Boiling and Condensation 2 3

8/2/2019 Boiling and Condensation 2 3

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Chapter 6: Boiling and

Condensation


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ObjectivesWhen you finish studying this chapter, you should be able to:

Differentiate between evaporation and boiling, and gainfamiliarity with different types of boiling,

Develop a good understanding of the boiling curve, andthe different boiling regimes corresponding to differentregions of the boiling curve,

Calculate the heat flux and its critical value associatedwith nucleate boiling, and examine the methods of boilingheat transfer enhancement,

Calculate the heat flux associated with condensationhorizontal plates, vertical and horizontal cylinders

Examine dropwise condensation and understand theuncertainties associated with them.


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Specific convection processes

Boiling

Condensation Change of phase

Boiling : Liquid to vapour phase

Condensation : Vapour to liquid phase


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Modes of Heat transfer finds wide application

1. Cooling of nuclear reactors and rocket motors


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3. Steam power plant

4. Refrigeration and air conditioning

5.Refineries and sugar mill


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1. Heat transfer to and fro occurs without affecting the fluid

temperature

2. The heat transfer coefficients and rates due to latent heat

associated with phase change are generally much higher

compared to normal convection process(without phase change)

Boiling and condensation entails following

features


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3. High rate of heat transfer is developed with small

temp diff

Phenomena of boiling and condensation is

complex due to following being significant

1.Latent heat2.Surface tension

3. Surface characteristics and other properties of two phase systems


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General ConsiderationsGeneral Considerations

Boiling is associated with transformation of liquid to vapor at a solid/liquid

interface due to convection heat transfer from the solid.

Agitation of fluid by vapor bubbles provides for large convection coefficients

and hence large heat fluxes at low-to-moderate surface-to-fluid temperature

differences.

Special form ofNewtons law of cooling:

s s sat eq h T T h T

saturation temperatur of liquidesatT

excess temperaturee s sat T T T


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Boiling Heat Transfer Evaporationoccurs at

the liquid

vapor

interface when the

vapor pressure is less

than the saturationpressure of

the liquid

at a given

temperature.

Boilingoccurs at the

solid

liquid interface

when a liquid is brought

into contact with a

surface maintained at atemperature sufficiently

above the saturation

temperature of the

liquid


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Classification of boilingPool Boiling

Boiling is called pool

boilingin the absenceof bulk fluid flow.

Any motion of the fluidis due to natural

convection currents andthe motion of thebubbles

under the

influence

of buoyancy.

Flow Boiling

Boiling is called flowboilingin the presenceof bulk fluid flow.

In flow boiling, the fluid

is forced to move in aheated pipe

or over a

surface by

externalmeans such

as a pump.


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Subcooled Boiling

When the temperature

of the main body of the

liquid is below thesaturation temperature.

Saturated Boiling

When the temperature

of the liquid is equal to

the saturationtemperature.

Classification of boiling


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Boiling Regimes

Pool boiling with liquid vapor interface


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Pool BoilingBoiling takes different forms, depending on the Texcess=Ts-Tsat


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The Boiling Curve

1 atm

Free convection boilingfluid motion isdetermined principally by free

convection


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The Boiling CurveNucleate boilingfrom A to B, we have isolated bubbles at

nucleation sites which separate from the surface, leads to

considerable fluid mixing.


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The Boiling CurveNucleate boilingfrom B to C, vapor escapes as jets or columns which merge

into slugs of vapor. Point P is an inflection point which corresponds to the

maximum heat transfer coefficient. Beyond P, q increases since Te grow faster

than h decreases. Beyond C, h decreases faster than Te increases, so q goes down.


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The Boiling Curve

Critical heat fluxconsiderable formation of

vapor making it difficult to continuously wet the

surface.


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Transition boilingbubble formation is so rapid that a vapor film or

blanket forms on the surface. Thermal conductivity of vapor is much less

than liquid, so q decreases.


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Film boilingPoint D is Leidenfrost point, heat flux is a

minimum, surface is completely covered by a vapor

blanket. Heat transfer from surface occurs by conduction

and radiation through the vapor.


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Experiment was first conducted with nichrome wire which burned out at

critical heat flux. Subsequent experiments with platinum wire allowed

cooling from Pt E to D. Beyond D (going to left), Te jumped to curve

on left.


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Natural Convection (to PointA on the

Boiling Curve)

Bubbles do not form on the heating surface until the

liquid is heated a few degrees above the saturation

temperature (about 2 to 6C for water)

the liquid is slightly superheatedin thiscase (metastable state).

The fluid motion in this mode of boiling is governed

by natural convection currents.

Heat transfer from the heating surface to the fluid is

by natural convection.


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Nucleate Boiling

The bubbles form at an increasing rate at an

increasing number of nucleation sites as wemove along the boiling curve toward point C.

RegionABisolated bubbles.

RegionBC numerous continuous columnsof vaporin the liquid.


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Nucleate Boiling

In regionAB the stirring and agitation caused by theentrainment of the liquid to the heater surface isprimarily responsible for the increased heat transfercoefficient.

In regionAB the large heat fluxes obtainable in thisregion are caused by the combined effect of liquidentrainment and evaporation.

