Consider Problem 6.14. The stationary plate, ambient air, and surroundings are at \(T_{\infty}=T_{\text {sur }}=20^{\circ} \mathrm{C}\). If the rotating disk temperature is \(T_{s}=80^{\circ} \mathrm{C}\), what is the total power dissipated from the disk's top surface for \(g=\) \(2 \mathrm{~mm}, \Omega=150 \mathrm{rad} / \mathrm{s}\) for the case when both the stationary plate and disk are painted with Parsons black paint? Over time, the paint on the rotating disk is worn off by dust in the air, exposing the base metal, which has an emissivity of \(\varepsilon=0.10\). Determine the total power dissipated from the disk's worn top surface.

Data From Problem 6.14:-

Consider the rotating disk of Problem 6.13. A diskshaped, 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 \(T_{\infty}=20^{\circ} \mathrm{C}\). 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
\[N u_{r}=\frac{h(r) r}{k}=70\left(1+e^{-140 G}\right) R e_{r_{o}}^{-0.456} R e_{r}^{0.478}\]
where \(R e_{r}=\Omega r^{2} / v\) [Pelle J., and S. Harmand, Exp. Thermal Fluid Science, 31, 165, 2007]. Determine the value of the average Nusselt number, \(\overline{N u}_{D}=\bar{h} D / k\) where \(D=2 r_{o}\). If the rotating disk temperature is \(T_{s}=50^{\circ} \mathrm{C}\), what is the total heat flux from the disk's top surface for \(g=1 \mathrm{~mm}\), \(\Omega=150 \mathrm{rad} / \mathrm{s}\) ? What is the total electric power requirement? What can you say about the nature of the flow between the disks?

Data From Problem 6.13:-

If laminar flow is induced at the surface of a disk due to rotation about its axis, the local convection coefficient is known to be a constant, \(h=C\), independent of radius. Consider conditions for which a disk of radius \(r_{o}=100 \mathrm{~mm}\) is rotating in stagnant air at \(T_{\infty}=20^{\circ} \mathrm{C}\) and a value of \(C=20 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) is maintained. 

If an embedded electric heater maintains a surface temperature of \(T_{s}=50^{\circ} \mathrm{C}\), what is the local heat flux at the top surface of the disk? What is the total electric power requirement? What can you say about the nature of boundary layer development on the disk?

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Air T. ro 12 r T -Support tube Connections to electric heater