Chapter 3, Problem 3.19P

The wall of a drying oven is constructed by sandwiching an insulation material of thermal conductivity $k=0.05\text{W/m}\cdot \text{K}$ between thin metal sheets. The oven air is at $T_{\infty ,i}=300°\text{C,}$ and the correspondingconvection coefficient is $h_i=30{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$ The inner wall surface absorbs a radiant flux of $q_{\text{rad}}^n=100{\text{W/m}}^{\text{2}}$ from hotter objects $T_{\infty ,o}=25°\text{C,}$ and the within the oven. The room air is at T overall coefficient for convection and radiation from the outer surface is $h_o=10{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$

1. Draw the thermal circuit for the wall and label all temperatures, heat rates, and thermal resistances.
2. What insulation thickness L is required to maintain the outer wall surface at a safe-to-touch temperature of $T_o=40°\text{C?}$