boiling and condensation 2 3
TRANSCRIPT
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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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Heat Transfer Correlations in Pool
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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Heat Transfer Correlations in Pool
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
1/3
, 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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Dropwise Condensation
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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Dropwise Condensation
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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