Consider a $5-$m$-$high, $8-$m$-$long, and $0\mathrm{.}22-$m$-$thick wall whose representative cross section is as given in the figure. The thermal conductivities of various materials used, in $\frac{W}{m}*K,$ are $k_A=k_F=2,k_B=8,k_C=20,k_D=15,$ and $k_E=35.$ The left and right surfaces of the wall are maintained at uniform temperatures of $300C$ and $100C,$ respectively. Assuming heat transfer through the wall to be one$-$dimensional, disregard any contact resistances at the interfaces, determine $($a$)$ the rate of heat transfer through the wall;

$($b$)$ the temperature at the point where the sections B$,$ D$,$ and E meet;

$($c$)$ the temperature drop across the section $F.$