Floor heating is used to keep a room at a toasty 25°C. On a cold day, the room loses heat through the walls, ceilings, door, and windows at the rate of 2,000 W. The heated floor area is 30 m². The heat transfer coefficient for convective transport from the heated floor area to the room air is estimated to be 5.0 W/m² K.

(a) Determine the floor temperature.

(b) If the maximum allowable floor temperature is to be 30°C, what should the value of the heat transfer coefficient be?