condensation

CONDENSATION

Prabal TalukdarAssociate Professor

Department of Mechanical Engineering

IIT DelhiE-mail: [email protected]

Condensation

fWhen a vapor is exposed to a surface at a temperature below Tsat, condensation in the form of a liquid film or individual d l t th fdroplets occurs on the surface.

Condensation can also occur on the free surface of a liquid or even in a gas other

P.Talukdar/Mech-IITD 2

surface of a liquid or even in a gas other than solid surfaces

Film vs. DropwiseFilm vs. Dropwise Infilmcondensation,thesurfaceisbl k d b li id fil f i iblanketedbyaliquidfilmofincreasingthickness,andthisliquidwallbetweensolidsurfaceandthevaporservesasaresistancetoheattransfer.

Indropwisecondensation,however,the droplets slide down when theythedropletsslidedownwhentheyreachacertainsize,clearingthesurfaceandexposingittovapor.Thereisnoliquidfilminthiscasetoresistheattransfer.

As a result heat transfer rates are Asaresult,heattransferratesaremorethan10timeslargerindropwisecondensation.


Film Condensation on a Vertical Plate

heat transfer in condensation also depends on whether the condensate flow is laminar or turbulent

===

4A4D

VDRe

c

l

llh

== 4P

Dh

= film thickness at the lowest part of the flow

llh m4VD &P.Talukdar/Mech-IITD 4

ll

llhp

m4VDRe ==

Hydraulic DiameterHydraulic Diameter

)TT(C)TT(C68.0hh satvpvssatplfg*fg ++=

Modified Latent Heat of Vaporization:

With these considerations, the rate of heat transfer can be expressed as

*fgsatsscondenser hm)TT(hAQ && ==


fgsatsscondenser )(Q

ll

llhp

m4VDRe == &

)TT(hA4Q4 &*fgl

ssats*fgl

conden

hp)TT(hA4

hpQ4

Re ==

the properties of the liquid should be evaluated atthe properties of the liquid should be evaluated at the film temperature Tf = (Tsat + Ts)/2, which is approximately the average temperature of the liquid

FlowRegimes


Heat Transfer Correlations for Film Condensation

Assumptions:

for Film Condensation

1.BothTsandTsat,aremaintainedconstantandthetemperatureacross the liquid filmacrosstheliquidfilmvarieslinearly.2.Heattransferacrosstheliquidfilmisbypureconductionconduction.3.Thevelocityofthevaporislow(orzero)sothatitexertsnodragonh d (thecondensate(noviscousshearontheliquidvaporinterface).4.Theflowofthecondensateislaminarandthepropertiesoftheliquidareconstant.5. The acceleration of


5.Theaccelerationofthecondensatelayerisnegligible.

Then Newtons second law of motion for the volume element in the vertical x-direction can be written as

0maF xx ==

duWeight = Viscous shear force + Buoyancy Force

)bdx)(y(g)bdx(dydu)bdx)(y(g vll +=

Canceling the plate width b and solving for du/dy gives

vl )y)((gdu =P.Talukdar/Mech-IITD 8

ldy =

Integrating from y = 0 where u = 0 (because of the no-slip boundary condition) to y = y where u = u(y) gives

=2

yy)(g)y(u2

l

vl

lThe mass flow rate of the condensate at a location x, where the boundary layer thickness is , is determined fromfrom

===

=A 0y l

3vll

l 3)(gbbdy)y(udA)y(u)x(m&

y l

whose derivative with respect to x is

d)(gbmd 2ll & This represents the dxd)(gb

dxmd

l

vll

= rate of condensation of vapor over a vertical distance dx

Th t f h t t f f th t th l tThe rate of heat transfer from the vapor to the plate through the liquid film is simply equal to the heat released as the vapor is condensed and is expressed as

== ssatlfg TT)bdx(kmdhQd &&


=

ssat

fg

l

lfg

TTh

bkdxmd

)(

&

dxh)(g

)TT(kd ssatll3 =

h)(g fgvll Integrating from x = 0 where = 0 (the top of the plate) to x = x where = (x) the liquid filmplate) to x x where (x), the liquid film thickness at any location x is determined to be

4/1x)TT(k4

fgvll

ssatllh)(g

x)TT(k4)x(

=

The heat transfer rate from the vapor to the plate at a location x can be expressed as

