bottom .title-link { z-index: 20=
; }

#font-controls, .search-controls { position: relative; padding: 0.5rem; tra=
nsition: all 0.2s ease-in-out 0s; text-decoration: none; }

#font-controls::before, .search-controls::before { font-family: SSFlow; con=
tent: "=EF=9C=86"; height: 45px; width: 45px; font-size: 1.1875rem; top: 8p=
x; position: relative; }

#font-controls.open, .search-controls.open { border-left: 1px solid rgb(119=
, 119, 119); background-color: rgb(34, 34, 34); border-top-right-radius: 2p=
x; border-bottom-right-radius: 2px; }

#font-controls.open::before, .search-controls.open::before { vertical-align=
: middle; top: 4px; color: rgb(246, 93, 34); font-family: SSFlow !important=
; content: "=E2=90=A1" !important; font-size: 21px !important; }

.touch .search-in-archive .search-archive-bar input { padding: 0.5rem 0px 0=
.4375rem 0.125rem; }

.no-zoom .search-in-archive .search-archive-bar { padding: 0.3125rem 0px 0.=
3125rem 0.375rem; }

.no-zoom .search-in-archive .search-archive-bar input { padding: 0.625rem 0=
px 0.4375rem 0.125rem; position: relative; top: -1px; }

.no-zoom #font-controls::before, .no-zoom .search-controls::before { top: 7=
px; }

.search-in-archive .sitb-title { float: left; width: 100%; }

.search-in-archive .sitb-title span { float: right; }

.search-in-archive.loading .search-archive-bar::before { content: ""; backg=
round-image: url("/static/images/loading.6b1710a5f2bc.gif"); position: abso=
lute; right: 30px; top: 15px; z-index: 1; width: 20px; height: 20px; backgr=
ound-size: 20px 20px; }

.search-in-archive .search-controls::before { content: "=F0=9F=94=8E"; back=
ground-color: transparent; left: -8px; top: 6px; padding: 0.4375rem 0.5rem =
0.1875rem 0.9375rem; border-radius: 0px 2px 2px 0px; background-clip: paddi=
ng-box; }

.search-in-archive.active { border: 1px solid rgb(204, 204, 204); border-ra=
dius: 0px 2px 2px 0px; background-clip: padding-box; margin-right: -58px; }

.search-in-archive.active .search-archive-bar, .search-in-archive.active .s=
earch-archive-results { visibility: visible; }

.search-in-archive.active .search-controls { background-color: transparent;=
 border-radius: 0px 2px 2px 0px; background-clip: padding-box; }

.search-in-archive.active .search-controls::before { color: rgb(255, 255, 2=
55); content: "=F0=9F=94=8E"; background-color: rgb(204, 204, 204); }

.search-in-archive.active .search-controls:hover::before { color: rgb(255, =
255, 255); background-color: rgb(246, 93, 34); }

.search-in-archive.result-active { border-radius: 0px 2px 0px 0px; backgrou=
nd-clip: padding-box; }

.search-in-archive .search-archive-bar { visibility: hidden; background-col=
or: rgb(255, 255, 255); padding: 0.3125rem 0px 0.4375rem 0.375rem; border-t=
op: 1px solid rgb(204, 204, 204); border-bottom: 1px solid rgb(204, 204, 20=
4); border-left: 1px solid rgb(204, 204, 204); border-image: initial; borde=
r-right: none; position: absolute; right: 46px; border-radius: 2px 0px 0px =
2px; background-clip: padding-box; top: -1px; z-index: 99; }

.search-in-archive .search-archive-bar input { min-width: 260px; display: i=
nline-block; padding: 0.4375rem 0.4375rem 0.4375rem 0.375rem; text-overflow=
: ellipsis; font-family: "source sans pro", sans-serif, arial, sans-serif; =
background-color: rgb(255, 255, 255); border-top: 1px solid rgb(204, 204, 2=
04); border-bottom: 1px solid rgb(204, 204, 204); border-left: 1px solid rg=
b(204, 204, 204); border-image: initial; border-right: none; position: rela=
tive; margin-top: 1px; -webkit-appearance: none; border-radius: 0px; backgr=
ound-clip: padding-box; font-size: 16px !important; }

.search-in-archive.result-active .search-archive-bar { border-bottom: none;=
 border-radius: 2px 0px 0px; background-clip: padding-box; }

.search-in-archive .search-archive-results { visibility: hidden; position: =
absolute; right: -1px; font-family: "source sans pro", sans-serif; width: 3=
14px; text-align: left; }

.search-in-archive .search-archive-results.results-error { right: 0px !impo=
rtant; }

.search-in-archive .search-archive-results.results-error h1 { font-size: 1.=
125rem; padding: 1.25rem 0.625rem; }

.search-in-archive .search-archive-results ul { overflow: hidden scroll; pa=
dding: 0px 10px; border-right: 1px solid rgb(204, 204, 204); border-bottom:=
 1px solid rgb(204, 204, 204); border-left: 1px solid rgb(204, 204, 204); b=
order-image: initial; border-top: none; border-radius: 0px 0px 2px 2px; bac=
kground-clip: padding-box; background-color: rgb(255, 255, 255); max-height=
: 100%; }

@media screen and (min-height: 26.25em) {
  .search-in-archive .search-archive-results ul { max-height: 200px; }
}

@media screen and (min-height: 570px) {
  .search-in-archive .search-archive-results ul { max-height: 400px; }
}

@media screen and (min-height: 840px) {
  .search-in-archive .search-archive-results ul { max-height: 550px; }
}

@media screen and (min-height: 1050px) {
  .search-in-archive .search-archive-results ul { max-height: 100%; }
}

.search-in-archive .search-archive-results li.pagination { text-align: cent=
er; padding: 0.625rem 0px; border-bottom: 0px; clear: left; color: rgb(64, =
64, 64); }

.search-in-archive .search-archive-results li.pagination a { height: 5px; w=
idth: 10px; position: relative; top: -8px; color: rgb(246, 93, 34); font-si=
ze: 0.875rem; }

.search-in-archive .search-archive-results li.no-results { color: rgb(64, 6=
4, 64); border-bottom: 1px solid rgb(221, 221, 221); padding: 10px 0px 15px=
; }

