The rear window of an automobile is defogged by attaching a thin, transparent, film-type heating element to its inner surface. By electrically heating this element, a uniform heat flux may be established at the inner surface.

(a) For 4-mm-thick window glass, determine the electrical power required per unit window area to maintain an inner surface temperature of 15°C when the interior air temperature and convection coefficient are T_∞,i = 25°C and h_i = 10 W/m ² ∙ K. while the exterior (ambient) air temperature and convection coefficient are T_∞,0 = -10°C and h_o = 65 W/m² ∙ K.

(b) In practice T_∞,0 and ho vary according to weather conditions and car speed. For values of h₀ = 2, 20, 65, and 100 W/m∙² K, determine and plot the electrical power requirement as a function of T_∞,0  for – 30  T_∞,0 ≤ T_∞,0 ≤ 0°C. From your results, what can you conclude about the need for heater operation at low values of ho? How is this conclusion affected by the value of T_∞,0? If h ∞ Vⁿ, where V is the vehicle speed and n is a positive exponent, how does the vehicle speed affect the need for heater operation?