HHeeaatt aanndd MMaassss TTrraannssffeerr CChhaapptteerr ... Data/Heat Transfer/Study/Chapter-8... · There are two modes in which condensation can take place on a cooling surface

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Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)

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PPuurrvvii BBhhoooosshhaann

In This Chapter We Cover the Following Topics

Art. Content Page

8.1 Condensation Heat Transfer 2

8.2 Laminar Film Condensation on a Vertical Plate 3

8.3 Film Condensation on Horizontal Tubes 8

8.4 Condensation Number 9

8.5 Turbulent Film Condensation 10

8.6 Film Condensation inside Horizontal Tubes 11

8.7 Boiling Heat Transfer

Regimes of Boiling

Correlations of Boiling Heat-Transfer Data

Factors Affecting Nucleate Boiling

13

13

15

16

References:

1- J. P. Holman, Heat Transfer, 9th Edn, MaGraw-Hill, New York, 2002.

2- James R. Welty, Charles E. Wicks, Robert E. Wilson, Gregory L. Rorrer

Fundamentals of Momentum, Heat, and Mass Transfer, 5th Edn, John Wiley & Sons,

Inc., 2008.

3- F. Kreith and M. S. Bohn, Principal of Heat Transfer, 5th Edn, PWS Publishing Co.,

Boston, 1997.

4- P. K. Nag, Heat and Mass Transfer, 2nd Edn, MaGraw-Hill, New Delhi 2005.

Please welcome for any correction or misprint in the entire manuscript and your

valuable suggestions kindly mail us [email protected].

Condensation occurs when a vapour contacts a surface that is at a temperature below

the saturation temperature of the vapour. When the liquid condensate forms on the

surface, it will flow under the influence of gravity.




2 Chapter 8: Condensation and Boiling

Heat energy is being converted into electrical energy with the help of water as a

working fluid. Water is first converted into steam when heated in a heat exchanger and

then the exhaust steam coming out of the steam turbine/engine is condensed in a

condenser so that the condensate (water) is recycled again for power generation.

Therefore, the condensation and boiling processes involve heat transfer with change of

phase. When a fluid changes its phase, the magnitude of its properties like density,

viscosity, thermal conductivity, specific heat capacity, etc., change appreciably and the

processes taking place are greatly influenced by them. Thus, the condensation and

boiling processes must be well understood for an effective design of different types of

heat exchangers being used in thermal and nuclear power plants, and in process cooling

and heating systems.

8.1 CONDENSATION HEAT TRANSFER

When a saturated vapour comes in contact with a surface the temperature of which is

maintained below the saturation temperature at the vapour pressure, the vapour cannot

but condense into liquid releasing the latent heat of condensation at that pressure with

a coolant (cooling water) carrying away this heat (Diagram 8.1).

Diagram 8.1 condensing of saturated

There are two modes in which condensation can take place on a cooling surface.

1. Dropwise condensation

2. Filmwise condensation

Film wise condensation: If the liquid wets the surface, a smooth film is formed, and

the process is called film condensation.

In the film-condensation process the surface is blanketed by the film, which grows in

thickness as it moves down the plate. A temperature gradient exists in the film, and the

film represents a thermal resistance to heat transfer.

In film condensation, a stable coherent film of liquid condensate is formed on the surface

through which the heat released during condensation is conducted into the surface

(Diagram 8.1). On a wettable cooling surface, film condensation takes place.

Drop wise Condensation: If the liquid does not wet the surface, droplets are formed

that fall down the surface in some random fashion. This process is named as dropwise

condensation.

In dropwise condensation a large portion of the area of the plate is directly exposed to

the vapor; there is no film barrier to heat flow, and higher heat-transfer rates are

experienced. In fact, heat-transfer rates in dropwise condensation may be as much as 10

times higher than in film condensation.

Saturation

vapour

Condensation

film

Cooling water

Saturation vapour




3 Heat and Mass Transfer By Brij Bhooshan

Diagram 8.2 Dropwise condensation

In dropwise condensation, vapour condenses on the surface in the form of drops, and

consequently a large part of cooling surface is always bare to vapour for undergoing

condensation (Diagram 8.2). The rate of heat transfer is many times larger than what is

achieved in film condensation. Dropwise condensation occurs on a nonwettabie cooling

surface where the liquid condensate drops do not spread.

