A common annoyance in cars in winter months is the formation of fog on the glass surfaces that blocks the view. A practical way of solving this problem is to blow hot air or to attach electric resistance heaters to the inner surfaces. Consider the rear window of a car that consists of a 0.4-cm-thick glass (k = 0.84 W/m · K and α = 0.39 × 10^-6 m²/s). Strip heater wires of negligible thickness are attached to the inner surface of the glass, 4 cm apart. Each wire generates heat at a rate of 25 W/m length. Initially the entire car, including its windows, is at the outdoor temperature of T_o = - 3°C. The heat transfer coefficients at the inner and outer surfaces of the glass can be taken to be h_i = 6 and h_o = 20 W/m² · K, respectively. Using the explicit finite difference method with a mesh size of Δx = 0.2 cm along the thickness and Δy = 1 cm in the direction normal to the heater wires, determine the temperature distribution throughout the glass 15 min after the strip heaters are turned on. Also, determine the temperature distribution when steady conditions are reached.

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Inner surface Heater 25 W/m Thermal symmetry line Outer surface Glass -0.2 cm -1 cm Thermal symmetry line