Problem #$1(30$ pts$)$

Heat is transferring from left to the right side of a $12$ cm thick aluminum $[k=164\frac{(W)}{m^2(K)}]$ plane wall. The temperature at the left side of wall is $55C$ and at right face is $50C.$ The temperature changes to $T_{}$ after heat transfers through convection from right face of the wall to the air. The convection co$-$efficient of air is $h=250\frac{(W)}{m^2{K}^2}.$

Determine:

$($a$)$ Draw the schematic

$($b$)$ Heat transfer through the aluminum wall in W $.$

$($c$)$ The temperature $T_{}$ in K $.$