.search-in-archive .search-archive-results li.sitb-item { padding: 10px 0px=
; border-bottom: 1px solid rgb(204, 204, 204); background-color: transparen=
t; color: rgb(64, 64, 64); font-size: 0.875rem; float: left; }

.search-in-archive .search-archive-results li.sitb-item .description { widt=
h: 300px; max-height: 240px; overflow: hidden; text-overflow: ellipsis; }

.search-in-archive .search-archive-results li .description { display: inlin=
e-block; padding-bottom: 10px; color: rgb(64, 64, 64); font-size: 1rem; }

.search-in-archive .search-archive-results li .description + span { float: =
right; }

.search-in-archive .search-archive-results li a.title { width: auto; height=
: auto; padding: 3px 0px; text-align: left; font-family: "source sans pro",=
 sans-serif; display: block; font-size: 0.875rem; color: rgb(64, 64, 64); }

.search-in-archive .search-archive-results li a.title:hover { color: rgb(24=
6, 93, 34); }

.search-in-archive .search-archive-results li.search-whole-site { clear: le=
ft; padding: 5px 0px 0px; margin: 0px 0px 0px 2px; text-align: center; bord=
er: none; }

.interface-controls .interface-control-btns::after, .interface-controls::af=
ter { clear: both; }

.search-in-archive .search-archive-results li.search-whole-site a { color: =
rgb(246, 93, 34); font-family: "source sans pro", sans-serif; width: auto; =
font-size: 100%; }

.font-flyout { opacity: 0; position: absolute; transition: opacity 0.2s eas=
e-in-out 0s; visibility: hidden; }

.font-flyout.open { opacity: 1; height: 49px; z-index: 99; visibility: visi=
ble; }

body.video .font-flyout { display: none; }

.icnTxLr { border-radius: 2px 0px 0px 2px; background-clip: padding-box; }

.pdf-size-changer { padding: 3px 18px 5px; background-color: rgb(34, 34, 34=
); border-left: 1px solid rgb(68, 68, 68); border-top: 1px solid rgb(68, 68=
, 68); border-bottom: 1px solid rgb(68, 68, 68); display: block; float: lef=
t; text-decoration: none !important; }

.pdf-size-changer.icnTxSm { border-right: 1px solid rgb(68, 68, 68); }

.pdf-size-changer span { display: inline-block; text-indent: -99999px; widt=
h: 0px; height: 0px; }

@media screen and (-webkit-min-device-pixel-ratio: 0) and (max-width: 49.43=
75em) {
}

@media screen and (max-width: 49.4375em) {
  #font-controls.open { position: relative; right: -170px; }
  .pdfdoc #font-controls.open { right: 0px; }
}

.font-controls-panel { font: 700 26px/45px Georgia, serif; background-color=
: rgb(34, 34, 34); border: 1px solid rgb(68, 68, 68); right: 0px; top: 0px;=
 position: absolute; height: 185px; width: 300px; border-radius: 2px 0px 2p=
x 2px; background-clip: padding-box; }

.font-controls-panel.is-android-device { height: 145px; }

.font-controls-panel .nightmodes ul { float: left; width: 100%; border-bott=
om: 1px solid rgb(68, 68, 68); }

.font-controls-panel .nightmodes ul li { display: inline-block; float: left=
; width: 33.3%; border-right: 1px solid rgb(68, 68, 68); background-color: =
rgb(34, 34, 34); }

.font-controls-panel .nightmodes ul li a { display: block; height: 48px; te=
xt-align: center; overflow: hidden; }

.font-controls-panel .nightmodes ul li a span { display: block; text-indent=
: -999999px; }

.font-controls-panel .nightmodes ul li a .fa { color: rgb(255, 255, 255); p=
osition: relative; top: 3px; }

.font-controls-panel .nightmodes ul li:hover a { background-color: rgb(0, 0=
, 0) !important; }

.font-controls-panel .nightmodes ul li.day { border-radius: 2px 0px 0px; ba=
ckground-clip: padding-box; background-color: rgb(0, 0, 0); }

.font-controls-panel .nightmodes ul li.day .fa { color: rgb(246, 93, 34); }

.font-controls-panel .nightmodes ul li.cloudy a svg { position: relative; t=
op: 3px; }

.font-controls-panel .nightmodes ul li.night { border-right: none; }

#reset { line-height: 1em; padding: 3px 10px; margin: 0px; font-size: 12px;=
 position: absolute; right: 10px; bottom: 10px; font-family: arial, sans-se=
rif; }

.resizer .draggable-containment-wrapper { width: 60%; height: 2px; backgrou=
nd-color: rgb(102, 102, 102); margin: 85px 20% 0px; border-radius: 2px; bac=
kground-clip: padding-box; }

.resizer .draggable-containment-wrapper::after, .resizer .draggable-contain=
ment-wrapper::before { font-weight: 700; font-size: 31px; font-family: geor=
gia, serif; position: absolute; color: rgb(255, 255, 255); top: 62px; }

.pdfdoc #font-controls::before, .pdfdoc .font-size-changer::before, .subscr=
ibe-nag { font-family: "source sans pro", sans-serif; }

.resizer .draggable-containment-wrapper .filler { height: 2px; display: blo=
ck; background-color: rgb(246, 93, 34); }

.mobile-menu, .sbo-toc-open .sbo-toc-container > .sbo-toc-thumb { display: =
none; }

.resizer .draggable-containment-wrapper::before { left: 15px; font-size: 18=
px; }

.resizer .draggable-containment-wrapper::after { right: 15px; }

.resizer .draggable-containment-wrapper .draggable { cursor: move; width: 1=
5px; height: 15px; padding: 0.5em; float: left; border-radius: 15px; backgr=
ound-clip: padding-box; margin-top: -14px; background-color: rgb(221, 221, =
221); top: 0px !important; }

.column-resizer .draggable-containment-wrapper, .font-resizer .draggable-co=
ntainment-wrapper { position: relative; }

.column-resizer .draggable-containment-wrapper .fa, .font-resizer .draggabl=
e-containment-wrapper .fa { color: rgb(255, 255, 255); position: absolute; =
top: -8px; }

