average heat transfer coefficient for dry operating conditions. For the moisture condensa-
tion situation, McQuiston, neglecting the thermal resistance of the condensate, postulated
that the local driving potential for simultaneous heat and mass transfer was the difference
between the enthalpy of air adjacent to the fin and that of saturated air at the local fin
temperature. By approximating the saturation curve on the psychrometric chart by a
straight line over a small range of temperatures, he expressed the slope a as
a = (ωs,2 - ωs,1)/(T2 - T1)
(54)
where ωs is the specific humidity of saturated air. The heat transfer coefficient hw for wet
conditions was expressed in terms of hd and a as follows:
ahfg
hw = hd 1 +
(55)
cp
where cp is the specific heat of moist air at constant pressure.
In an earlier paper, Ware and Hacha (1960) recommended the following expression
for hw:
hw = hd b/cp
(56)
where b is the slope of the enthalpytemperature curve for saturated air.
With hw specified by either eq 55 or 56, the conventional fin theory can be employed to
obtain the efficiency of a wet fin. For boundary conditions of constant base temperature
and insulated tip, the fin efficiency can be expressed as
tanh N *
ηw
=
(57)
N*
where N * = (2hw / kf w)
1/2
L.
Radial fins
Elmahdy and Biggs (1983) considered a radial fin of base radius rb, tip radius rt,
thickness w, and thermal conductivity k, exposed to a stream of moist air at temperature Ta
and with specific humidity ωa. If the average heat and mass transfer coefficients are h and
hm, respectively, then the differential equation governing the temperature distribution in
the fin can be written as
d2Tf 1 dTf 2h
2hm
(Ta - Tf ) - kw (ω a - ω T,s ) hfg = 0
+
-
(58)
dr 2 r dr kw
where ωT,s is the saturated specific humidity of air corresponding to the local fin tempera-
ture Tf. Assuming a constant fin base temperature Tfb and insulated fin tip, the boundary
conditions for eq 58 can be written as
dTf
r = rb , Tf = Tfb ;
r = rt ,
= 0.
(59)
dr
Next ωT,s is assumed to be a linear function of temperature Tf, that is,
ωT,s = c + a Tf
(60)
18
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