Tfb
Tfb
kf
b
b
kf
Air
Flow
dx
Air
Flow
Ta , φ
dx
Ta , φ
L
x=
w
0
x=
(a)
(b)
0
Figure 16. a) Vertical rectangular fins; (b) Vertical triangular
fins.
Assuming a constant base temperature and an insulated tip, an approximate analytical
solution of eq 84 was derived using the quasi-linearization technique. For a fixed profile
area (wL), the expression for heat transfer rate was maximized to yield the following
implicit relations for w and L:
w
hL
= m1
(85)
L
k
1/ 3
wL kf
L=
(86)
m1h
where
Bhm hfg Ps,Tr
m1 = 1 +
(87)
h RvTaTr2
tanh mL
Tr = Ta - (Ta - Tfb )
and
.
(88)
mL
Here Ps, Tr is the saturation pressure at reference temperature Tr.
A sample solution of eq 8588 is shown in Figure 17 for atmospheric air with a relative
humidity of 50%. The details of evaluation of hm/h and B can be found in Kilic and Onat
(1981). Figure 17 shows that the optimum value of N = mL for a wet fin is lower than that
for a dry fin (Nopt = 1.4192). Also, Nopt for a wet fin decreases as the fin base temperature
Tb and the free-stream air temperature Ta increase.
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