Chapter 5, Problem 5.51P

The 150-mm-thick wall of a gas-fired furnace is constructed of fireclay brick $\left(k=1.5\text{W/m}\cdot \text{K,}\rho =2600{\text{kg/m}}^{\text{3}},c_p=1000\text{J/kg}\cdot \text{K}\right)$ and is well insulated at its outer surface. The wall is at a uniform initial temperature of $20°\text{C,}$ when the burners are fired and the inner surface is exposed to products of combustion for which $T_{\infty }=950°\text{C}$ and $h=100{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$

1. How long does it take for the outer surface of the wall to reach a temperature of $750°\text{C?}$
2. Plot the temperature distribution in the wall at the foregoing time. as well as at several intermediate times.