TTk)TT(hq ssat&

)x(kh

k)TT(hq

lx

ssatlssatxx

===

4/13kh)(g )x(ssatl

lfgvll

x)TT(4kh)(g

)x(h

=

L 41P.Talukdar/Mech-IITD 10

LxL

0xave h3

4dxhL1hh ====

Including the effects of the nonlinear temperature profile in the liquid film and the cooling of the liquid below the saturation

4/13l

*fgvll kh)(g9430h

cooling of the liquid below the saturation temperature, the average h for a vertical plate of length L is:

ssatl

lfgvllvertical L)TT(

)(g943.0h

=

W/m2 C, 0 < Re < 30h4hh

lllLx

k4k)L(kh ====

Lxavevertical h34hh ===

verticalLxLx h3h

)L()L(

h ==4/1

ssatll4/1

ssatll x)TT(k4x)TT(k4)x( = =

lv

Then the heat transfer coefficient h inThen the heat transfer coefficient hvert in terms of Re becomes:

All properties of the liquid are to be evaluated at the film temperature Tf = (Tsat + Ts)/2. The hfg and v are to be evaluated at the saturation temperature Tsat.


Wavy Laminar FlowyThe increase in heat transfer due to the wave effect is, on average, about 20 percent, but it can exceed 50 percentexceed 50 percent.The exact amount of enhancement depends on the Reynolds number


Turbulent FlowAt a Reynolds number of about 1800, the condensate flow becomes turbulent.Several empirical relations of varying degrees of

l it d f th h t t fcomplexity are proposed for the heat transfer coefficient for turbulent flow.


Nondimensionalised h for vertical plates

Inclined PlatesInclined Plates

This approximation gives satisfactory results especially for 60especially for 60 .

4/1 4/1verticalinclined )(coshh =

This equation is developed for laminar flow of condensate, but it can also be used for wavy laminar flows as an approximation


Vertical Tube/Horizontal TubesTube/Horizontal Tubes

& SpheresRelations for vertical plates can also be used to calculate the average heat transfer coefficient for laminar film condensation on the outer surfaces of vertical tubes provided that the tube diameter is large relative to the thickness of the liquid film

Nusselts analysis of film condensation on verticalNusselt s analysis of film condensation on vertical plates can also be extended to horizontal tubes and spheres

Tube = 0.729, Sphere = 0.815

A comparison of the heat transfer coefficient relations for a vertical tube of height L and a horizontal tube of diameter D yields


Settinghvertical =hhorizontal givesL=(1.29)4 D=2.77D,whichimpliesthatforatubewhoselengthis2.77timesitsdiameter,theaverageheattransfercoefficient for laminar filmcoefficientforlaminarfilmcondensationwillbethesamewhetherthetubeispositionedphorizontallyorvertically

ForL>2.77D,theheattransfercoefficientwillbehigherinthehorizontalposition

Thatisthereasonwhythetubesareplacedhorizontally inacondensercondenser


Effect of Vapor Velocity

If h fl d d i h If the vapor flows downward : increases the average velocity of the liquid and thus decrease the film thickness. This, in turn, will d th th l i t f th li iddecrease the thermal resistance of the liquid film and thus increase heat transfer

Upward vapor flow has the opposite effects: thickens the liquid film, and thus decreases heat transfer


Film Condensation inside Horizontal Tubesinside Horizontal Tubes

Most condensation processes encountered in refrigeration and air-conditioning applications, however, involve condensation on the innerinvolve condensation on the inner surfaces of horizontal or vertical tubes

For low vapor velocities: For low vapor velocities:

19P.Talukdar/Mech-IITD

Dropwise Condensation

heattransfercoefficientscanbe more than 10bemorethan10timeslargerthanfilmcondensation

Dropwisecondensation,characterizedbycountlessdropletsofvaryingdiametersonthecondensingsurfaceinsteadofacontinuousliquidfilm,isoneofthemosteffectivemechanismsofheattransfer,andextremelylargeheattransfercoefficientscanbeachievedwiththismechanism


Heat PipeHeat Pipe

A heat pipe is a simple device with no moving parts that can transfer large quantities of heatparts that can transfer large quantities of heat over fairly large distances essentially at a constant temperature without requiring any power inputpower inputA heat pipe is basically a sealed slender tube containing a wick structure lined on the inner surface and a small amount of fluid such as


surface and a small amount of fluid such as water at the saturated state.

condensation

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