For a uniform flow U of a fluid at temperature T? across a flat plate
at temperature Tw, if we assume that the
temperature profile inside the boundary layer is given by
(T - Tw)/(T? - Tw) = 1 - (1 - (y/?t)^2)

and that the ratio ?t(x)=?(x) is a constant, use the von Karman
integral analysis to determine:
(a) an equation for K = ?t(x)=?(x) in terms of the Prandtl number Pr =
v/? (simplify this relation in the limit
that Pr >> 1)
(b) the local heat flux at the wall qw(x)
(c) the relationship between the Nusselt number Nu and the Reynolds number Re.

Assume the velocity profile is given by: vx/U = sin ((?*y)/(2?))