.column-resizer .draggable-containment-wrapper .fa.left, .font-resizer .dra=
ggable-containment-wrapper .fa.left { left: -40px; font-size: 18px; }

.column-resizer .draggable-containment-wrapper .fa.right, .font-resizer .dr=
aggable-containment-wrapper .fa.right { top: -10px; right: -40px; }

.column-resizer .draggable-containment-wrapper .fa.right.fa-font, .font-res=
izer .draggable-containment-wrapper .fa.right.fa-font { top: -14px; }

.column-resizer .draggable-containment-wrapper { margin: 35px 20% 0px; }

.subscribe-nag { overflow: hidden; }

.pdfdoc #font-controls::before { content: "+/=E2=88=92"; font-weight: 700; =
font-size: 22px; top: 5px; }

.pdfdoc .font-size-changer::before { font-weight: 700; font-size: 31px; pos=
ition: relative; top: 2px; }

.pdfdoc .font-size-changer#increase-font::before { content: "+"; }

.pdfdoc .font-size-changer#decrease-font::before { content: "=E2=88=92"; }

.icnTxSm::before { position: relative; top: 7%; font-size: 80%; }

.toc-contents { width: 100%; border: 10px solid rgb(221, 221, 221); backgro=
und-color: rgb(255, 255, 255); overflow: hidden; max-height: 0px; opacity: =
0; transition: all 0.4s ease-in-out 0s; }

.toc-contents, .toc-contents.open { top: 0px; transition: all 0.4s ease-in-=
out 0s; }

.toc-contents.open { opacity: 1; transition: all 0.4s ease-in-out 0s; }

.tocList { line-height: 1.125; padding-bottom: 15px; }

@media screen and (min-height: 420px) and (min-width: 521px) {
  .toc-contents { position: fixed; overflow-y: scroll; left: 50%; bottom: 0=
px; margin-left: -330px; max-width: 725px; }
  .tocList { padding-bottom: 0px; }
}

.tocList .minutes { color: rgb(153, 153, 153); }

.tocList li:last-child { border-bottom: 0px; }

.tocList .toc-level1 { color: rgb(119, 119, 119); background-color: rgb(255=
, 255, 255); border-bottom: 1px solid rgb(221, 221, 221); }

.tocList .toc-level1 > a.toc-link { padding: 0.625rem 1.875rem 0.625rem 0.9=
375rem; }

.tocList .toc-level1.currently-reading { background-color: transparent !imp=
ortant; }

.tocList .toc-level1.currently-reading > a, .tocList [class*=3D"toc-level"]=
.currently-reading { background-color: rgb(240, 240, 240); }

.tocList [class*=3D"toc-level-"] a.toc-link { padding: 0.375rem 0.9375rem 0=
.375rem 2.1875rem; line-height: 1.35em; }

.tocList [class*=3D"toc-level-"] a.toc-link::before { content: "=E2=80=A2";=
 color: rgb(153, 153, 153); font-size: 21px; line-height: 0; margin-left: -=
10px; position: relative; left: -5px; }

.tocList .toc-level-3 a.toc-link { padding-left: 3.4375rem; }

.tocList .toc-level-4 a.toc-link { padding-left: 4.6875rem; }

.tocList .toc-level-5 a.toc-link { padding-left: 5.9375rem; }

.tocList a.toc-link { font-weight: 400; display: block; }

.tocList a.toc-link:focus { background-color: rgba(0, 134, 202, 0.01); }

.progress-indicator { font-size: 0.75rem; line-height: 1px; font-family: ss=
-flow; color: rgb(231, 229, 222); border: 2px solid rgb(231, 229, 222); tex=
t-align: center; float: left; width: 20px; height: 20px; margin: 0px 0.9375=
rem 0px 0px; padding: 0.5625rem 0.125rem 0.375rem; transition: all 0.2s eas=
e-in-out 0s; border-radius: 45px; background-clip: padding-box; position: a=
bsolute; left: 5px; top: 10px; }

.progress-indicator.completed { background-color: rgb(246, 93, 34); border:=
 2px solid rgb(246, 93, 34); }

.progress-indicator.completed::before { color: rgb(255, 255, 255); }

li:hover.video-pagination-item .progress-indicator, li:hover > .progress-in=
dicator { width: 24px; height: 24px; padding: 0.6875rem 0.25rem 0.5rem; mar=
gin: -0.125rem -0.5rem 0px 0px; }

.toc-contents .toc-level2 .progress-indicator { left: 30px; top: 12px; }

.toc-contents .rec-fav { outline: 0px; position: absolute; right: 15px; top=
: 13px; z-index: 9; }

h1.video-toc-title { font-family: "source sans pro", sans-serif, sans-serif=
; color: rgb(119, 119, 119); font-size: 13px; letter-spacing: 1px; line-hei=
ght: 1.35em; }

@media screen and (max-width: 51.3125em) {
  h1.video-toc-title { margin: 1em 1.5em 0px; }
}

h1.video-toc-title a { color: rgb(246, 93, 34); text-decoration: none; bord=
er: none !important; }

h1.video-toc-title a:hover { text-decoration: underline; }

.video #sbo-rt-content h1.video-title { margin: 0.4em 0px 0.8em !important;=
 }

.mobile-menu select { display: inline-block; width: 100%; padding: 1.25rem =
3.125rem 0.9375rem 1.25rem; color: rgb(119, 119, 119); background: rgb(245,=
 245, 245); cursor: pointer; text-overflow: ellipsis; font-size: 1.125rem; =
-webkit-appearance: none; }

.mobile-menu label { margin: 0px; position: relative; }

.mobile-menu label::after { padding-bottom: 2px; position: absolute; top: 2=
0px; right: 8px; content: "<>"; font: 20px Consolas, monospace; color: rgb(=
170, 170, 170); border-bottom: 1px solid rgb(213, 213, 213); pointer-events=
: none; transform: rotate(90deg); }

@media screen and (max-width: 51.25em) {
  .desktop-menu { display: none; }
  .mobile-menu { display: block; height: 58px; border: none; }
}

