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v v
Here, S is a thickness of velocity boundary layer and related to wall shear
v stress by
Tw1.571y=022(46)
v Substituting Egs.(10) and (45) into Eq.(11) and integrating,
for Pr > 1
for Pr < 1
u mS6
6a at(6vgw)+16~ ax[gw6t{St15(St}3}] C(47)
vvPp ,
uSS
6X at(St~gw}+16X 3x~gw6t6v{8 5(St}+24(St}2}]
vv
+ 6X ax{qw6t( 1 -S!)3} =P(48)
u
•
t P
As shown in Eq.(47) the contribution of (S t/6v) is considerably larger than
that of 15 (6t/6 v)3 in the second term of the left hand side of Eq.(47),
even if (St/6 v) is close to unity. As already shown in previous sections
transient heat transfer coefficients are largerthan those of steady state .
This means the thickness of thermal boundary layer, S t, is thinner in tran-
sient case than in steady state case. Since velocity boundary layer
is assumed to be steady state one in this analysis,(S
, Sy,
t/Sv) is smaller in
transient case than in steady state case. Therefore, in transient case ,
the contribution of (dt/Sv)is much greater than that of15(6t/v
second term of the left hand side of Eq.(47). In view of this
6)3 in the
, if one
approximates {6t/6v 5(6t/6v)3} by (St/6 v) in Eq.(47), Eq.(47) becomes
the same equation as Eq.(29) which is for Pr >> 1. Therefore
124
, it may