Chapter 6, Problem 6.15P

An experimental procedure for validating results of Problem 6.14 involves preheating a copper disk to an initial elevated temperature $T_i$ and recording its temperature history $T\left(t\right)$ as it is subsequently cooled by the impinging flow to a final temperature $T_f.$ The measured temperature decay may then be compared with predictions based on the correlation for ${\overline{Nu}}_D.$ Assume that values of $a=0.30$ and $n=2$ are associated with the correlation.
  Consider experimental conditions for which a disk of diameter $D=50\text{mm}$ and length $L=25\text{mm}$ is preheated to $T_i=1000\text{K}$ and cooled to $T_f=400\text{K}$ by an impinging airflow at $T_{\infty }=300\text{K}\text{.}$ The cooled surface of the disk has an emissivity of $\epsilon =0.8$ and is exposed to large, isothermal surroundings for which $T_{sur}=T_{\infty }.$ The remaining surfaces of the disk are well insulated, and heat transfer through the supporting rod may be neglected. Using results from Problem 6.14, compute and plot temperature histories corresponding to air velocities of $V=4,20,$ and $50\text{m/s}\text{.}$ Constant properties may be assumed for the copper $\left(\rho =8933{\text{kg/m}}^{\text{3}},c_p=425\text{J/kg}\cdot \text{K,}k=386\text{W/m}\cdot \text{K}\right)$ and air $\left(v=38.8\times {10}^{-6}{\text{m}}^{\text{2}}\text{/s,}k=0.0407\text{W/m}\cdot \text{k,}\mathrm{Pr}=0.684\right).$