After pointB the heat flux increases at a lower rate

with increasing Texcess, and reaches a maximum atpoint C.

The heat flux at this point is called the critical (ormaximum)heat flux, and is of prime engineeringimportance.


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Transition Boiling

When Texcess is increased past point C, the heat fluxdecreases.

This is because a large fraction of the heater surface is

covered by a vapor film, which acts as an insulation.

In the transition boiling regime, both nucleate and film

boiling partially occur.


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Film Boiling Beyond PointDthe heater surface is completely

covered by a continuous stable vapor film.

PointD, where the heat flux reaches a minimum is

called the Leidenfrost point.

The presence of a vapor film between the heater

surface and the liquid is responsible for the low heattransfer rates in the film boiling region.

The heat transfer rate increases with increasing excess

temperature due to radiation to the liquid.


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Burnout Phenomenon

A typical boiling process does not follow the boilingcurve beyond point C.

When the power applied to the

heated surface exceeded the

value at point Ceven slightly,the surface temperature

increased suddenly to pointE.

When the power is reducedgradually starting from pointE

the cooling curve follows Fig. 108 with a sudden

drop in excess temperature when pointD is reached.

C

D

E


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Heat Transfer Correlations in Pool

Boiling

Boiling regimes differ considerably in their

character

different heat transfer relations need

to be used for different boiling regimes.

In the natural convection boiling regime heat

transfer rates can be accurately determined

using natural convection relations.


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Boiling Nucleate Boiling

No general theoretical relations for heat transfer in

the nucleate boiling regime is available.

Experimental based correlations are used.

The rate of heat transfer strongly depends on thenature of nucleation and the type and the condition of

the heated surface.

A widely used correlation proposed in 1952 byRohsenow:


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Rohsenows equation:

1 32

,

, Pr

p l el v

s l fg n

s f fg l

c Tgq h

C h

This was the first and still is the most widely used correlation for nucleate boiling.


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qs= surface heat flux ,W/m2

l =Liquid viscosity,kg/ms

Hfg=Enthalpy of vaporisation, j/kg


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Rohsenows correlation applies only to clean

surfaces. When used to estimate heat flux, errors

can amount to plus/minus 100%.

However, since Te is proportional to (q)^(1/3), this

error is reduced by a factor of 3 when the expressionis used to estimate Te from q.

Since q is proportional to hfg^-2, and hfgdecreases with increasing saturation pressure

(temperature), the nucleate boiling heat flux will

increase as the liquid is pressurized.


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Rohsenows correlation does not predict q max. For this, we must use

Zubers equation:

1

4

max 2

l v

fg v

v

gq Ch


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Boiling Nucleate Boiling

The values in Rohsenow equation can be used for anygeometry since it is found that the rate of heat transferduring nucleate boiling is essentially independent ofthe geometry and orientation of the heated surface.

The correlation is applicable to clean and relativelysmooth surfaces.

Error for the heat transfer rate for a given excesstemperature: 100%.

Error for the excess temperature for a given heattransfer rate for the heat transfer rate and by 30%.


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Minimum Heat Flux

Minimum heat flux, which occurs at the Leidenfrostpoint, is of practical interest since it represents thelower limit for the heat flux in the film boiling regime.

Zuber derived the following expression for theminimum heat flux for a large horizontal plate

the relation above can be in error by50% or more.

14

max 20.09

l v

v fg

l v

gq h


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Film Boiling

The heat flux for film boiling on a horizontal

cylinderor sphere of diameterDis given by

At high surface temperatures (typically above 300C), heattransfer across the vapor film by radiation becomes significantand needs to be considered.

The two mechanisms of heat transfer (radiation and convection)

adversely affect each other, causing the total heat transfer to beless than their sum.

Experimental studies confirm that the critical heat flux andheat flux in film boiling are proportional to g1/4.

143

0.4v v l v fg pv s sat film film s sat

v s sat

gk h C T T q C T T

D T T


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Enhancement of Heat Transfer in Pool

Boiling The rate of heat transfer in the nucleate boiling regime

strongly depends on the number of active nucleation sites onthe surface, and the rate of bubble formation at each site.

Therefore, modification that enhances nucleationon theheating surface will also enhance heat transferin nucleateboiling.

Irregularities on the heating surface, including roughness anddirt, serve as additional nucleation

sites during boiling.

The effect ofsurface roughness is

observed to decay with time.


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Enhancement of Heat Transfer in Pool

Boiling

Surfaces that provide enhanced heat transfer innucleate boilingpermanently are being manufactured

and are available in the market.

Heat transfer can be enhanced by a factor of up to 10

during nucleate boiling, and the

critical heat flux by a factor of 3.

Thermoexcel-E


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Condensation

Condensation occurs when the temperature of

a vapor is reduced below its saturation

temperature.

Only condensation on solid surfaces is

considered in this chapter.

Two forms of condensation:

Film condensation,

Dropwise condensation.


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Film condensation

The condensate wets thesurface and forms a liquid

film. The surface is blanketed by

a liquid film which serves asa resistance to heat transfer.

Dropwise condensation

The condensed vapor formsdroplets on the surface.

