al. (1982) concluded that surface tension was indeed the force controlling the condensate
drainage from the fin surface. Using a linear surface tension model, Rudy and Webb
(1983b) developed the following expression for the heat transfer coefficient on the fin
surface:
1/ 4
1/ 4
ρlkl hfg
3
8σ
1 1
hf = 0.943
+
.
(94)
l (Tsat - Tb )
w s
(do - dr )2
Pursuing the surface tension drainage approach, Adamek (1981) considered a family of
convex liquid/vapor interfaces that promote surface tension drainage. The radius of
curvature of the family of profiles is described by the equation
ξ
1 θm ξ + 1 s
1 -
=
(95)
r sm ξ sm
where r = local radius of interface,
s = distance along the curved interface profile,
sm = maximum length of the curved interface,
θm = rotation angle from tip to fin base
ξ = interface shape parameter, 1 < ξ < ∞.
These quantities are illustrated for a typical convex liquid-vapor interface in Figure 22.
The relationship between sm, θm, ξ, and tip radius ro is given by
ξ+1
sm
=
.
(96)
roθm
ξ
For the condensate profiles described by eq 96, Adamek (1981) obtained the following
expression for the condensation heat transfer coefficient:
1/ 4
ρl σ hfgθm sm
ξ+1
k
hf = 2.149 l
⋅
.
(97)
3
lkl (Tb - Tsat ) (ξ + 2)
sm
Condensate surface
ro
for a typical value of ξ
S
Base
Surface
Sm
θ
r
δ
Figure 22. Typical film profile for condensation
θm
on a fin with small tip radius, with increasing
radius along the arc length.
34
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