# For parallel boundary layer flow over a flat plate, the

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For parallel boundary layer flow over a flat plate, the thermal integral equation is,
(aT
u(T. - T)dy = a
dy.
Let,
T, - T = (To - T)m(p), u = Um(n), where
m(n) =(3 - n2), n = y/8, p = y/8r, and n = pA (where A= dr/8)
-12
8(x)
8(x) is the momentum boundary layer thickness, and found to be
12
[2(dm/dn),n
/2
= 4.641,
dn'n=0
280
and with the above assumed m(n), a
where a, =
L m(1-m)đn
13
87(x) is the thermal boundary layer thickness, and A= 87/8.
Show that, for the case of large Pr,
A3=
(a,)? S, p[1 – m(p)]dp
Pr-1
Show also that, correspondingly,
Nu, = 0.331RE,, 2Pr3