
Forced Convection Heat Transfer: Internal Flows 265
This is a parabolic velocity prole with the maximum velocity occurring halfway
between the two plates,
. (11.48)
The mean velocity for this ow is
U
A
UdA
b
dP
dx
ybdy
bdP
dx
m
c
c
A
c
== −=−
∫
11
22 3
22
2
1
µµ
()
−−
∫
b
b
. (11.49)
Note that the maximum uid velocity is 1.5 times its mean velocity. Solving Equation
11.49 for pressure gradient gives
(11.50)
Substituting Equation 11.50 for pressure gradient into Equation 11.47 gives the veloc-
ity prole in terms of the mean uid velocity,
(11.51)
Since the ow is fully developed, pressure gradient is independent of x