the other hand, if dropwise condensation occurs, the increased surface roughness and the
resultant high turbulence intensity of the fin surface can slightly enhance the heat and
mass transfer to the fin.
Kazeminejad et al. model
Kazeminejad et al. (1993) considered a downward pointing vertical fin of rectangular
profile (Fig. 4b) with moist air (temperature Ta, relative humidity φ) flowing upward with
a uniform velocity Ua. They neglected the condensate film thickness ∆ in eq 73 but
allowed h, appearing in the definition of F3, to be a function of x, that is h = h(x) where x is
measured from the fin tip. To obtain h(x) the nonsimilar boundary layer equations for
upward flow over a nonisothermal vertical surface were written as
f
f
1
f ′′′ +
f f ′′ = x f
- f ′′
(75)
x
x
2
f
g
1
1
g′′ + fg′ + n(1 - g) f ′ = x f ′
- g′
(76)
x
Pr
2
x
f (x, 0) = f ′(x, 0) = 0 , f ′(x, ∞) = 1 ; g(x, 0) = 0 , g(x, ∞) = 1
(77)
where
f (η) = ψ /(Ua νx)1/2 , η = y /(Ua νx)1/2
g = [Tf (x) - T(x, η)]/[Tf (x) - Ta ]
(78)
x d (Tf - Ta )
h=
Tf - Ta
dx
and primes denote differentiation with respect to η. The local heat transfer coefficient h(x)
relates to g'(0) as follows
1/ 2
U
h (x) = ka ∞
g′ (0) .
(79)
νx
The coupled problem consisting eq 73 with ∆ = 0, and the boundary layer equations
(7577) were solved numerically by Kazeminejad et al. (1993) to obtain the fin tempera-
ture distribution, total heat transfer to the fin, and the fin efficiency. These results show
that the conjugate conductionboundary layer analysis gives higher fin temperatures and
higher fin efficiencies than those predicted by the Coney et al. (1989a) model. This conclu-
sion applies to both dry and wet fins.
Example 4
Air at 25C and 4 m/s flows over a vertical rectangular fin as shown in Figure 13. The
fin that is 240 mm long, 220 mm wide, and 20 mm thick is made of copper (kf = 380 W/m
K). The base of the fin is cooled and maintained at a temperature of 0C. Assuming that
the results of Figures 14 and 15 apply to this fin, calculate the tip temperature and total
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