Question $2$

Consider the steady$-$state temperature distributions within a composite wall composed of Material A and Material B for the two cases shown. There is no internal generation, and the conduction process is one$-$dimensional.

Answer the following questions for each case. Which material has the higher thermal conductivity? Does the thermal conductivity vary significantly with temperature? If so$,$ how? Describe the heat flux distribution $q_x^{\text{'}\text{'}}(x)$ through the composite wall. If the thickness and thermal conductivity of each material were both doubled and the boundary temperatures remained the same, what would be the effect on the heat flux distribution?

Case $1$: Linear temperature distributions exist in both materials.

Case $2$: Nonlinear temperature distributions exist in both materials.