The elemental unit of an air heater consists of a long circular rod of diameter D, which is encapsulated by a nned sleeve and in which thermal energy is generated by ohmic heating. The N ns 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 airow over the sleeve. Required:
a. Under conditions for which a uniform surface temperature Ts is maintained around the circumference of the heater and the temperature Tinf and convection coefficient h of the airflow are knonwn obtain an expression for the rate of heat transfer per unit length to the air. Evaluate the heat rate for Ts ​= 300C, D= 20 mm, an aluminum sleeve (ks​= 240 W/mK), w= 40 mm, N =16, t=4 mm, L=20 mm, Tinf ​= 50C, and h= 500 W/m^2K.

b. For the foregoing heat rate and a copper heater of thermal conductivity kh=400W/mK, what is the required volumetric heat generation within the heater and its corresponding centerline temperature?
c. With all other quantities unchanged, explore the effect of variations in the n parameters (N, L,t) on the heat rate, subject to the constraint that the n thickness and the spacing between ns cannot be less than 2 mm.