KURENAI : Kyoto University Research Information Repository

u
for x*>t*h* = ----------------------2 *(22)
{ 1 - exp(-t )}
Equations (21) and (22) indicate that for large time, heat transfer coeffi-
* cient attains a asymptotic value, h a, which is given by
*
h a= ----------------------2*(23)
{ 1 - exp(-x )}
On the other hand, steady state heat transfer coefficient, h st, can be
obtained by putting w 0 in Eqs.(21)and (22), since for small value of w
heat flux increases slowly enough to be regarded as quasi-steady state.
Then steady state heat transfer coefficient is given by
or in dimensionless form by
Here Nu st and Pex are defined by.
h=2(--)(24)
stxa •
Nut= 0.82 Pe x(25)
Nu -hstx
st A
u x•(26)
Pe E —
x a
From Eqs.(23) and (26), the ratio between asymptotic transient heat tran-
sfer coefficient and steady state one, h a/hst, can be obtained
h Nu*'
a ( _a) = -----------------------h
st - Nust{ 1 - exp(-x*)} •
This ratio is expressed in term of dimensionless parameter , x (=xw/u .),
and shown in Fig. 4 in h a/hst vs. x plot. As shown in this figure, the
120
(27)