The vertical rear window of an automobile is of thickness L = 8 mm and height H = 0.5 m and contains fine-meshed heating wires that can induce nearly uniform volumetric heating, q (W/m3).

(a) Consider steady-state conditions for which the interior surface of the window is exposed to quiescent air at 10°C, while the exterior surface is exposed to air at - 10°C moving in parallel flow over the surface with a velocity of 20 m/s. Determine the volumetric heating rate needed to maintain the interior window surface at Ts,i = 15°C.

(b) The interior and exterior window temperatures, Ts,i and Ts.o, depend on the compartment and ambient temperatures, T'∞,i and T∞.o, as well as on the velocity U x of air flowing over the exterior surface and the volumetric heating rate q. Subject to the constraint that Ts,i is to be maintained at 15°C, we wish to develop guidelines for varying the heating rate in response to changes in T∞,i, T∞.o, and/or u∞, If T∞.i is maintained at 10°C, how will q and Ts.o vary with T∞.o for -25 < T∞.o < 5°C and u∞,o = 10, 20, and 30 m/s? If a constant vehicle speed is maintained, such that u∞ = 30 m/s, how will q and Ts,o vary with T∞.i for 5 < T∞,i < 20°C and T∞,o = –25, - 10, and 5°C?