Let us explain briefly what is a wettable or a nonwettable surface. The surface of a

liquid always tends towards a minimum. A freely suspended drop of liquid always takes

the shape of a sphere which is of the geometrical shape having the minimum surface

area for the same volume. This is due to the effect of surface tension. Surface tension

always exists whenever there is a discontinuity in the material medium. Mercury in

contact with air has a certain surface tension. With water, mercury has another surface

tension. Let us consider the equilibrium of a liquid drop on a solid surface (Diagram 8.3),

σ being the surface tension as shown.

Diagram 8.3 Equilibrium of a liquid drop on a solid surface

If σ1 cos 1 + σ3 = σ2, the liquid drop remains in equilibrium and does not spread. The

surface is nonwettable (e.g. mercury in glass).

where is the angle of contact.

If σ1 cos 1 + σ3 > σ2, me liquid drop spreads and the surface is wettable (e.g. water in

glass). When is obtuse, the surface is nonwettable, and if is acute, the surface is

wettable.

Dropwise condensation is much desirable because of its higher heat transfer rates.

However, it hardly occurs on a cooling surface. When the surface is coated with some

promoter like teflon, grease, mercaptan, oleic acid and so on, drop condensation can

occur for some time. But the effectiveness of the promoter gradually decays due to

fouling, oxidation or its slow removal by the flow of the condensate. Condensers are

usually designed on the basis that film condensation would prevail.

8.2 LAMINAR FILM CONDENSATION ON A VERTICAL PLATE

Numerous experimental and theoretical investigations have been conducted to

determine the heat transfer coefficient for film condensation on surfaces. The first

fundamental analysis in this aspect was given by Nusselt in 1916. Nusselt's theory of

film condensation of pure vapours on a vertical plate is presented below. It serves as a

basis to better understand heat transfer during condensation.

Liquid drop

Solid

Air

Bore surface

Liquid condensate

drop





Nusselt's Theory:

Let us consider condensation of a vapour on a vertical plate as shown in Diagram 8.4.

Here x is the axial coordinate, measured downward along the plate, and y is the

coordinate normal to the condensing surface. The condensate thickness is represented

by (x). Nusselt made the following assumptions:

1. The vapour is pure, dry and saturated.

2. The condensate flow is under the action of gravity and is laminar.

3. The vapour at the liquid-vapour interface is stagnant so that there is no shear

stress or drag on the flow of condensate.

4. The plate is maintained at a uniform temperature Tw that is less than the

saturation temperature of the vapour Tg.

5. The liquid temperature at the interface is that of saturated vapour.

6. Fluid properties are constant.

7. Heat transfer across the condensate layer is by pure conduction, and the liquid

temperature profile is linear.

8. Heat transfer is at steady state.

Diagram 8.4 Film condensation on a vertical flat plate.

The plate temperature is maintained at Tw, and the vapor temperature at the edge of

the film is the saturation temperature Tg. The film thickness is represented by δ, and we

choose the coordinate system with the positive direction of x measured downward, as

shown. It is assumed that the viscous shear of the vapor on the film is negligible at y = δ.

It is further assumed that a linear temperature distribution exists between wall and

vapor conditions.

The weight of the fluid element of thickness dx between y and δ per unit length

Viscous shear force at y

Buoyancy force due to the displaced vapor

Under steady state condition force balance equation is





where ρ = density of liquid film, ρv = density of vapour, u = velocity of the liquid film.

Integrating and using the boundary condition that u = 0 at y = 0 gives

The mass flow of condensate through any x position of the film is thus given by

when unit depth is assumed. The heat transfer at the wall in the area dx is

since a linear temperature profile was assumed. As the flow proceeds from x to x + dx,

the film grows from δ to δ + dδ as a result of the influx of additional condensate. The

amount of condensate added between x to x + dx is

The heat removed by the wall must equal this incremental mass flow times the latent

heat of condensation of the vapor.

Thus

Equation (8.9) may be integrated with the boundary condition δ = 0 at x = 0 to give

The heat-transfer coefficient is





The average value of the heat-transfer coefficient is obtained by integrating over the

length of the plate:

Equation (8.13) may be used for vertical plates and cylinders and fluids with Pr >0.5

and cT/hfg ≤1.0.

