Chapter 3, Problem 3.79P

The air inside a chamber at $T_{\infty ,i}=50°\text{C}$ is heated convectively with $h_i=20{\text{W/m}}^{\text{2}}\cdot \text{K}$ by a 200-mm-thick wall having a thermal conductivity of $4\text{W/m}\cdot \text{K}$ and a uniform heat generation of $1000{\text{W/m}}^{\text{3}}.$ To prevent any heat generated within the wall from being lost to the outside of the chamber at $T_{\infty ,o}=25°\text{C}$ with $h_o=5{\text{W/m}}^{\text{2}}\cdot \text{K,}$ a very thin electrical strip heater is placed on the outer wall to provide a uniform heat flux, $q_o^n.$

1. Sketch the temperature distribution in the wall on $T-x$coordinates for the condition where no heat generated within the wall is lost to the outside of the chamber.
2. What are the temperatures at the wall boundaries, $T\left(0\right)$ and $T\left(L\right),$for the conditions of pan (a)?
3. Determine the value of $q_o^n$ that must be supplied by the strip heater so that all heat generated within the wall is transferred to the inside of the chamber.
4. If the heat generation in the wall were switched off while the heat flux to the strip heater remained constant, what would be the steady-state temperature, $T\left(0\right),$of the outer wall surface?