Example 2
Pure saturated steam at 60C condenses on the outside surface of a 50-mm diameter
horizontal tube maintained at a uniform temperature of 34C. Calculate the rate at which
heat is transferred to the tube and the condensate flow rate. To enhance the rate of
condensation, the tube is fitted with a vertical fin of rectangular profile. The fin is 2 mm
thick and 7.5 mm long, and has a thermal conductivity of 48 W/m K. Calculate the rate at
which steam condenses on the two faces of the fin and compare this with the rate of
condensation on the fin's base area if the fin is absent.
Solution
For saturated steam at 60C, we have
ρv = 0.129 kg/m3, hfg = 2358 kJ/kg .
Evaluating the properties of condensate at a mean temperature of 47C, we have
ρl = 989.1 kg/m3, l = 577 106 N s/m2, kl = 0.640 W/m K.
The average heat transfer coefficient for laminar film condensation on an isothermal
horizontal tube is given by eq 3 with θ = 1 (isothermal):
gρl (ρ - ρv ) kl hfg
1/ 4
3
h = 0.728
= 6864 W/m2K .
l (Tsat - Tfb ) D
l
The rate at which heat is transferred to the tube is given by
q = h πD(Tsat - Tf b ) = 28, 033 W/m .
˙
The condensate flow rate m is given by
q
= 1.19 10-2 kg/s m .
m=
˙
hfg
˙
To evaluate q and m (L), we first calculate F1 and F2 as follows:
gρl (ρl - ρv ) kfgL3
F1 =
= 9.94 108 ≅ 109
lkl (Tsat - Tfb )
kf w
F2 =
= 10.
2klL
For F1 = 109 and F2 = 10, Table 2 gives η = 0.2823. Using eq 28, the condensate flow rate,
˙
m (L) is
m (L) = 1.8854kl (Tsat - Tfb ) η F1 / 4 / hfg = 6.67 104 kg/s m .
1
˙
(π)(0.05) = 1.51 104 kg/s m. Comparing this with the figure of 6.67 104 kg/s m, the fin
is seen to enhance condensation by a factor of 4.4.
10
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