The droplets slide downwhen they reach a certainsize.

No liquid film to resist heat

transfer. As a result, heat transfer

rates that are more than 10times larger

than with film

condensation

can be achieved.


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Film Condensation on a Vertical Plate

liquid film starts forming at the topof the plate and flows downwardunder the influence of gravity.

dincreases in the flow directionx

Heat in the amount hfgis releasedduring condensation and istransferredthrough the film to theplate surface.

Tsmust be below the saturationtemperature for condensation.

The temperature of the condensateis Tsat at the interface and decreasesgradually to Tsat the wall.


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Vertical Plate Flow Regimes

The dimensionless parametercontrolling the transition betweenregimes is the Reynolds numberdefined as:

Three prime flow regimes:

Re


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Heat Transfer Correlations for Film

Condensation Vertical wall

Assumptions:1. Both the plate and the vapor are

maintained at constant temperatures ofTsand Tsat, respectively, and the temperatureacross the liquid film varies linearly.

2. Heat transfer across the liquid film is bypure conduction.

3. The velocity of the vapor is low (or zero)so that it exerts no drag on the condensate(no viscous shear on the liquidvapor

interface).4. The flow of the condensate islaminar(Re


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Hydrodynamics

Netwons second law of motion

Weight=Viscous shear force +Buoyancy force

or

Canceling the plate width band solving for du/dy

Integrating fromy=0 (u =0) toy (u=u(y))

l l vdu

g y bdx bdx g y bdxdy

d d

l v

l

g ydu

dy

d

2( )

2

l v

l

g yu y y

d

(10-12)


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0

( ) ( ) ( )l lA y

m x u y dA u y bdy

d

(10-13)

The mass flow rate of the condensate at a locationx is determined from

Substituting u(y) from Eq. 1012 into Eq. 1013

whose derivative with respect toxis

3( )

3

l l v

l

gbm x

d

(10-14)

2l l v

l

gbdm d

dx dx

d d

(10-15)


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Thermal Considerations

The rate of heat transfer from the vapor to the plate

through the liquid film

sat s fg l

l sat s

fg

T TdQ h dm k bdx

k b T T dm

dx h

d

d

(10-16)


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Equating Eqs. 1015 and 1016 and separating

the variables give

Integrating fromx=0 (d=0) tox (d=d(x)), the

liquid film thickness atx is determined to be

3 l l sat s

l l v fg

k T Td dx

g h

d d

(10-17)

1 4

4( )

l l sat s

l l v fg

k T T xx

g h

d

(10-18)

Si th h t t f th liq id film i m d t b b


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Since the heat transfer across the liquid film is assumed to be by

pure conduction, the heat transfer coefficient can be expressed

throughNewtons law of cooling and Fourier law as

Substituting d(x) from Eq. 1018, the local heat transfer coefficient

is determined to be

The average heat transfer coefficient over the entire plate is

sat s l x x sat s l xT T kq h T T k hd d (10-19)

1 43

4

l l v fg l

x

l sat s

g h kh

T T x

(10-20)

1 43

0

1 40.943

3

L l l v fg l

x x L

l sat s

g h kh h dx h

L T T L

(10-21)


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It is observed to underpredict heat transfer

because it does not take into account the

effects of the nonlinear temperature profile in

the liquid film and the cooling of the liquid

below the saturation temperature.

Both of these effects can be accounted for by

replacing hfgby modified h*fg to yield

1 4* 3

0

1 4

0.9433

L l l v fg l

x x L

l sat s

g h k

h h dx h L T T L

(10-22)

0


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Wavy Laminar Flow on Vertical


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Wavy Laminar Flow on Vertical

Plates

The waves at the liquidvapor interface tend to

increase heat transfer.

Knowledge is based on experimental studies.

The increase in heat transfer due to the wave effect is,on average, about 20 percent, but it can exceed 50

percent.

Based on his experimental studies, Kutateladze (1963)

recommended the following relation

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, v1.22 2

Re;

1.08Re 5.2

lavg wavy l

l

k gh


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Turbulent Flow on Vertical Plates

Labuntsov (1957) proposed the following relation

for the turbulent flow of condensate on vertical

plates:

The physical properties of the condensate are to be

evaluated at the film temperature.

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, 20.5 0.75

Re

8750 58Pr Re 253

l

avg turbulent

l

k g

h


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Dropwise Condensation


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One of the most effective mechanisms ofheat transfer,and extremely large heat transfer coefficients can beachieved.

Small droplets grow as a result of continuedcondensation, coalesce into large droplets, and slidedown when they reach a certain size.

Large heat transfer

coefficients enable designers

to achieve a specified heattransfer rate with a smaller

surface area.

i d i


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The challenge in dropwise condensation is not to

achieve it, but rather, to sustain it for prolonged

periods of time.

Dropwise condensation has been studiedexperimentally for a number of surfacefluid

combinations.

Griffith (1983) recommends these simple

correlations for dropwise condensation ofsteam oncopper surfaces:

0 0

0

51,104 2044 22 100

255,310 100

sat sat

sat

T C T C hdropwise

T C


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Boiling and Condensation 2 3