6. Boiling - Heat and Mass Tran= sfer, 2nd Edition

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6 Boiling

= 6.1 BOILING HEAT TRANSFER

Boiling heat transfer is asso= ciated with the change in phase from liquid to vapor. When a solid surface = is exposed to a liquid and maintained above the saturation temperature of t= he liquid, boiling occurs. High heat fluxes may be achieved in boiling phen= omena. The two basic types of boiling are pool boiling and flow boiling. Po= ol boiling occurs on a heated surface submerged in a liquid pool and flow b= oiling occurs in a flowing stream. The boiling of water in a kettle on a st= ove and the boiling of water in boiler tubes under pressurized conditions a= re examples of pool boiling and flow boiling, respectively. The liquid and = vapor flow associated with flow boiling is a case of two-phase flow. Genera= lly, boiling phenomena are studied with respect to excess temperature, (T_w =E2=88=92 T_s= ), which is the difference between the temperature of the solid surface (T_w) and the saturation temperature of the= liquid (T_s).

If the liquid temperature is= below the saturation temperature, the boiling is known as the local or sub= cooled boiling. In this case, the bubbles formed from the solid surface col= lapses before reaching the liquid surface. If the temperature of the liquid= is equal to its saturation temperature, bubbles rise to the liquid surface= due to buoyancy and then burst. This type of boiling is called bulk or sat= urated boiling.

= 6.2 BOILING CURVE

The behavior of boiling heat = transfer is studied by immersing an electrically heated wire into water poo= l and the corresponding rate of heat transfer as a function of the excess t= emperature is shown in Fig. 6.1= .

Figure 6.1 Boiling Curve for Water at Atmospheric Pressure

The mechanism of heat transf= er can be divided into three distinct zones:

Free convection or pool boiling (= Zone I),
Nucleate boiling (Zone II),
Film boiling (Zone III).

6.2.1 = Zone I: Free Convection

In this zone, boiling takes p= lace with the excess temperature of about 5=C2=B0C. The flow produced by fr= ee convection in the liquid is sufficient to transfer the heat from the sur= face. The heat transfer rate in this zone can be calculated using free conv= ection heat transfer relationships.

6.2.2 = Zone II: Nucleate Boiling

Due to an increase in the exc= ess temperature, bubbles start to form at some locations on the heater surf= ace and formed bubbles leave the surface but collapse before reaching the l= iquid surface. As the excess temperature is increased further, bubble-gener= ation rate also increases due to numerous nucleate locations formed on the = solid surface. The bubbles in this region do not collapse inside the liquid= , but they rise to the liquid surface and then collapse. In this region, he= at transfer rate will be very high with the increase in excess temperature.= The heat transfer rate increases with temperature upto a point =E2=80= =98b=E2=80=99 and then drops. The condition at =E2=80=98b=E2=80=99= is known as critical heat flux. If boiling takes place beyond this po= int, due to high temperature, the solid surface may get damaged or it may e= ven melt. So, this point is also called as burnout point. Normally, the tem= perature of the solid surface must be maintained just below this temperatur= e.

6.2.3 = Zone III: Film Boiling

Initially, increase in excess= temperature accelerates the bubble-formation and the entire surface is cov= ered with vapor film. This film prevents the direct heat transfer to the fr= esh liquid. Film resistance causes a reduction in heat transfer rate with i= ncrease in excess temperature. In this temperature range, the film is not s= table. The vapor film is stable after this range and the heat transfer rate= to the liquid is further reduced. With further increase in surface tempera= ture (i.e., T_s =E2=88=92 T_w > 1000=C2=B0C), a major portion of the heat lost by the = surface is due to thermal radiation, which increases the heat transfer rate= from the surface. Most of the practical boiling equipments are designed ba= sed on nucleate boiling processes, which have high heat transfer rate.