.sbo-inpage-toc { color: rgb(119, 119, 119); position: relative; margin: 0p=
x auto 2em; font-family: "source sans pro", sans-serif, sans-serif; font-si=
ze: 16px; border-radius: 2px; background-clip: padding-box; border: 1px sol=
id rgb(230, 230, 230); display: none; }

.sbo-inpage-toc .tocList li a.toc-link { border-bottom: 1px solid rgb(238, =
238, 238); }

.sbo-inpage-toc .section-title { width: 100%; display: block; padding: 10px=
 0px; border-bottom: 1px solid rgb(238, 238, 238); }

.sbo-inpage-toc .tabs { height: 51px; z-index: 20; }

.sbo-inpage-toc .tabs li { padding: 15px 20px; float: left; border-bottom: =
1px solid rgb(216, 216, 216); color: rgb(119, 119, 119); background-color: =
rgb(230, 230, 230); }

.sbo-inpage-toc .tabs li::selection { background-color: transparent !import=
ant; }

.sbo-inpage-toc .tabs li.item-1, .sbo-inpage-toc .tabs li.item-2, .sbo-inpa=
ge-toc .tabs li.item-3, .sbo-inpage-toc .tabs li.item-4 { border-left: 1px =
solid rgb(216, 216, 216); }

.sbo-inpage-toc .tabs li:hover { color: rgb(64, 64, 64); background-color: =
rgb(216, 216, 216); cursor: pointer; }

.sbo-inpage-toc .toc-bottom, .sbo-inpage-toc .toc-contents { background-col=
or: transparent; }

.sbo-inpage-toc .tabs li.active-tab { cursor: default; background-color: tr=
ansparent; border-bottom: none; }

.sbo-inpage-toc .tabs li.active-tab:hover { color: rgb(119, 119, 119); }

.sbo-inpage-toc .rec-fav { color: rgb(74, 60, 49); }

.sbo-inpage-toc #description-tab .sbo-book-meta, .sbo-inpage-toc #resources=
-tab .sbo-book-meta, .sbo-inpage-toc #transcripts-tab .sbo-book-meta { bord=
er: none; }

.sbo-inpage-toc #resources-tab ul li { margin: 10px 0px; }

.sbo-inpage-toc #description-tab p { line-height: 1.5em; margin: 10px 0px; =
}

.sbo-inpage-toc .tab-content { display: none; }

.sbo-inpage-toc .tab-content.active-tab, .sbo-inpage-toc.arrived { display:=
 block; }

.sbo-inpage-toc .tab-inner { margin: 0px 2%; padding: 10px 10px 20px; }

@media screen and (max-width: 51.3125em) {
  .sbo-inpage-toc { margin: 0px 20px 30px; }
}

.sbo-inpage-toc .sbo-inpage-toc-inner { position: relative; }

.sbo-inpage-toc .transcripts-wrapper abbr.begin, .sbo-inpage-toc .transcrip=
ts-wrapper abbr.end { display: none; }

.sbo-inpage-toc .transcripts-wrapper p, .sbo-inpage-toc .transcripts-wrappe=
r span.text { display: inline; }

.sbo-inpage-toc .transcripts-wrapper p { line-height: 2em; }

.sbo-inpage-toc .transcripts-wrapper #js-transcription-region { max-height:=
 500px; overflow: hidden scroll; }

.sbo-inpage-toc .toc-bottom { width: 96%; margin: 0px 2%; border-top: 1px s=
olid rgb(221, 221, 221); text-align: right; height: 80px; }

.sbo-inpage-toc .toc-bottom .to-top { position: relative; top: 24px; font-s=
ize: small; }

.sbo-inpage-toc h2 { font-size: 21px; color: rgb(119, 119, 119); margin: 1.=
25rem 0px; }

.sbo-inpage-toc .sbo-book-meta { background-color: rgb(255, 255, 255); widt=
h: 96%; z-index: 1; margin: 0px 2%; padding: 0.625rem 0.625rem 1.25rem; bor=
der-radius: 2px 2px 0px 0px; background-clip: padding-box; }

.sbo-inpage-toc .sbo-book-meta .cover img { max-width: 75px; box-shadow: no=
ne; }

.sbo-inpage-toc .tocList { width: 100%; overflow-y: scroll; list-style-type=
: none; padding: 0.3125rem 2.5rem 0px; height: 16.25rem; border-radius: 0px=
 0px 2px 2px; background-clip: padding-box; }

@media screen and (max-width: 30.9375em) {
  .sbo-inpage-toc .tocList { height: 15.9375rem; }
}

.sbo-inpage-toc .tocList [class*=3D"toc-level-"] a.toc-link { padding-left:=
 3.75rem; margin-right: 3.75rem; }

.sbo-inpage-toc .tocList .toc-level1 { padding-top: 0px; }

.sbo-inpage-toc .tocList .toc-level1 > a.toc-link { padding-left: 2.1875rem=
; }

.sbo-inpage-toc .tocList li { padding: 0.3125rem 0px 0px; border: none; }

.sbo-inpage-toc .tocList li a.toc-link::before { content: ""; margin-left: =
-3px; }

.sbo-inpage-toc .tocList .minutes { font-size: smaller; }

.sbo-inpage-toc li { position: relative; }

.sbo-inpage-toc .sbo-toc-thumb { display: none; }

.sbo-inpage-toc .toc-contents { position: relative; overflow: initial; marg=
in: 0px; border: none; opacity: 1; max-height: 100%; max-width: 100%; left:=
 0px; bottom: 0px; padding: 0px; }

.progress-percent-complete { height: 8px; font-size: 12px; display: table; =
margin: 10px 0px 0px 90px; width: calc(100% - 90px); }

.progress-percent-complete .percent-complete-bar { display: table-cell; ver=
tical-align: middle; white-space: nowrap; width: 100%; }

.progress-percent-complete .percent-complete { background-color: rgb(213, 2=
13, 213); position: relative; text-indent: -999999px; border-radius: 2px; b=
ackground-clip: padding-box; display: block; height: 8px; padding: 0px; wid=
th: 100%; }

