The heat transfer rate per unit width (normal to the page) from a longitudinal section, x2 x1, can be expressed as q 12
′
= h
ˉ
12
(x 2
−x 1
)(T s
−T [infinity]
), where h
ˉ
12
is the average coefficient for the section of length (x 2
−x 1
). Consider laminar flow over a flat plate with a uniform temperature, T s
. The spatial variation of the local convection coefficient is of the form h x
= Cx −1/2
, where C is a constant. Beginning with the convection rate equation in the form dq ′
=h x
dx(T s
−T [infinity]
), derive an expression for h
ˉ
12
in terms of C,x 1
,x 2
.