Chapter 2, Problem 144P

Consider a 20-cm-thick large concrete plane wall $(k=0.77\text{W/m}\text{.K)}$ and subjected to convection on both sides with $T_{\infty 1}={22}^o\text{C}$ and $h_1=8{\text{ W/m}}^{\text{2}}\text{.K}$ on the inside and $T_{\infty 2}=8^o\text{C}$ and $h_2=12{\text{ W/m}}^{\text{2}}\text{.K}$ on the outside. Assuming constant thermal conductivity with no heat generation and negligible radiation, (a) express the differential equations and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the vall by solving the differential equation, and (c) evaluate the temperatures at the inner and outer surfaces of the wall.