Since ρ >>>>ρv, then equation (8.13) will be

Equations (8.13) and (8.14) are the Nusselt's equations for laminar film condensation on

a vertical plate, which can also be applied to condensation outside a tube of large

diameter. These give conservative values of heat transfer coefficient McAdams

suggested 20% increase over this value so that

The bulk temperature of the condensate is always less than saturation temperature and

hence, subcooled.

If TB is the bulk temperature, then by energy balance,

Assuming a linear temperature profile (Diagram 8.4),

and since the velocity distribution (Eq. (8.5)) is given by

at y = 0, u = 0, then

at y = , u = u, then

Equation (8.16) becomes

Again T = my + C





at y = 0, T = Tw = Tg,

at y = , T = Tsat = Ts = Tg, then

From equation 8.17, then we have

The average enthalpy change during condensation with subcooling,

From equations (8.13) and (8.19),

If the surface is inclined at an angle with the horizontal (Diagram 8.5), the average

coefficient is

Diagram 8.5 Flimwise condensation on an inclined plane surface

For Pr > 0.5 and Ja = (cpf /h'fg) < 1.0, where Ja is the Jakob number, it yields results

similar to Eqns. (8.13) - (8.15) and (8.20), except that h'fg is replaced by

then

Eq. (8.13) in terms of commonly used dimensionless products

where GrL is based on the plate length

PrL is the liquid Prandtl number, and Ja is the Jakob number defined as





As in forced-convection flow problems, the criterion for determining whether the flow is

laminar or turbulent is the Reynolds number, and for the condensation system it is

defined as

where DH = hydraulic diameter, A = flow area, P = shear, or “wetted,” perimeter, V =

average velocity in flow.

But

ṁ = ρAV

so that

The Reynolds number is sometimes expressed in terms of the mass flow per unit depth

of plate , so that

In calculating the Reynolds numbers the mass flow may be related to the total heat

transfer and the heat-transfer coefficient by

But A = LW and P = W, where L and W are the height and width of the plate,

respectively, so that

8.3 FILM CONDENSATION ON HORIZONTAL TUBES

The condensate film on the outside of horizontal tubes flows around the tube and off the

bottom in a sheet, as shown in Diagram 8.6.

The liquid film is very thin so that the above analysts applies here except that g is

replaced by g sin and average value of h follows from integration over the range of

values from 0 to 180°, as given below:

Diagram 8.6 Condensate film on horizontal tubes





where D0 is the outside diameter of the tube. This is the Nusselt's equation for film

condensation on a horizontal tube.

Therefore, hm D01/4, smaller D0 would yield higher hm. But smaller D0 means less

surface area D0L exposed for condensation, and so less heat transfer. Thus there is an

optimum tube diameter.

The heat transfer coefficient on a horizontal tube decreases from a maximum value at

= 0 to essentially zero for = 180°. The condensing rate on the upper half of the tube is

46% greater than on the lower half.

Dividing Eq. (8.29) by Eq. (8.13),

If L/D0 = 2.87, then (hm)H = (hm)V,

If L > 2.87 D0, then (hm)H > (hm)V.

For a bank of horizontal tubes in a vertical tier

where N is the number of tubes in the tier.

Thus, hm 1/N1/4. Therefore, as N increases, hm decreases. Thus, the film thickness is

greater for the lower tubes, increasing the resistance to heat transfer.

For condensation on a sphere, it can similarly be shown,

where D is the diameter of sphere.

The total heat transfer to the surface is

The physical properties of the liquid film should be evaluated at an effective film

temperature.

Average temperature

8.4 CONDENSATION NUMBER

Because the film Reynolds number is so important in determining condensation

behavior, it is convenient to express the heat-transfer coefficient directly in terms of Re.

We include the effect of inclination and write the heat-transfer equations in the form

where the constant is evaluated for a plate or cylindrical geometry. From Equation

(8.26) we can solve for Tg −Tw as





From equations (8.33) and (8.34), we have

We now define a new dimensionless group, the condensation number Co, as

From equations (8.35) and (8.36), we have

For a vertical plate A/PL = 1.0, and we obtain, using the constant from Equation (8.14),

For a horizontal cylinder A/PL = and

When turbulence is encountered in the film, an empirical correlation by Kirkbride may

be used:

8.5 TURBULENT FILM CONDENSATION

Just as a fluid flowing over a surface undergoes a transition from laminar to turbulent

flow, in the same way the motion of the condensate becomes turbulent when its

Reynolds number exceeds a critical value of 2000.

