Chapter 6, Problem 6.14P

Experiments to determine the local convection heat transfer coefficient for uniform flow normal to a heated circular disk have yielded a radial Nusselt number distribution of the form

$N{u}_D=\frac{h\left(r\right)D}{k}=N{u}_o\left[1+a{\left(\frac{r}{r_o}\right)}^n\right]$

where both n and a are positive. The Nusselt number at the stagnation point is correlated in terms of the Reynolds $\left({\mathrm{Re}}_D=VD{/}_v\right)$ and Prandtl numbers

$N{u}_o=\frac{h\left(r=0\right)D}{k}0.814{\mathrm{Re}}_D^{1/2}{\mathrm{Pr}}^{0.36}$

Obtain an expression for the average Nusselt number, ${\overline{Nu}}_D=\bar{h}D\text{/}k,$ corresponding to heat transfer from an isothermal disk. Typically, boundary layer development from a stagnation point yields a decaying convection coefficient with increasing distance from the stagnation point. Provide a plausible explanation for why the opposite trend is observed for the disk.