Consider one$-$dimensional conduction in a plane composite wall. The outer surfaces are exposed to a fluid at $25C$ and a convection heat transfer coefficient of $1200\frac{W}{m^2}.$ K$.$ The middle wall B experiences uniform heat generation B$,$ while there is no generation in walls A and C $.$ Thermal conductivities of A is $25\frac{W}{m}K$ and that of C is $35\frac{W}{m}K,$ respectively. The temperatures at the interfaces are $T_1=281C$ and $T_2=221C.$ Determine the volumetric heat generation $q_B^{}($in $\frac{W}{m^3}).(35$ points$)$