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errors. In view of this, one can obtain Eq.(75) by substituting Eq.(70)
into Eq.(74)
EHCpp N
This equation can be rewritten as
7q w
(T - T )S-1/7y-6/7,(75)
w cct
T-
wE
T
.7 ------7qw1/7 y6/7(76)
HCpp t
For the case of Pr = 1, the turbulent diffusivity of heat, EH, can be app-
roximated by the turbulent diffusivity of momentum, c., that is,
From Eqs.(73),(76) and (77), one obtains
EH = EM •(77)
T- T= 33.82 u Cpw-------Re°*2 (St)1/7(78)
wco co pv
Under steady state condition and .Pr = 1, thermal boundary layer has appro-
ximately same thickness as velocity turbulent boundary layer, then (St/S v)
= 1. Therefore, Eq.(78) gives, of course, the same result as Reynolds
analogy.
Substituting Eqs.(60) and (61) into Eq.(3) and integrating,from 0 to
t, one obtains,
8/7
2(T S ) + ua(T -------t)clw(79)
8 3t' w t 72ax wS1/7C
pp ,
v In Eq.(3), thermal diffusivity, a, should be replaced by (a+EH). However,
in the limit of y -> 0, one obtains,
lim (a +EH)(
y
40pp
131
80)