For Re > 2000, Colburn's relation can be used

We obtain average values of heat transfer coefficient, using Eq. (8.13) for 4/f < 2000

and Eq. (8.39) for 4/f > 2000.

Turbulent flow of condensate is hardly ever reached on a horizontal tube, where flow is

almost always laminar, but it may occur on the lower part of a vertical surface, when hm

becomes larger due to turbulence with larger length.

Kirkbride proposed the following empirical correlation for film condensation on a

vertical plate after the start of turbulence.

8.6 FILM CONDENSATION INSIDE HORIZONTAL TUBES





For refrigeration and air conditioning systems, condensers often involve condensation

inside horizontal or vertical tubes. Conditions within the tube are complicated and

greatly depend on the vapour velocity inside the tube. If the vapour velocity is small, the

condensate flow is from the upper portion of the tube to the bottom, from which it flows

in a longitudinal direction with the vapour (Diagram 8.7).

Diagram 8.7 Film condensation in a horizontal tube

For low vapour velocities such that

where i refers to the tube inlet, Chato recommends the following equation

where

Equation (8.41) is restricted to low vapor Reynolds numbers such that

where Rev is evaluated at inlet conditions to the tube.

For higher flow rates an approximate empirical expression is given by Akers, Deans, and

Crosser as

where now Rem is a mixture Reynolds number, defined as

The mass velocities for the liquid Gf and vapor Gv are calculated as if each occupied the

entire flow area.

Carpenter and Colburn correlated their experimental data for condensation with high

vapour velocity

Gm = Mean value of mass velocity of vapour kg/m2s.

Condensate

Vapour





G1 = mass velocity at the top of tube, G2 = mass velocity at the bottom of tube.

f = fraction of co-efficient evaluated at the average vapour velocity

w = wall shear stress N/m2.

All physical properties of equation (8.46) are evaluated at a reference temperature of

(0.25Tg + 0.75Tw).

Problem 8.1: A square pan with its bottom surface maintained at 350 K is exposed to

water vapor at 1 atm pressure and 373 K. The pan has a lip all around, so the

condensate that forms cannot flow away. How deep will the condensate film be after 10

min have elapsed at this condition?

Solution: We will employ a ‘‘pseudo-steady-state’’ approach to solve this problem. An

energy balance at the vapor–liquid interface will indicate that the heat flux and rate of

mass condensed,

The condensation rate, ṁcond, may be expressed as follows:

where dδ/dt is the rate at which the condensate film thickness, δ, grows.

The heat flux at the interface

This heat flux is now equated to that which must be conducted through the film to the

cool pan surface. The heat flux expression that applies is

This is a steady-state expression; that is, we are assuming d to be constant. If δ is not

rapidly varying, this ‘‘pseudo-steady-state’’ approximation will give satisfactory results.

Now, equating the two heat fluxes, we have

and, progressing, the condensate film thickness is seen to vary with time according to

A quantitative answer to our example problem now yields the result





8.7 BOILING HEAT TRANSFER

Boiling heat transfer is associated with a change in phase from liquid to vapor.

Extremely high heat fluxes may be achieved in conjunction with boiling phenomena,

making the application particularly valuable where a small amount of space is available

to accomplish a relatively large energy transfer. One such application is the cooling of

nuclear reactors. Another is the cooling of electronic devices where space is very critical.

The advent of these applications has spurred the interest in boiling, and concentrated

research in this area in recent years has shed much light on the mechanism and

behavior of the boiling phenomenon

There are two basic types of boiling: pool boiling and flow boiling. Pool boiling occurs on

a heated surface submerged in a liquid pool that is not agitated. Flow boiling occurs in a

flowing stream, and the boiling surface may itself be a portion of the flow passage. The

flow of liquid and vapor associated with flow boiling is an important type of two-phase

flow.

When a surface is exposed to a liquid and is maintained at a temperature above the

saturation temperature of the liquid, boiling may occur, and the heat flux will depend on

the difference in temperature between the surface and the saturation temperature.

