The vertical rear window of an automobile is of thick- ness 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.

The interior and exterior window temperatures, Ts,i and Ts,o, depend on the compartment and ambient temperatures, Too,i and Too,o, as well as on the velocity uoo 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 Too,i, Too,o, and/or uoo. If Too,i is maintained at 10°C, how will q· and Ts,o vary with Too,o for -25 Too,o 5°C and uoo = 10, 20, and 30 m/s? If a constant vehicle speed is maintained, such that uoo = 30 m/s, how will q· and Ts,o vary with Too,i for 5 Too,i 20°C and Too,o = -25, -10, and 5°C?