.progress-percent-complete .percent-complete .percent { background-color: r=
gb(153, 144, 130); display: block; height: 8px; width: 0px; border-radius: =
2px; background-clip: padding-box; }

@media screen and (min-height: 26.25em) and (min-width: 41.9375em) {
  .tocList .toc-level1 > a { padding-left: 4.375rem; }
  .tocList [class*=3D"toc-level-"] a.toc-link { padding-left: 5.625rem; }
  .tocList .toc-level-3 a.toc-link { padding-left: 6.875rem; }
  .tocList .toc-level-4 a.toc-link { padding-left: 8.125rem; }
  .tocList .toc-level-5 a.toc-link { padding-left: 9.375rem; }
}

.sbo-toc .close { width: auto; position: absolute; top: 0px; right: 20px; c=
ursor: pointer; background: 0px 0px; }

.sbo-toc .close span { display: none; }

.sbo-toc .close::before { font-family: SSFlow; font-size: 14px; content: "=
=E2=90=A1"; color: rgb(119, 119, 119); }

.sbo-book-meta { background: rgb(247, 247, 247); border-bottom: 1px solid r=
gb(221, 221, 221); color: rgb(119, 119, 119); overflow: auto; padding: 10px=
; line-height: 1.25em; }

.sbo-book-meta .cover { float: left; }

.sbo-book-meta .cover a { display: block; margin-right: 10px; }

.sbo-book-meta .cover a:focus { background-color: rgb(246, 93, 34); }

.sbo-book-meta .cover img { border: 1px solid rgb(221, 221, 221); max-width=
: 50px; height: auto; }

.sbo-book-meta span { display: block; font-size: 13px; }

.sbo-book-meta span.title { font-size: 18px; margin-bottom: 5px; }

.sbo-book-meta .title { padding-right: 25px; }

.video .sbo-book-meta .title { padding-right: 0px; }

.sbo-book-meta .publisher-logo { max-width: 105px; max-height: 35px; float:=
 right; padding: 3px 30px 0px 0px; }

.video .sbo-book-meta .publisher-logo { padding: 0px; max-width: 75px; }

@media only screen and (max-width: 32.5625em) {
  .sbo-book-meta .publisher-logo { padding: 3px 3px 0px 0px; max-width: 76p=
x; }
}

.sbo-book-meta .publishers { font-style: italic; }

.bitlist-header { padding: 1rem 3.125rem 1rem 1rem; color: rgba(64, 64, 64,=
 0.75); font-size: 21px; }

.pagination-title { white-space: nowrap; text-overflow: ellipsis; overflow:=
 hidden; }

.pagination-label::after, .pagination-label::before { font-family: SSFlow; =
color: rgb(119, 119, 119); font-size: 12px; height: 100%; position: relativ=
e; top: 11px; }

.sbo-next .pagination-label::after { content: "=E2=8F=AD"; float: right; ma=
rgin-left: 7px; }

.no-zoom .sbo-next .pagination-label { margin-right: 20px; }

.no-zoom .sbo-next .pagination-label::after { position: relative; top: -4px=
; }

.sbo-prev .pagination-label::before { content: "=E2=8F=AE"; margin-right: 7=
px; float: left; }

.sbo-next, .sbo-prev { display: inline-block; width: 50%; position: relativ=
e; float: left; z-index: 10; }

.video .sbo-next, .video .sbo-prev { top: auto; }

.sbo-next .nav-link, .sbo-prev .nav-link { width: 100%; height: 62px; backg=
round: rgb(247, 247, 247); display: inline-block; padding: 9px 15px; font-s=
ize: 14px; overflow: hidden; white-space: nowrap; text-overflow: ellipsis; =
z-index: 30; }

.interface-controls .interface-control-btns::after, .interface-controls .in=
terface-control-btns::before, .interface-controls::after, .interface-contro=
ls::before { content: " "; display: table; }

.sbo-next .nav-link:hover, .sbo-prev .nav-link:hover { text-decoration: non=
e; }

.sbo-next { float: right; }

.sbo-prev .nav-link { border-style: solid; border-color: rgb(221, 221, 221)=
; border-image: initial; border-width: 1px 1px 1px 0px; text-align: left; }

.sbo-next .nav-link { border-bottom: 1px solid rgb(221, 221, 221); text-ali=
gn: right; }

.sbo-nav-bottom { top: 107px; }

.prodsample-book .sbo-nav-bottom { top: 140px; }

.pagination-label { color: rgb(119, 119, 119); font-size: 12px; letter-spac=
ing: 1px; }

.interface-controls { position: relative; margin: 0px auto; padding: 0px; w=
idth: 200px; z-index: 15; list-style-type: none; text-align: center; top: 7=
0px; }

@media screen and (min-height: 420px) and (min-width: 32.5625em) {
  .interface-controls { top: 24px; }
}

@media screen and (min-height: 420px) and (min-width: 49.4375em) {
  .interface-controls { top: 100px; }
}

.interface-controls a:hover { text-decoration: none !important; }

.interface-controls li { float: right; background-color: rgb(255, 255, 255)=
; position: relative; }

@media screen and (max-width: 32.5625em) {
  .interface-controls li { background-color: transparent; }
}

.interface-controls .queue-control .rec-fav { outline: 0px; }

.interface-controls .queue-control .rec-fav::before { position: relative; t=
op: 2px; }

.interface-controls a, .interface-controls button { display: inline-block; =
height: 49px; width: 48px; text-align: center; vertical-align: middle; colo=
r: rgb(179, 179, 179); font-size: 20px; }

.interface-controls a::before, .interface-controls button::before { transit=
ion: color 0.2s ease-out 0s; text-align: center; line-height: 1; font-size:=
 19px; }

.no-touch .interface-controls a:not(.rec-fav):hover::before, .no-touch .int=
erface-controls button:not(.rec-fav):hover::before { color: rgb(246, 93, 34=
); }

.interface-controls .sharing-controls .trigger { width: 48px; height: 49px;=
 display: inline-block; background-color: transparent; }

.interface-controls .sharing-controls .trigger .fa { position: relative; to=
p: 13px; visibility: visible; }