= 6.3 EMPIRICAL CORRELATIONS FOR BOILING

In the boiling process, the b= asic governing equation is

Q =3D = hA(T_w =E2=88=92 T_s) (6.1)

where = Q is the rate of heat transfer, h is the boiling heat tra= nsfer coefficient, (T_w =E2=88=92 T_s) is the excess temperature, and A is the a= rea of contact between liquid and solid surfaces.

Boiling is more complex phen= omena due to latent heat effects, surface tension, surface characteristics,= and other properties of two-phase systems. Hence, mostly empirical relatio= ns are used for boiling heat transfer calculations.

= 6.4 NUCLEATE POOL BOILING

The following equation is use= d for nucleate pool boiling heat flux.

where the explanation for the= variables is given in the box.

=CE=BC_l =E2=88=92 saturated liquid viscosity (kg/m-s),=

h_fg =E2=88=92 latent heat of vaporization (J/kg),

g =E2=88=92 acc= eleration due to gravity (m/s²),

=CF=81_l =E2=88=92 density of saturated liquid (kg/m³),

=CF=81_v =E2=88=92 density of saturated vapor (kg/m³),

=CF=83 =E2=88= =92 surface tension for liquid vapor interface (N/m),

C_pl =E2=88=92 specific heat of saturated liquid (J/kgK),

C_sl =E2=80=93 constant based on heating surface and liquid (Table 6.1),

Pr_l =E2=88=92 Prandtl number of saturated liquid, and

n =E2=88=92 1.= 0 for water and 1.7 for other liquids.

Ta= ble 6.1 C_sl values for surface= liquid combinations

The following correlations a= re used for nucleate boiling at atmospheric pressure on flat and vertical p= lates.

Nu =3D= 0.16(Gr =C2=B7 Pr)^0.33 (Flat = plate) (6.3)

Nu =3D= 0.61(Gr =C2=B7 Pr)^0.25 (Verti= cal plate) (6.4)

= 6.5 CRITICAL HEAT FLUX FOR NUCLEATE POOL BOILING=

The following equation is use= d for critical heat flux in pool boiling:

= 6.6 FILM BOILING

Normally film boiling is avoi= ded, but it occurs in cryogenic liquids. In stable film boiling, heat loss = is due to convection and radiation. The following relation is used for the = heat transfer coefficient from the outer surface of horizontal tubes,

h_total =3D h_c + 0.= 75h_r (6.6)=

where the convection heat tra= nsfer coefficient is

where d is the diame= ter of horizontal tube and the radiation heat transfer coefficient is

where =CF=83 is the = Stefan=E2=80=93Boltzmann's constant (5.67 =C3=97 10^{8 W/m²K⁴) and =
=CE=B5 is the emissivity of the solid surface.}

The properties of vapor are = to be calculated at the film temperature and the latent heat of vaporizatio= n is to be taken at the saturation temperature.

= 6.7 FLOW BOILING OR FORCED CONVECTION BOILING

If boiling occurs when a liqu= id is flowing inside a heated tube, it is known as flow boiling. Boilers in= power plants use this principle to produce steam for power generation. The= correlation to calculate the heat transfer coefficient is

h =3D h_nucleate + h_convection= .

The forced convection heat t= ransfer coefficient is modified as

where d is the tube = diameter (m).

The Reynolds number is given= by the equation

The correction factor F<= /em> depends on the variables x, where m is the mass flow= rate (kg/s), x is the dryness fraction of steam, and F i= s the correction factor.

where the parameter Xt is given by

The nucleate boiling heat tr= ansfer coefficient is given by

where =E2=88=86P is = the difference between saturation pressures of the liquid at T_w and T_s and S is the suppression factor.

The factor S is cal= culated using the following:

S =3D 0.1 for Re_T > 70

and Re_T =3D F^1.25 =C3= =97 Re_l.

= 6.8 CONCLUSIONS

When a liquid comes in contac= t with a solid surface, which is higher than the saturation temperature of = the liquid at the given pressure, then the liquid undergoes phase transform= ation and becomes vapor by absorbing the latent heat of vaporization known = as boiling.

