A 2-ft-square section of panel heater is installed in the corner of the ceiling of a room having a 9-by-12-ft floor area with an 8-ft ceiling. If the surface of the heater, made from oxidized iron, is at 300°F and the walls and the air of the room are at 68°F in the steady state, determine 

(a) The rate of heat transfer to the room by radiation, 

(b) The rate of heat transfer to the room by convection (h_c = 2 Btu/(h ft² °F), 

(c) The cost of heating the room per day if the cost of electricity is 7 cents per kWhr.

GIVEN

• A 2 ft square panel heater in the corner of the ceiling of a room
• Room dimensions: 9 ft x 12 ft x 8 ft high
• Heater has oxidized iron surface
• Surface temperature (T_s) = 300°F = 760 R
• Room air and walls (T_∞) = 68°F = 528 R
• Convective heat transfer coefficient = 2 Btu/(h ft² °F)

ASSUMPTIONS

• The walls of the room are black (ε_w = 1)
• Steady state conditions
• Effect of H₂O and CO₂ in the air is negligible

Heater T = 760R 8 ft 9 ft 12 ft