The elemental unit of an air heater consists of a long circular rod of diameter D, which is encapsulated by a finned sleeve and in which thermal energy is generated by ohmic heating. The N fins of thickness t and length L are integrally fabricated with the square sleeve of width w. Under steady-state operating conditions, the rate of thermal energy generation corresponds to the rate of heat transfer to airflow over the sleeve. (a) Under conditions for which a uniform surface temperature Ts is maintained around the circumference of the heater and the temperature T[infinity] and convection coefficient h of the airflow are known, obtain an expression for the rate of heat transfer per unit length to the air. Evaluate the heat rate for Ts = 320°C, D = 15 mm, an aluminum sleeve (ks = 240 W/m·K), w = 40 mm, N = 16, t = 4 mm, L = 20 mm, T[infinity] = 50°C, and h = 500 W/m2·K. (b) For the foregoing heat rate and a copper heater of thermal conductivity kh = 400 W/m·K, what is the required volumetric heat generation within the heater and its corresponding