If a heated surface is fully= submerged under the stagnant liquid during boiling, then it is called as p= ool boiling. In pool boiling, if the temperature of the heating surface inc= reases to a level slightly more than the saturation temperature of the liqu= id, more vapor bubbles are formed, and they move to the free surface absorb= ing more heat. This process is called as nucleate boiling. Material, shape,= and condition of the heating surface, liquid proper= ties, pressure, and mechanical agitation are the factors influencing the nu= cleate boiling.

Critical heat flux is the po= int of maximum heat flux on the boiling curve at which transition from nucl= eate to film boiling initiates. In the boiling curve, after the critical he= at flux, the heat flux decreases as the excess temperature continues to inc= rease. The minimum heat flux point is called the Leidenfrost point and the = corresponding temperature of the surface is called the Leidenfrost temperat= ure.

KEY CONCEPTS

Boiling is a convection heat transfer process associated with = a change in the phase of the fluid from liquid to vapour.
Due to fluid movement, this process is classified as a convection h= eat transfer process.
Larger heat transfer is possible with boiling mode with smaller tem= perature difference.
Combined latent heat and bouyancy induced flows make the heat trans= fer coefficient larger.
Boiling of liquid is common in power plant boilers and refrigeratio= n systems.
Boiling is the process of liquid evaporation that occurs at the int= erface of a solid and liquid when solid surface temperature is higher than = that of the liquid.
Boiling process starts with formation of vapour bubbles which later= get detached after growing in size.
The growth of bubbles also depend on surface tension.
At pool boiling stage, free convection mechanism prevails near the = surface. Forced convection boiling can also be initiated with external forc= e.
Nucleate boiling regime provides the high heat transfer rate due to= the seperation of bubbles and better fluid mixing at surface level.
At transition boiling or unstable film boiling bubble formation is = very rapid and a vapour film or blanket forms at the surface resulting in d= ecreased heat transfer.
Heat transfer from surface is by conduction once a complete vap= our blanket is formed and this regime is known as film boiling.

= EXAMPLE PROBLEMS

6.1 A specially co= ated stainless steel heating element with surface area 0.05 m² (A), maintained at an uniform temperature of 110=C2= =B0C (T_w), (T_w) is immersed in saturated water at atmospheric pressure. Find t= he rate of evaporation assuming nucleate boiling.

The required properties = of saturated water and vapour are taken as

Therefore, substituting = the above properties

The rate of heat transfe= r,

6.2. A Teflon-coat= ed stainless steel surface, maintained at an uniform temperature of 106=C2= =B0C (T_w) is used to boil water at atmospheric p= ressure. Determine the heat flux and critical heat flux for nucleate boilin= g. Also find the heat flux for a water=E2=80=93brass system.<= /p>

Nucleate boiling

The properties of satura= ted steam and water at atmospheric pressure are the same as given in Proble= m 1.
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Assume C_sl =3D 0.006 for the water=E2=80=93Teflon-coated stai= nless steel interface Therefore,

C= ritical heat flux,

Here, the heat flux, Q/A, is less than the critical heat flux, q_c=
ritical. Hence, nucleate pool boiling exists.
Heat flux for a water=E2=80=93bras= s system
The heat flux is functio= n of

Therefore,

Therefore,

6.3. An electri= cally heated horizontal brass wire of diameter 0.2 cm (d) is immersed in sa= turated water at atmospheric pressure. The wire is maintained at a temperat= ure of 750=C2=B0C (T_w). Calculate (i) the boilin= g heat transfer coefficient (ii) the radiant heat transfer coefficient if = =CE=B5 =3D0.8 and (iii) the heat flux

Since the excess tempera= ture (T_w =E2=88=92 T_s) is 650 =C2=B0C, this is a film boiling process.