.interface-controls .sharing-controls .trigger::before { border-radius: 0px=
 2px 2px 0px; background-clip: padding-box; font-family: SSFlow; content: "=
=E2=90=A1"; font-size: 21px; line-height: 57px; position: absolute; height:=
 49px; width: 48px; color: rgb(246, 93, 34); left: 0px; top: 0px; overflow:=
 hidden; opacity: 0; visibility: hidden; transition: opacity 0.2s ease-in-o=
ut 0s; }

.interface-controls .sharing-controls ul li:first-child a { border-left: 1p=
x solid rgb(102, 102, 102); border-radius: 2px 0px 0px 2px; background-clip=
: padding-box; }

.interface-controls .sharing-controls.active a { background-color: rgb(34, =
34, 34); border-top: 1px solid rgb(102, 102, 102); border-bottom: 1px solid=
 rgb(102, 102, 102); }

.interface-controls .sharing-controls.active .trigger .fa { visibility: hid=
den; }

.interface-controls .sharing-controls.active .trigger::before { background-=
color: rgb(34, 34, 34); visibility: visible; opacity: 1; }

@media screen and (max-width: 26.25em) {
  .interface-controls .sharing-controls .trigger::before { border-radius: 2=
px 0px 0px 2px; background-clip: padding-box; }
}

.adjustable-column { margin: 0px auto; }

body.video { font-family: Georgia, serif; }

body.video .application { margin-top: 1em; }

body.video .sbo-nav-bottom { display: none; }

@media screen and (max-width: 51.3125em) {
  body.video .interface-controls-top { display: none; }
}

body.video .reading-controls-bottom .interface-controls { top: -15px; }

body.video [role=3D"document"] #sbo-rt-content { background: center 150px n=
o-repeat rgb(0, 0, 0); min-height: 250px; padding: 0px; display: block; mar=
gin-bottom: 30px !important; margin-top: 20px !important; }

body.video [role=3D"document"] #sbo-rt-content .kaltura-player { background=
-color: transparent !important; }

body.video [role=3D"document"].javascript-ready #sbo-rt-content { backgroun=
d: no-repeat; }

@media screen and (min-height: 26.25em) and (min-width: 32.5625em) {
  body { background-color: rgb(221, 221, 221); }
  .ss-list { margin-right: 5px; }
  .sbo-reading-menu { background-color: rgb(255, 255, 255); }
  .sbo-next, .sbo-prev { top: -49px; }
  .pagination-title, .sbo-nav-bottom { display: none; }
  .pagination-label { font-size: 0px; }
  .pagination-label::after, .pagination-label::before { position: relative;=
 top: 13px; font-size: 14px; }
  .sbo-title { font-size: 18px; }
  .sbo-next .nav-link, .sbo-prev .nav-link { background-color: rgb(255, 255=
, 255); border-top-width: 0px; position: fixed; top: 0px; text-decoration: =
none; width: 55px; }
  .sbo-prev .nav-link { left: 55px; transition: left 0.2s ease-in-out 0s; r=
ight: auto; }
  .sbo-menu-top, .sbo-prev .nav-link { transition: left 0.2s ease-in-out 0s=
; }
  .sbo-menu-top { height: 62px; top: 0px; right: 0px; left: 109px; margin-r=
ight: 55px; position: fixed; border-bottom: 1px solid rgb(221, 221, 221); b=
order-right: 1px solid rgb(221, 221, 221); border-left: 1px solid rgb(221, =
221, 221); transition: left 0.2s ease-in-out 0s; }
  .sbo-next .nav-link { right: 0px; left: auto; }
  .sbo-book-meta .title { margin-bottom: 5px; }
  .sbo-book-meta .title a:focus, .sbo-book-meta .title a:hover { color: rgb=
(246, 93, 34); }
}

@media screen and (min-height: 26.25em) and (min-width: 41.9375em) {
  .pagination-label { font-size: 12px; }
  .pagination-label::after, .pagination-label::before { top: 14px; }
  .pagination-title { display: block; }
  .sbo-next .nav-link, .sbo-prev .nav-link { width: 23%; }
  .sbo-menu-top { left: 54px; margin-left: 23%; right: 22.5%; margin-right:=
 0px; z-index: 29; position: fixed; transition: left 0.2s ease-in-out 0s; }
}

footer.pagefoot { padding: 1.25rem; }

footer.pagefoot .copyright { text-align: left; display: inline; }

footer.pagefoot ul a { text-decoration: none; }

@media screen and (min-height: 26.25em) and (min-width: 49.4375em) {
  #font-controls { height: 49px; border-bottom: 1px solid rgb(204, 204, 204=
); }
  #font-controls::before { font-size: 24px; }
  #font-controls.open { border-radius: 0px; background-clip: padding-box; b=
order: none; }
  .font-flyout { position: fixed; }
  .interface-controls { position: fixed; right: 20px; left: auto; z-index: =
25; width: auto; }
  .interface-controls .interface-control-btns { padding: 0px; color: rgb(20=
4, 204, 204); border-radius: 2px; background-clip: padding-box; border: 1px=
 solid rgb(204, 204, 204); }
  .interface-controls .interface-control-btns li:first-child a { border-rad=
ius: 2px 2px 0px 0px; background-clip: padding-box; }
  .interface-controls .interface-control-btns .video-highlight-control { bo=
rder-top: 1px solid rgb(204, 204, 204); }
  .interface-controls .interface-control-btns .video-highlight-control a > =
span::before { content: "=EF=9C=87"; font-family: SSFlow; font-size: 1.3125=
rem; position: relative; top: 18px; }
  .interface-controls .search-in-archive { font-family: "source sans pro", =
sans-serif, sans-serif; border-bottom: 1px solid rgb(204, 204, 204); }
  .interface-controls .search-in-archive.active { border-top: none; border-=
right: none; border-left: none; border-image: initial; border-bottom: 1px s=
olid rgb(204, 204, 204); margin-right: 0px; }
  .interface-controls .search-in-archive .search-archive-bar input { min-wi=
dth: 320px; top: 1px; }
  .interface-controls .search-in-archive .search-archive-results { right: 4=
8px; width: 325px; }
  .interface-controls li { float: none; }
  .interface-controls li:first-child { border-radius: 2px 2px 0px 0px; back=
ground-clip: padding-box; }
  body.video .interface-controls li:first-child { border-radius: 2px; backg=
round-clip: padding-box; }
  body.video .interface-controls li:first-child button { border-bottom: non=
e; }
  .interface-controls li:last-child { border-radius: 0px 0px 2px 2px; backg=
round-clip: padding-box; border-bottom: none; }
  .interface-controls .sharing-controls.active .trigger { border-top-right-=
radius: 0px; }
  .interface-controls .sharing-controls.active .trigger::before { border-ra=
dius: 0px 0px 2px; background-clip: padding-box; }
  .interface-controls button { border-bottom: 1px solid rgb(204, 204, 204);=
 }
  .interface-controls button::before { font-size: 21px; }
}