When the heated surface is submerged below a free surface of liquid, the process is

referred to as pool boiling. If the temperature of the liquid is below the saturation

temperature, the process is called subcooled, or local, boiling. If the liquid is maintained

at saturation temperature, the process is known as saturated, or bulk, boiling.

Regimes of Boiling

An electrically heated horizontal wire submerged in a pool of water at its saturation

temperature is a convenient system to illustrate the regimes of boiling heat transfer. A

plot of the heat flux associated with such a system as the ordinate vs. the temperature

difference between the heated surface and saturated water is depicted in Diagram 8.8.

There are six different regimes of boiling associated with the behavior exhibited in this

Diagram.

Diagram 8.8 Pool boiling in water on a horizontal wire at atmospheric

In regime I, the wire surface temperature is only a few degrees higher than that of the

surrounding saturated liquid. Natural convection currents circulate the superheated

0.1 1.0 10 100 1000 10000

Sp

hero

idal

state

begin

nin

g

Interface evaporation Bubbles Film

I II III IV V VI

Boiling

curve

Radiation

coming into play

Sta

ble

fil

m b

oil

ing P

artia

l nu

cleate

boilin

g a

nd

un

stable

film N

ucl

eate

boil

ing.

Bu

bble

s ri

se t

o

inte

rface

Nu

cleate

boil

ing.

Bu

bble

s

Free

convection





liquid, and evaporation occurs at the free liquid surface as the superheated liquid

reaches it.

An increase in wire temperature is accompanied by the formation of vapor bubbles on

the wire surface. These bubbles form at certain surface sites, where vapor bubble nuclei

are present, break off, rise, and condense before reaching the free liquid surface. This is

the process occurring in regime II.

At a still higher wire surface temperature, as in regime III, larger and more numerous

bubbles form, break away from the wire surface, rise, and reach the free surface.

Regimes II and III are associated with nucleate boiling.

Beyond the peak of this curve, the transition boiling regime is entered. This is region IV

on the curve. In this regime, a vapor film forms around the wire, and portions of this

film break off and rise, briefly exposing a portion of the wire surface. This film collapse

and reformation and this unstable nature of the film is characteristic of the transition

regime. When present, the vapor film provides a considerable resistance to heat

transfer; thus, the heat flux decreases.

When the surface temperature reaches a value of approximately 400°F above the

saturated liquid, the vapor film around the wire becomes stable. This is region V, the

stable film-boiling regime.

For surface temperatures of 1000°F or greater above that of the saturated liquid,

radiant energy transfer comes into play, and the heat flux curve rises once more. This is

designated as region VI in Diagram 8.8.

The curve in Diagram 8.8 can be achieved if the energy source is a condensing vapor. If,

however, electrical heating is used, then regime IV will probably not be obtained

because of wire ‘‘burnout.’’ As the energy flux is increased, ΔT increases through regions

I, II, and III. When the peak value of q/A is exceeded slightly, the required amount of

energy cannot be transferred by boiling. The result is an increase in ΔT accompanied by

a further decrease in the possible q/A. This condition continues until point b is reached.

As ΔT at point b is extremely high, the wire will long since have reached its melting

point. Point a on the curve is often referred to as the ‘‘burnout point’’ for these reasons.

As the mechanism of energy removal is intimately associated with buoyant forces, the

magnitude of the body-force intensity will affect both the mechanism and the magnitude

of boiling heat transfer. Other than normal gravitational effects are encountered in

space vehicles.

Note the somewhat anomalous behavior exhibited by the heat flux associated with

boiling. One normally considers a flux to be proportional to the driving force; thus, the

heat flux might be expected to increase continuously as the temperature difference

between the heated surface and the saturated liquid increases. This, of course, is not the

case; the very high heat fluxes associated with moderate temperature differences in the

nucleate-boiling regime are much higher than the heat fluxes resulting from much

higher temperature differences in the film-boiling regime. The reason for this is the

presence of the vapor film, which covers and insulates the heating surface in the latter

case.

Correlations of Boiling Heat-Transfer Data





As the fluid behavior in a boiling situation is very difficult to describe, there is no

adequate analytical solution available for boiling transfer. Various correlations of

experimental data have been achieved for the different boiling regimes; the most useful

of these follow.

In the natural convection regime, regime I of Diagram 8.8, the correlations presented in

Chapter 7 for natural convection may be used.

