Chapter 6, Problem 6.69P

Using the naphthalene sublimation technique. the radial distribution of the local convection mass transfer coefficient for uniform flow normal to a circular disk has been correlated by an expression of the form

$S{h}_D\equiv \frac{h_m\left(r\right)D}{D_{AB}}=S{h}_o\left[1+a{\left(\frac{r}{r_o}\right)}^n\right]$

The stagnation point Sherwood number $\left(S{h}_o\right)$ depends on the Reynolds $\left({\mathrm{Re}}_D=VD/v\right)$ and Schmidt $\left(Sc=v/D_{AB}\right)$ numbers, and data have been correlated by the following expression:

$S{h}_o=\frac{h_m\left(r=0\right)D}{D_{AB}}=0.814{\mathrm{Re}}_D^{1/2}S{c}^{0.36}$

Obtain an expression for the average Nusselt number $\left({\overline{Nu}}_D=\bar{h}D/k\right)$ corresponding to heat transfer from an isothermal disk exposed to the foregoing flow conditions. If $a=1.2$ and $n=5.5,$ what is the rate of heat transfer from a disk of diameter $D=20\text{mm}$ and surface temperature $T_s=125°\text{C}$ to an airstream for which ${\text{Re}}_{\text{D}}=5\times {10}^4$ and $T_{\infty }=25°\text{C?}$ 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.