Chapter 2, Problem 60P

Consider a 20-cm-thick concrete plane wall $\left(k=0.77\text{ W/m}\text{.K}\right)$ subjected to convection on both sides $T_{\infty 1}={27}^{\circ }C$ and $h_1=5{\text{W/m}}^{\text{2}}{}^{\text{.}}\text{K}$ on the inside and $T_{\infty 2}=8^{\circ }C$ and $h_2=12{\text{ W/m}}^{\text{2}}{}^{\text{.}}\text{K}$ on the outside. Assuming constant thermal conductivity with no heat generation and negligible radiation. (a) Express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the temperature at the inner and outer surface of the wall.