dθ
q = 2kl (Tsat - Tfb ) F2
.
(22)
dX X =1
The ideal heat transfer, qideal, occurs when the entire fin is at temperature Tfb and is given
by
qideal = 2h L (Tsat - Tfb )
(23)
gρl (ρ - ρv ) kl hfg
1/ 4
3
h = 0.943
(24)
l (Tsat - Tfb ) L
l
which in terms of F1 becomes
kl 1/ 4
h = 0.943
.
(25)
F
L 1
Combining eq 23 and 25 and noting that η = q/qideal, we have
F2 dθ
ηf = 1.0604 1/ 4
.
(26)
dX X =1
F1
The efficiency values obtained from eq 26 appear in Table 2.
The film thickness δ at x = L, the condensate flow rate m at x = L, and the heat conducted
˙
into the base of the fin q, can all be expressed in terms of F1 and ηf giving
-1/ 4
δ (L) = 1.412Lηf1/ 3 F1
(27)
m (L) = 1.8856kl (Tsat - Tfb ) ηf F1 / 4 / hfg
1
˙
(28)
q = 1.8856kl (Tsat - Tfb ) ηf F1 / 4 .
1
(29)
Table 2. Condensation efficiency of a rectangular ver-
tical fin.
104
103
102
F1/F2
10
107
0.9988
0.9857
0.8745
0.4603
108
0.9979
0.9747
0.7981
0.3612
109
0.9955
0.9563
0.6969
0.2823
1010
0.9919
0.9254
0.5776
--
1011
0.9857
0.8745
0.4603
--
1012
0.9747
0.7989
0.3612
--
1013
0.9562
0.6969
0.2823
--
1014
0.9254
0.5776
--
--
1015
0.8745
0.4603
--
--
1016
0.7989
0.3612
--
--
1017
0.6969
--
--
--
9
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