Chapter 5, Problem 5.63P

A long pyroceram rod of diameter 20 mm is clad with a very thin metallic tube for mechanicalprotection. The bonding between the rod and the tube has a thermal contact resistance of $R_{t,c}^{\text{'}}=0.12\text{m}\cdot \text{K/W}\text{.}$

1. If the rod is initially at a uniform temperature of 900 K and is suddenly cooled by exposure to an airstream for which $T_{\infty }=300\text{K}$ and $h=100{\text{W/m}}^{\text{2}}\cdot \text{K,}$ at what time will the centerline reach 600 K?
2. Cooling may be accelerated by increasing the air-speed and hence the convection coefficient. For values of $h=100,500,$ and $1000{\text{W/m}}^{\text{2}}\cdot \text{K,}$ compute and plot the centerline and surface temperatures of the pyroceram as a function of time for $0\le t\le 300\text{s}\text{.}$ Comment on the implications of achieving enhanced cooling solely by increasing h.