1.0
0.8
0.6
η
0.4
Downward Pointing
Upward Pointing
Vertical Fin
Vertical Fin
0.2
Horizontal
Fin
Figure 3. Efficiencies of
horizontal and vertical fins
0
20
40
60
80
100
N
with condensation.
The efficiency, ηf, of the fin can be found by computing the heat conducted into the base
of the fin and dividing it by qideal = h (x = 0) πDL (Tsat - Tfb ). The resulting expression for ηf is
1 dθ
ηf = -
.
(6)
N dX
X =0
The efficiency values calculated from the numerical solution and using eq 6 are plotted in
Figure 3. The figure also contains the results for the vertical fins that are discussed in the
next section. If N = 10 is selected to design the fin, then the corresponding ηf read from
Figure 3 is 0.34 or 34%, which is rather low. This low value for η is inevitable if a
significant increase in condensation rate is to be realized.
Example 1
Saturated steam at 0.15 bar condenses on a surface at 25C. It is desired to enhance the
rate of condensation by attaching a cylindrical fin made of brass to the primary surface.
Suggest some suitable design options.
Solution
For saturated steam at 0.15 bar, the following data apply:
Tsat = 54C, ρv = 0.098 kg/m3 , hfg = 2373 kJ/kg .
Evaluating the properties of condensate at a mean temperature of (54 + 25)/2 = 39.5C, the
following values for properties result:
ρl = 992 kg/m3, l = 663 10-6 N s/m2 , kl = 0.631 W/m K .
For good design, take N = 10. Using eq 5, a relationship between length L and diameter
D can be established as follows:
gρl (ρl - ρv )kl hfgL8
1/8
3
1/2
N
L
= 0.2244 m 3/8 .
=
kf l (Tsat - Tfb )
2.912
4
D5/8
4
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