Consider a $15-cm20-cm$ printed circuit board $($PCB$)$ that has electronic components on one side. The board is placed in a room at $20C.$ The heat loss from the back surface of the board is negligible. If the circuit board is dissipating $8$ W of power in steady operation, determine the average temperature of the hot surface of the board, assuming the board is:

$($a$)$ vertical,

$($b$)$ horizontal with hot surface facing up$,$ and

$($c$)$ horizontal with hot surface facing down.

Take the emissivity of the surface of the board to be $0\mathrm{.}8$ and assume the surrounding surfaces to be at the same temperature as the air in the room.