The defroster of an automobile functions by discharging warm air on the inner surface of the windshield. To prevent condensation of water vapor on the surface, the temperature of the air and the surface convection coefficient (T∞,i hi) must be large enough to maintain a surface temperature Ts.; that is at least as high as the dew point (Ts,i > Tdp)

Consider a windshield of length L = 800 mm and thickness t = 6 mm and driving conditions for which the vehicle moves at a velocity of V = 70 mph in ambient air at T∞,o = -15°C. From laboratory experiments performed on a model of the vehicle, the average convection coefficient on the outer surface of the windshield is known to be correlated by an expression of the form NUL = 0.030 Re L0.8 pr1/3, where Re L == VL/v. Properties of the ambient air may be approximated as k = 0.023 W/m ∙ K, v = 12.5X 10-6 m2 /s, and Pr = 0.71. If TdP = 10°C and T∞,i = 50°C, what is the smallest value of Ii; required to prevent condensation on the inner surface?

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-T,i