Regime II, the regime of partial nucleate boiling and partial natural convection, is a

combination of regimes I and III, and the results for each of these two regimes may be

superposed to describe a process in regime II.

The nucleate-boiling regime, regime III, is of great engineering importance because of

the very high heat fluxes possible with moderate temperature differences. That data for

this regime are correlated by equations of the form

The parameter Nub in equation (8.48) is a Nusselt number defined as

where q/A is the total heat flux, Db is the maximum bubble diameter as it leaves the

surface, Tw Ts is the excess temperature or the difference between the surface and

saturated liquid temperatures, and kL is the thermal conductivity of the liquid. The

quantity, PrL, is the Prandtl number for the liquid. The bubble Reynolds number, Reb, is

defined as

where Gb is the average mass velocity of the vapor leaving the surface and L is the

liquid viscosity.

The mass velocity, Gb, may be determined from

where hfg is the latent heat of vaporization

Rohsenow has used equation (8.48) to correlate Addoms’s pool-boiling data for a 0.024-

in.-diameter platinum wire immersed in water.

This correlation is

where cpL is the heat capacity for the liquid.

An analysis of conditions at burnout modified by experimental results is expressed in

Regime IV, that of unstable film boiling, is not of great engineering interest, and no

satisfactory correlation has been found for this region as yet.

The stable-film-boiling region, regime V, requires high surface temperatures; thus, few

experimental data have been reported for this region.





Stable film boiling on the surface of horizontal tubes and vertical plates has been

studied both analytically and experimentally by Bromley. Considering conduction alone

through the film on a horizontal tube, Bromley obtained the expression

where D0, which is the outside diameter of the tube.

A modification in equation (8.54) was proposed by Berenson to provide a similar

correlation for stable film boiling on a horizontal surface. In Berenson’s correlation, the

tube diameter, D0, is replaced by the term [/g( v]1/2, and the recommended

expression is

where kvf, vf, and vf are to be evaluated at the film temperature as indicated.

Hsu and Westwater considered film boiling for the case of a vertical tube. Their test

results were correlated by the equation

where

ṁ being the flow rate of vapor at the upper end of the tube.

Hsu states that heat-transfer rates for film boiling are higher for vertical tubes than for

horizontal tubes when all other conditions remain the same.

In regime VI, the correlations for film boiling still apply; however, the superimposed

contribution of radiation is appreciable, becoming dominant at extremely high values of

ΔT. Without any appreciable flow of liquid, the two contributions may be combined, as

indicated by equation (8.58).

The contribution of radiation to the total heat-transfer coefficient may be expressed as

where h is the total heat-transfer coefficient, hc is the coefficient for the boiling

phenomenon, and hr is an effective radiant heat-transfer coefficient considering

exchange between two parallel planes with the liquid between assigned a value of unity

for its emissivity.

Factors Affecting Nucleate Boiling

Since high heat transfer rates and convection coefficients are associated with small

values of the excess temperature, it is desirable that many engineering devices operate

in the nucleate boiling regime. It is possible to get heat transfer coefficients in excess of

104 W/m2 in nucleate boiling regime and these values are substantially larger than those

normally obtained in convection processes with no phase change. The factors which

affect the nucleate boiling are:





(a) Pressure: Pressure controls the rate of bubble growth and therefore affects the

temperature difference causing the heat energy to flow. The maximum allowable

heat flux for a boiling liquid first increases with pressure until critical pressure is

reached and then decreases.

(b) Heating Surface Characteristics: The material of the heating element has a

significant effect on the boiling heat transfer coefficient. Copper has a higher

value than chromium, steel and zinc. Further, a rough surface gives a better heat

transfer rate than a smooth or coated surface, because a rough surface gets wet

more easily than a smooth one.

(c) Thermo-mechanical Properties of Liquids: A higher thermal conductivity of the

liquid will cause higher heat transfer rates and the viscosity and surface tension

will have a marked effect on the bubble size and their rate of formation which

affects the rate of heat transfer.

(d) Mechanical Agitation: The rate of heat transfer will increase with the increasing

degree of mechanical agitation. Forced convection increases mixing of bubbles

and the rate of heat transfer.

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HHeeaatt aanndd MMaassss TTrraannssffeerr CChhaapptteerr ... Data/Heat Transfer/Study/Chapter-8... · There are two modes in which condensation can take place on a cooling surface