Chapter 6, Problem 6.32P

Experimental results for heat transfer over a flat plate with an extremely rough surface were found to be correlated by an expression of the form

$N{u}_x=0.04{\mathrm{Re}}_x^{0.9}{\mathrm{Pr}}^{1/3}$

where $N{u}_x$ is the local value of the Nusselt number at a position x measured from the leading edge of the plate. Obtain an expression for the ratio of the average heat transfer coefficient ${\bar{h}}_x$ to the local coefficient $h_x.$