The boiling heat transfer coeffic= ient (h_c)

Properties of the vapour= are taken at T_f =3D (T_w + T_s)/2 =3D 425= =C2=B0C. They assume the following values:

Water density (=CF= =81_l) and h_fg at T_s are =CF=81_l, =3D 960.6 kg/m³; h<= sub class=3D"EBsub">fg=3D2257 =C3=97 l0^{3 J/kg}

Therefore,
The radiation heat transfer coefficien= t (h_r)
=

Here,

Therefore,
The heat flux
Due to film boiling and = radiation, the total heat transfer coefficient, h_t, is given by

Therefore, the heat flux= ,

6.4. Saturated wat= er is flowing at a rate of 0.1 kg/s (m) through a pipe of inner diameter 25= mm (d_i ) at atmospheric pressure. The tube wall= is maintained at an uniform temperature of 120=C2=B0C (T_w). Calculate the two-phase heat transfer coefficient at the locat= ion where the vapour mass quality (x) is 0.25.

Two phase heat transfer = coefficient, h =3D h_c + h_nb, with the variables defined as given below.

Therefore,

h_c =E2=80=93 convection heat transfer coefficient

h_nb<=
/sub> =E2=80=93 heat transfer coefficient for nucleate boiling

The properties of satura= ted water and steam at T_s =3D 100=C2=B0= C are taken as

T= o determine F, we have to calculate

The corresponding value = of F is 10.6.

Therefore,

The nucleate boiling hea= t transfer coefficient, h_nb is

Here,

To determine S,= we need to know Re_T =3D F1.25Re_l

Therefore,

Two phase heat transfer = coefficient,

6.5 At the rate of= 0.06 kg/s (m), water flows through a copper tube with 0.6 cm inne= r radius (R) at 1 bar pressure (P). The tube outer wall temperature (T_w ) is maintained at 140=C2=B0C by condensing steam. = Find the tube length required to make dryness fraction (x) as 0.4.

T= he properties of water are

=CF=81_l =3D 958= kg/m³; =CE=BC_l =3D 280 =C3= =97 10⁶ N-s/m²

Pr_l<= /em> =3D 1.8; k_l =3D 0.68 W/mK= ;

C_pl<= /em> =3D 4.18 kJ/kg; h_fg =3D 2258 kJ/kg=

The properties of steam = are

The convection heat tran= sfer coefficient,

where =E2=80=98F=E2=80=99 is the correction factor.

The value of F = from the graph at

The heat transfer coeffi= cient for nucleate boiling (h_nb)

where S is the = suppression factor.

Two-phase Reynolds numbe= r,

F= rom the graph, at Re_t_p<=
/sub> =3D 584208; S =3D 0.1

Heat transfer,

REVIEW QUESTIONS

Define boiling heat transfer.
Discuss the various concepts in boilin= g heat transfer with the help of the boiling curve.

State and explain the various paramete= rs involved in the heat flux equation for nucleate pool boiling recommended= by Rohsenow.

What is critical heat flux for nucleat= e boiling? How will you estimate it?

Explain the concept of film boiling an= d discuss the various parameters involved in convection and radiation heat = transfer coefficients of film boiling.

What is flow boiling?

State and discuss the various paramete= rs involved in forced convection heat transfer coefficients.

Compare the boiling heat transfer = for vertical and flat plates.

OBJECTIVE QUESTIONS

Boiling occurs at a solid=E2=80= =93liquid interface when the temperature of the surface

exceeds the saturation temperatur= e corresponding to the liquid pressure

is lower than the saturation temperatu= re corresponding to the liquid pressure

exceeds the saturation temperature cor= responding to half of the liquid pressure

all of the above

In pool boiling

the liquid is quiescent

motion near the surface is due to free= convection

mixing induced by bubble growth and de= tachment

all of the above

The is a part of pool boiling

free convection boiling

nucleate boiling

film boiling

all of the above

In free convection boiling there is va= pour in contact with the liquid phase to cause boiling at the saturation te= mperature

insufficient

sufficient

more than sufficient

no

In nucleate boiling, the convection he= at transfer coefficient will be in excess of W/m^{2 K

