Chapter 3, Problem 3.41P

From Figure 2.5 it is evident that, over a wide temperature range, the temperature dependence of the thermal conductivity of many solids may be approximated by a linear expression of the form $k=k_o+aT,$ where $k_o$ is a positive constant and a is a coefficient that may be positive or negative. Obtain an expression for the heat flux across a plane wall whose inner and outer surfaces are maintained at $T_o$ and $T_1.$ respectively. Sketch the forms of the temperature distribution corresponding to $a>0,a=0,$ and $a<0.$