Consider the conditions of Problem 7.43, but now allow for radiation exchange between the surface of the heating element (δ = 0.8) and the walls of the duct, which form a large enclosure at 27°C.

(a) Evaluate the steady-state surface temperature.

(b) If the heater is activated from an initial temperature of 27°C, estimate the time required for the surface temperature to come within 10°C of the steady-state value.

(c) To guard against overheating due to unanticipated excursions in the blower output, the heater controller is designed to maintain a fixed surface temperature of 275°C. Determine the power dissipation required to maintain this temperature for air velocities in the range 5 < V< 10 m/s.