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A common annoyance in cars during winter 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 $0\mathrm{.}4-$cm$-$thick glass $(k=0\mathrm{.}84\frac{W}{m}*K$ and $=0\mathrm{.}39{10}^{-6}\frac{m}{s}).$ 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 $25\frac{W}{?}$

m length. Initially, the entire car, including its windows, is at the outdoor temperature of $T_O=-3C.$ The heat transfer

coefficients at the inner and outer surfaces of the glass can be taken to be $h_i=6$ and $h_O=20\frac{W}{m^2}*K,$ respectively. Use

the implicit method with a time step of $1$ min with a mesh size of $x=0\mathrm{.}2cm$ along the thickness and $y=1cm$ in the

direction normal to the heater wires.

Determine the temperature at node $8,15$min after the strip heaters are turned on$.$