10
1000
10000
1}

Transition boiling is also termed as

unstable film boiling

partial film boiling

both (a) and (b)

free convection boiling
<= /li>
The increased s= urface roughness can cause a large increase in heat flux for the regime

free convection boiling

nucleate boiling

film boiling

all

The excess temperature of a surface ma= intained at 120=C2=B0C, that cause boiling of water at 1 atm is

120 =C2=B0C

20 =C2=B0C

100 =C2=B0C

110=C2=B0C

In forced convection boiling, fluid fl= ow is due to

directed motion

buoyancy effect

both (a) and (b)

none of the above

Internal forced convection boiling= is commonly referred to as

two-phase flow

single-phase flow

multiphase flow

all of the above

Answers:

(a)

(d)

(d)

(a)

(c)

(c)

(b)

(b)

(c)

(a).

EXERCISE PROBLEMS

A stainless steel plate electrica= l heater is kept inside water at 385 K and the water is at saturated condit= ion at atmospheric pressure. If the surface area of the plate is 5 m², find the rate of evaporation, assuming nucleate pool= boiling. (Ans. 4.9 tons/hr)

Water at saturated condition at atmosp= heric pressure is to be evaporated at the rate of 135 g/s with the help of = a stainless steel electrical heater with its surface temperature maintained= at 383 K. What should be the surface area of the stainless steel plate for= nucleate pool boiling? (Ans. 0.5 m^2<=
/sup>)

Saturated water at atmospheric pressur= e is boiled using a specially coated stainless steel plate that is ground a= nd polished and maintained at a temperature of 380 K. If the area of the st= ainless steel plate is 2 m², what will be the ra= te of heat transfer from it to the water when nucleate boiling exists? Assu= me that the value of C_sl is 0.008. (Ans. 690 kW)

Saturated water at atmospheric pressur= e is heated by a horizontal brass wire of 20 mm diameter maintained at 925 = K. Find the rate of heat transfer (film boiling) to the water for 2 m² surface area of the wire. What is the required wire = length for this heat transfer? (Ans. 419 kW)

In case of critical heat flux for Prob= lem 4, what will be the critical heat transfer rate? (Ans.= 3047 kW)

A tube with inner radius of 1.25 cm is= maintained at 395 K and is used to carry saturated water at atmospheric pr= essure. The flow rate of water is 360 kg/hr. Is the flow is laminar or turb= ulent? What is the convection heat transfer coefficient? (Ans. Turbulent, 17 kW/m²K)

Find the evaporation rate of water at = 1 bar from a copper pan of 0.299 m in diameter maintained at 390 K. What is= the boiling heat transfer rate? (Ans. 90 kg/hr, 56 kW)
Saturated water at atmospheric pre= ssure is boiled using a horizontally kept platinum wire of 0.1265 cm diamet= er. If the temperature difference is 649.95=C2=B0C, find the boiling heat t= ransfer coefficient. (Ans. 368 W/m^{2 K)}

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Table= of Contents for =20 Heat and Mass Transfer, 2nd Edition =20

6

Boiling

= 6.1 BOILING HEAT TRANSFER

= 6.2 BOILING CURVE

6.2.1 = Zone I: Free Convection

6.2.2 = Zone II: Nucleate Boiling

6.2.3 = Zone III: Film Boiling

= 6.3 EMPIRICAL CORRELATIONS FOR BOILING

= 6.4 NUCLEATE POOL BOILING

= 6.5 CRITICAL HEAT FLUX FOR NUCLEATE POOL BOILING=

= 6.6 FILM BOILING

= 6.7 FLOW BOILING OR FORCED CONVECTION BOILING

= 6.8 CONCLUSIONS

KEY CONCEPTS

= EXAMPLE PROBLEMS

REVIEW QUESTIONS

OBJECTIVE QUESTIONS

Answers:

EXERCISE PROBLEMS

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Table= of Contents for
=20 Heat and Mass Transfer, 2nd Edition =20