The non-dimensional fluid temperature profile near the surface of a convectively cooled flat plate is given by $\frac{T_w-T}{T_w-T_w}$ = $a+b\frac{y}{L}+c\bigg(\frac{y}{L}\bigg)^2$, where y is measured perpendicular to the plate, L is the plate length, and a, b and c are arbitrary constants. TW and $T_\omega$ are wall and ambient temperatures, respectively. If the thermal conductivity of the fluid is k and the wall heat flux is q², the Nusselt number $Nu=\frac{q''}{T_w-T_\infty}\frac{L}{K}$ is equal to
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