Problem $2(30$ points$)$

A thin electrical heater that dissipates $2$ kW of thermal energy is position between two plane walls. The thickness of each wall is shown in the figure below. The thermal conductivities of sections A and $B$ are $3\frac{W}{m}C$ and $0\mathrm{.}8\frac{W}{m}C$ respectively. The electrical heater is assumed to be highly conductive $(k=200\frac{W}{m}C).$ The exterior surface of each wall experiences convective conditions as summarized below.

$($a$)$ Construct the thermal circuit representing the steady state heat transfer for the system. Label all nodes, resistances and relevant terms.

$($b$)$ Determine the temperate of the electrical heater.