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Condensation(Chapter 13)Zan Wu [email protected] Room: 5123
Film condensation along a vertical wall
Steam
Liquid
Condensation - Nusselt’s film theory; assumptions Neglected convective transport in both the liquid and
vapor layers Pure heat conduction through the film Constant temperature in the vapor layer Laminar condensate flow Fluid properties are constant
Condensation – force balance
ff f f f
weight of viscous shear buoyancy forcethe liquid at y due toelement displaced vapor
vdug y dx dx g y dxdy
f 2f f
f
12
v gu y y
Integrating and using the B.C. uf = 0 at y = 0
Velocity profile in the liquid film, largest at y = δf
Nusselt’s film theory
wf f fg
f0
s
y
t ttQ dx dx h dmy
i.e., Heat balance for an element dx
f 3f f f
f f0
Mass flow per unit width = 3
v gm u dy
The mass flow of condensate per unit width through any x position of the film:
The heat transfer at the wall per unit width in the area dx is:
3 3 2f f f f f f f f f
f ff3 3
v v vg g gdd m d d dd
Nusselt’s film theory
Integrating and using the B.C. δf = 0 at x = 0
2f f fw
f fg ff
vs gt t dx h d
4/1
2ffg
wsfff
)(4
gh
xtt
Nusselt’s film theory
f
f
4/1
wsf
3f
2ffg
)(4
xtt
gh
0
1 43
L
x LdxL
Nusselt’s film theory cont.4/1
wsf
3f
2ffg
)(943.0
Ltt
gh
ff
fmf
f
fmf
Re
muu
4/3
3/5ffg
wsf3/13/2
f
4/3
2ffg
wsff2f
2f )(943.0)(4
31Re
f
hxttg
ghxttg
Nusselt’s film theory valid to Ref~ 6
(13-16)
Condensation - empirical correlations
1
22.03/12
f
f
f
f Re3.1Re47.1
)/(
gL 450Re6
f
)Pr/)5.89(Re412188(Re
)/( 0.5f
75.03/12f
f
f
f
gL 450Ref
3/1
2f
2f
3f4.0
feR0077.0
g
Turbulent flow
Condensation – alternate Reynolds number
P4eR
f
totf
m
width for a vertical plate P
for a vertical pipe
b
D
Condensation – improvements of Nusselt’s film theory
Ja)68.01(fgfg hh
due to subcooling of the liquid layer
The constant 0.943 is replaced by 1.13
fg
wsp )(Ja f
h
ttc
4/1
wsf
3f
2ffg
)(13.1
Ltt
ghf
Re 450
Condensation – Inclined plate
' sing g
Applicable range for finite plate?
Reference temperature for physical properties Liquid properties: (ts+tw)/2
Vapor properties: ts
Latent heat of vaporization: ts
Film condensation along a vertical tube?
Condensation on the outer surface of tubes (pipes)
(a) (b)
4/1
wsf
3f
2ffg
)(728.0
Dtt
gh
4/1
wsf
3f
2ffg
)(728.0
DttN
gh
2f f fv
ref 2s wt tt
Latent heat of vaporization evaluated at ts
Condensation inside tubes (pipes)
low flow velocities
vv m 3v,i
v i
Re 35 10u D
1/43fg f f v f
f s w
( )0.555
( )D
h gt t D
steam
condensate
If tw is unkown?
Condensation-inside horizontal tubes (pipes)
high flow velocities
0.81/3 1/2f f v f
f f
Nu 0.026 Pr ( ( / ) )vD D G G
/v vG m A AmG /ff
condensate
steam
Dropwise condensation
By adding chemicals to the vaporTreat the surface with appropriate chemicalsApply a teflon layer on the surfaceApply a thin layer of gold or any other noble metal on the surface (controversy?)
Disadvantages?
The mechanism is still a mystery.Significant progress recently
Non-condensable gases
Non-condensable gas presents an additional thermal resistance which reduces the heat transfer coefficient
As vapor condenses, the noncondensable gases are accumulated at the surface and the vapor has to diffuse across the vapor-gas mixture
Heat pipe
