g
A
Film Condensation
– on a vertical wall
T
s
< T
sat
< T
∞
T
∞
Ts
T
T
∞
T
s
T
T
sat
T
∞
Ts < T
∞
ρ
l
u
u,v,T
≡
u
l
,v
l
,T
l
Without Phase Change
With Phase Change
Governing Differential Equations and Boundary Conditions
Momentum
:
()
2
g
2
uu
uv
g
xy
y
∂∂
∂
ρ+
=
ρ
−
ρ
+
µ
u
∂
AA
A
Continuity
:
0
+=
Thermal Energy
:
2
2
2
TT
u
T
Cp
u
v
k
y
y
∂
∂
=
+
µ
∂
∂
A
A
Boundary Conditions
:
At y = 0:
u = 0, v = 0, T = T
w
< T
sat
At
( )
yx
:u
u
max,T T
sat
=
δ=
=
Further approximation
: The film moves very slowly
Therefore, inertia and dissipation are neglected.
Reduced Equations
Continuity Equation remains unchanged.
Momentum
:
( )
2
g
2
g
u
y
−ρ −ρ
∂
=
µ
∂
A
A
(10.16)
1
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View Full DocumentThermal Energy
:
2
2
T
0
y
∂
=
∂
The Momentum and Thermal Energy equations are linear and
uncoupled and, hence, can be solved analytically.
Solution of Thermal Energy Equation to obtain T(y)
2
2
w
T
0w
i
t
h
T
(
0
)
T
,
T
(
)
T
sat
y
∂
==
∂
δ
=
.
Integrating twice gives
( )
Tx
,y
Cy
C
12
=+
The constants C
1
and C
2
are determined by using the boundary conditions.
T(0)
T
T
C
ww
2
=⇒ =
TT
w
sat
T( )
T
T
C
T
C
w
sat
sat
11
−
δ=
⇒
=
δ+
⇒
=
δ
()
w
sat
y
T
w
−
∴
δ
(G4)
Note:
Temperature varies linearly with y in the condensation film.
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 Winter '06
 Ghia
 Fluid Dynamics, Thermodynamics, Energy, Heat, Heat Transfer, Trigraph

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