heat transferred to the fin for (i) perfectly dry air and (ii) moist air with a relative
humidity of 50 %. Also for moist air, calculate the sensible heat and latent heat contribu-
tions to the total heat transfer. Use the following correlations for calculating the average
convective heat transfer coefficient h:
0.60
U D
hDh
= 0.590 ∞ h
for dry conditions
νa
ka
0.69
U D
hDh
= 0.231 ∞ h
for wet conditions
νa
ka
where Dh is the hydraulic diameter and equals 2bL/(b+L). These correlations are dis-
cussed in the next section.
Solution
The hydraulic diameter Dh is given by
2bL
Dh =
= 0.23 m .
b+L
= 15.5 106 m2/s.
(i) For dry conditions, the average heat transfer coefficient h is given by
h = 47.83 W/m K.
The Biot number Bi can now be calculated as follows:
2hL2 (b + w)
Bi =
= 0.79
kfbw
Using Figure 14c to read θ at ξ = 1 (fin tip) on the dry fin curve, we get
T - Tft
θt = a
= 0.8
Ta - Tfb
Tft = Ta - (0.8) (Ta - Tfb ) = 5C.
or
The efficiency of a dry fin is given by the equation
tanh (Bi)1/ 2
ηd =
= 0.8
Bi1/ 2
The ideal heat transfer, qideal, is given by
qideal = 2h (b + w) L (Ta - Tfb ) = 137.75 W .
Thus the actual heat transfer qd is
qd = ηd qideal = 110.2 W.
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