Chapter 6, Problem 6.17P

Consider the rotating disk of Problem 6.16. A disk-shaped, stationary plate is placed a short distance away from the rotating disk, forming a gap of width g. The stationary plate and ambient air are at $T_{\infty }=20°\text{C}\text{.}$ If the flow is laminar and the gap-to-radius ratio, $G=g/r_o,$ is small. the local radial Nusselt number distribution is of the form

$N{u}_r=\frac{h\left(r\right)r}{k}=70\left(1+e^{-140G}\right){\mathrm{Re}}_{ro}^{-0.456}{\mathrm{Re}}_r^{0.478}$

where ${\mathrm{Re}}_r=\Omega r^2/v$ [Pelle J., and S. Harmand, Exp. Thermal Fluid Science, 31, 165, 2007]. Determine the value of the average Nusselt number, ${\overline{Nu}}_D=\bar{h}D/k$ where $D=2r_o.$ If the rotating disk temperature is $T_s=50°\text{C,}$ what is the total heat flux from the disk's top surface for $g=1\text{mm,}\Omega =150\text{rad/s?}$ What is the total electric power requirement? What can you say about the nature of the flow between the disks?