Consider three sequential one$-$dimensional plane walls of thickness $L_1,L_2$ and $L_3,$

respectively; heat is being transferred through this set of plane walls since the surface

temperatures of the walls are maintained at $T_{s,1}$ and $T_{s,2}$ as shown in the sketch. The first

and third ones experience no heat generation; the middle one involves uniform

volumetric heat generation $q^{}.$ All properties are constant.

Write all design$/$balance equations and corresponding boundary conditions

Determine the temperature profile $T(x)$ and heat flux distribution $q^{\text{'}\text{'}}(x).$