$($b$)$ Consider the rotating disc above. A stationary disc is placed on top of the rotating disc

at a small distance away, forming a gap with a width $g.$ The stationary disc has the same

temperature as the stagnant air, which is $20C.$ The local radial Nusselt number

distribution is given by

${}_r=\frac{h(r)r}{k}=70(1+e^{-140G})R{e}_{r_r}^{-0\mathrm{.}456}R{e}_r^{0\mathrm{.}478},$ where $G=\frac{g}{r_o},R{e}_r=\frac{r^2}{v},$ and $r_o$ is the outer

radius of the disc.

Show that the expression of the average Nusselt number, $\frac{?}{\text{b}\text{a}\text{r}}({}_{r_o})\frac{?}{b}=ar(h)\frac{r_o}{k}$ is given by

$\frac{?}{\text{b}\text{a}\text{r}}({}_{r_0})=71\mathrm{.}6(1+e^{-140G})R{e}_{r_0}^{0\mathrm{.}022}$