@media screen and (min-width: 30em) {
  .articlelist { padding-left: 15px; }
  .related .articlelist { padding: 0px 15px; }
}

@media screen and (max-width: 32.5625em), (max-height: 26.25em) {
  .sbo-menu-top { margin-right: 0px; }
  .sbo-next .nav-link { border-top: 1px solid rgb(221, 221, 221); }
  .prodsample-video .nav-link { position: relative; }
}

.cancel-button:hover { border-bottom: 1px solid rgb(246, 93, 34) !important=
; }

.cancel-button { border-bottom: 1px solid rgb(0, 0, 0) !important; }

.video #sbo-rt-content { max-width: 100%; }

@media (min-width: 32.5625em) {
  .video [role=3D"document"] { max-width: 50rem; }
}

@media (min-width: 78.125em) {
  .video [role=3D"document"] { max-width: 60rem; }
}

[role=3D"document"] { padding: 0px; margin: 0px auto; }

[role=3D"document"]::after, [role=3D"document"]::before { content: " "; dis=
play: table; }

[role=3D"document"]::after { clear: both; }

@media screen and (max-width: 32.5em), screen and (max-height: 26.25em) {
  [role=3D"document"] { margin: 0px auto 5px; position: relative; top: -49p=
x; }
  .video [role=3D"document"] { top: 0px; }
  .js-preview-content [role=3D"document"], .video [role=3D"document"] { mar=
gin: 0px auto; z-index: 0; }
}

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  .note, .tip, .warning, body, pre { background-color: rgb(255, 255, 255); =
}
  body { color: rgb(0, 0, 0); font-size: 7pt; }
  .note p, pre { font-size: 1.4em; }
  @page { margin: 1in 1.25in; }
  h1, h2, h3, h4, h5, h6 { text-shadow: none; color: rgb(0, 0, 0); }
  .note, .tip, .warning { box-shadow: none; }
  a[href^=3D"http://"]::after { content: " (" attr(href) ")"; font-size: 75=
%; }
}

.mfp-bg, .mfp-wrap { left: 0px; top: 0px; position: fixed; }

.mfp-bg, .mfp-container, .mfp-wrap { width: 100%; height: 100%; }

.mfp-container::before, .mfp-figure::after { content: ""; }

.mfp-bg { z-index: 1042; overflow: hidden; background: rgb(11, 11, 11); opa=
city: 0.8; }

.mfp-wrap { z-index: 1043; backface-visibility: hidden; outline: 0px !impor=
tant; }

.mfp-container { text-align: center; position: absolute; left: 0px; top: 0p=
x; padding: 0px 8px; box-sizing: border-box; }

.mfp-container, img.mfp-img { box-sizing: border-box; }

.mfp-container::before { display: inline-block; height: 100%; vertical-alig=
n: middle; }

.mfp-align-top .mfp-container::before { display: none; }

.mfp-content { position: relative; display: inline-block; vertical-align: m=
iddle; margin: 0px auto; text-align: left; z-index: 1045; }

.mfp-ajax-holder .mfp-content, .mfp-inline-holder .mfp-content { width: 100=
%; cursor: auto; }

.mfp-ajax-cur { cursor: progress; }

.mfp-zoom, .mfp-zoom-out-cur, .mfp-zoom-out-cur .mfp-image-holder .mfp-clos=
e { cursor: pointer; }

.mfp-zoom { cursor: zoom-in; }

.mfp-auto-cursor .mfp-content { cursor: auto; }

.mfp-arrow, .mfp-close, .mfp-counter, .mfp-preloader { user-select: none; }

.mfp-loading.mfp-figure { display: none; }

.mfp-hide { display: none !important; }

.mfp-preloader { color: rgb(204, 204, 204); position: absolute; top: 50%; w=
idth: auto; text-align: center; margin-top: -0.8em; left: 8px; right: 8px; =
z-index: 1044; }

.mfp-preloader a { color: rgb(204, 204, 204); }

.mfp-close, .mfp-preloader a:hover { color: rgb(255, 255, 255); }

.mfp-s-error .mfp-content, .mfp-s-ready .mfp-preloader { display: none; }

button.mfp-arrow, button.mfp-close { overflow: visible; cursor: pointer; ba=
ckground: 0px 0px; border: 0px; -webkit-appearance: none; display: block; o=
utline: 0px; padding: 0px; z-index: 1046; box-shadow: none; }

.mfp-figure::after, .mfp-iframe-scaler iframe { position: absolute; left: 0=
px; box-shadow: rgba(0, 0, 0, 0.6) 0px 0px 8px; }

.mfp-close { width: 44px; height: 44px; line-height: 44px; position: absolu=
te; right: 0px; top: 0px; text-decoration: none; text-align: center; opacit=
y: 0.65; padding: 0px 0px 18px 10px; font-style: normal; font-size: 28px; f=
ont-family: Arial, Baskerville, monospace; }

.mfp-close:focus, .mfp-close:hover { opacity: 1; }

.mfp-close:active { top: 1px; }

.mfp-close-btn-in .mfp-close { color: rgb(51, 51, 51); }

.mfp-iframe-holder .mfp-close, .mfp-image-holder .mfp-close { color: rgb(25=
5, 255, 255); right: -6px; text-align: right; padding-right: 6px; width: 10=
0%; }

.mfp-counter { position: absolute; top: 0px; right: 0px; color: rgb(204, 20=
4, 204); font-size: 12px; line-height: 18px; }

