A thin-walled plate separates the interior of a large furnace from surroundings at 300 K. The plate is fabricated from a ceramic material for which diffuse surface behavior may be assumed and the exterior surface is air cooled. With the furnace operating at 2400 K, convection at the interior surface may be neglected.

(a) If the temperature of the ceramic plate is not to exceed 1800 K, what is the minimum value of the outside convection coefficient, h₍₎, that must be maintained by the air-cooling system? 

(b) Compute and plot the plate temperature as a function of h_o for 50 < h_o < 250 W/m². K.