Q$1.(30$ pints$)$ Experimental measurements of the temperature distribution during the flow of air at atmospheric pressure over the wing of an airplane indicate that the temperature distribution near the surface can be approximated by equation:

$\frac{T_s-T}{T_s-T_{}}=\frac{1}{2}(\frac{y}{0\mathrm{.}0075}{)}^3+\frac{3}{2}(\frac{y}{0\mathrm{.}0075})$

where $T_s$ is surface temperature, $T_{}$ is free$-$stream temperature, and $y$ is perpendicular distance from surface.

$($a$)$ Estimate the convection heat transfer coefficient, assuming surface temperature is $40C.$

$($b$)$ Calculate the heat flux from the wing.