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not make serious errors when one assumes the approximate solution of Eq.(47)
can be expressed in similar form to Eqs.(37) and (38) for Pr >> 1. In
particular, when time, t, is small and convection terms can be neglected,
Eq.(47) reduces to a same equation as Eq.(38). Therefore, for small time,
the solution of Eq.(47) can be given by
St = { 1 - exp(-t*)}(49)
On • the other hand, the solution of Eq.(47) for large time can be approxi-
mated by Eq.(50) which is similar to Eq.(37) for Pr >> 1
4.
St = { 1 - exp(-A Pr x*I.5)}o,33(50)
It is well known that for Pr > 0.5, the steady state heat transfer co-
efficient for a flat plate is given by Eq.(51) under constant heat flux
Nu st = 0.458 RexkPr°•33(51)
On the other hand, one obtains the steady state heat transfer coefficient
by putting w } 0 in Eq.(50)
=2 1Nu
st13r°,.33/TRe13r°,.33(52)
A° .33 x
From Egs.(51) and (52), the- value of A must be
A = 5.67 ,(53)
Then one obtains approximate solution of Eq.(47) for large t
St ={1 - exp(-5.67
I.5"
Pr x* )}°.33. (54)
Therefore, the transient heat transfer coefficient for Pr > 0.5 can be
approximated by Eqs.(55) and (56) in view of Eqs.(49) through (54)
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