Q$3){?}^{-}$Consider a large plane wall of thickness $L$ and constant thermal conductivity $k_{\text{w}\text{a}\text{l}\text{l}}.$ The two sides of the wall are maintained at constant temperatures of $T_{s1}$ and $T_{s2},$ respectively, as shown in the figure. The heat is generated in the wall at a rate of $e_{\text{g}\text{e}\text{n}}^{}=A+Bx$ where A and $B$ are constants.

Assuming steady one$-$dimensional heat transfer,

a$)$ Express the differential equation and the boundary conditions for heat conduction through the wall. Start with the general heat conduction equation. Write the assumptions and make necessary simplifications. $(5pts)$

b$)$ Obtain a relation for the temperature

$($ variation $T(x)$ in terms of $k_{\text{w}\text{a}\text{l}\text{l}},A,B,L,T_{s1}$ and $T_{s2}$ in the wall by solving the differential equation. $(15$ pts $)$