Problem $2.(30$ pts$)$ A composite wall is composed of two solids. Sandwiched between the two

walls is a foil heater of negligible thickness. The foil heater has an interface temperature, $T_i,$ and

supplies a heat flux of $q_x^{\text{'}\text{'}}=1000\frac{W}{m^2}.$ The left wall surface is insulated, and the right wall

surface is exposed to convection. The heat transfer is one$-$dimensional, steady, with no heat

generation, and contact resistance is negligible.

$($a$)$ Sketch the equivalent thermal circuit of the system and express all resistances in terms of

relevant variables.

$($b$)$ Determine the left wall surface temperature $(T_1).$

$($c$)$ Determine the right wall surface temperature $(T_2).$