.mfp-figure, img.mfp-img { line-height: 0; }

.mfp-arrow { position: absolute; opacity: 0.65; margin: -55px 0px 0px; top:=
 50%; padding: 0px; width: 90px; height: 110px; -webkit-tap-highlight-color=
: transparent; }

.mfp-arrow:active { margin-top: -54px; }

.mfp-arrow:focus, .mfp-arrow:hover { opacity: 1; }

.mfp-arrow .mfp-a, .mfp-arrow .mfp-b, .mfp-arrow::after, .mfp-arrow::before=
 { content: ""; display: block; width: 0px; height: 0px; position: absolute=
; left: 0px; top: 0px; margin-top: 35px; margin-left: 35px; border: inset t=
ransparent; }

.mfp-arrow .mfp-a, .mfp-arrow::after { border-top-width: 13px; border-botto=
m-width: 13px; top: 8px; }

.mfp-arrow .mfp-b, .mfp-arrow::before { border-top-width: 21px; border-bott=
om-width: 21px; opacity: 0.7; }

.mfp-arrow-left { left: 0px; }

.mfp-arrow-left .mfp-a, .mfp-arrow-left::after { border-right: 17px solid r=
gb(255, 255, 255); margin-left: 31px; }

.mfp-arrow-left .mfp-b, .mfp-arrow-left::before { margin-left: 25px; border=
-right: 27px solid rgb(63, 63, 63); }

.mfp-arrow-right { right: 0px; }

.mfp-arrow-right .mfp-a, .mfp-arrow-right::after { border-left: 17px solid =
rgb(255, 255, 255); margin-left: 39px; }

.mfp-arrow-right .mfp-b, .mfp-arrow-right::before { border-left: 27px solid=
 rgb(63, 63, 63); }

.mfp-iframe-holder { padding-top: 40px; padding-bottom: 40px; }

.mfp-iframe-holder .mfp-content { line-height: 0; width: 100%; max-width: 9=
00px; }

.mfp-image-holder .mfp-content, img.mfp-img { max-width: 100%; }

.mfp-iframe-holder .mfp-close { top: -40px; }

.mfp-iframe-scaler { width: 100%; height: 0px; overflow: hidden; padding-to=
p: 56.25%; }

.mfp-iframe-scaler iframe { display: block; top: 0px; width: 100%; height: =
100%; background: rgb(0, 0, 0); }

.mfp-figure::after, img.mfp-img { display: block; width: auto; height: auto=
; }

img.mfp-img { box-sizing: border-box; padding: 40px 0px; margin: 0px auto; =
}

.mfp-figure::after { top: 40px; bottom: 40px; right: 0px; z-index: -1; back=
ground: rgb(68, 68, 68); }

.mfp-figure small { color: rgb(189, 189, 189); display: block; font-size: 1=
2px; line-height: 14px; }

.mfp-figure figure { margin: 0px; }

.mfp-bottom-bar { margin-top: -36px; position: absolute; top: 100%; left: 0=
px; width: 100%; cursor: auto; }

.mfp-title { text-align: left; line-height: 18px; color: rgb(243, 243, 243)=
; overflow-wrap: break-word; padding-right: 36px; }

.mfp-gallery .mfp-image-holder .mfp-figure { cursor: pointer; }

@media screen and (max-width: 800px) and (orientation: landscape), screen a=
nd (max-height: 300px) {
  .mfp-img-mobile .mfp-image-holder { padding-left: 0px; padding-right: 0px=
; }
  .mfp-img-mobile img.mfp-img { padding: 0px; }
  .mfp-img-mobile .mfp-figure::after { top: 0px; bottom: 0px; }
  .mfp-img-mobile .mfp-figure small { display: inline; margin-left: 5px; }
  .mfp-img-mobile .mfp-bottom-bar { background: rgba(0, 0, 0, 0.6); bottom:=
 0px; margin: 0px; top: auto; padding: 3px 5px; position: fixed; box-sizing=
: border-box; }
  .mfp-img-mobile .mfp-bottom-bar:empty { padding: 0px; }
  .mfp-img-mobile .mfp-counter { right: 5px; top: 3px; }
  .mfp-img-mobile .mfp-close { top: 0px; right: 0px; width: 35px; height: 3=
5px; line-height: 35px; background: rgba(0, 0, 0, 0.6); position: fixed; te=
xt-align: center; padding: 0px; }
}

@media (max-width: 900px) {
  .mfp-arrow { transform: scale(0.75); }
  .mfp-arrow-left { transform-origin: 0px center; }
  .mfp-arrow-right { transform-origin: 100% center; }
  .mfp-container { padding-left: 6px; padding-right: 6px; }
}

.mfp-ie7 .mfp-img { padding: 0px; }

.mfp-ie7 .mfp-bottom-bar { width: 600px; left: 50%; margin-left: -300px; ma=
rgin-top: 5px; padding-bottom: 5px; }

.mfp-ie7 .mfp-container { padding: 0px; }

.mfp-ie7 .mfp-content { padding-top: 44px; }

.mfp-ie7 .mfp-close { top: 0px; right: 0px; padding-top: 0px; }

.mfp-fade.mfp-bg { opacity: 0; transition: all 0.15s ease-out 0s; }

.mfp-fade.mfp-bg, .mfp-fade.mfp-wrap .mfp-content { transition: all 0.15s e=
ase-out 0s; }

.mfp-fade.mfp-bg.mfp-ready { opacity: 0.8; }

.mfp-fade.mfp-bg.mfp-removing { opacity: 0; }

.mfp-fade.mfp-wrap .mfp-content { opacity: 0; transition: all 0.15s ease-ou=
t 0s; }

.mfp-fade.mfp-wrap.mfp-ready .mfp-content { opacity: 1; }

.mfp-fade.mfp-wrap.mfp-removing .mfp-content { opacity: 0; }
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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Content-Location: https://learning.oreilly.com/library/view/heat-and-mass/9789332515680/images/pg47_img01a.png

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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl----
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------MultipartBoundary--RkpIvkyUsdopYy9YIn1i9BImqisJMdKvQAvLLJ6xJl------
