Problem $3(6$ points$)$: In the plane wall shown, Wall A has negative heat generation. Wall B does not have any heat generation. Using info from the figure,

Start with the HDE, using proper $BC$ and proper control surfaces where energy balance is performed, determine the temperature profile along walls A and $B,$ respectively, including the values of the respective constants in the temperature expression.

Sketch the temperature profile of both walls as a function of distance. State whether the curves are linear, quadratic, cubic, etc.

Prove heat flux across wall $B$ is a constant. What is heat flux at $x=40mm?$ Determine temperature at interface between walls A and $B.$

Sketch the heat flux profile along the walls as a function of distance. Determine the location along wall A where the flux is equal to zero?