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The following equation describes the temperature distribution in a flat rectangular metal plate. The temperature on three sides is held constant at T 1 ,

The following equation describes the temperature distribution in a flat rectangular metal plate. The temperature on three sides is held constant at T1, and at T2 on the fourth side (see Figure 1). The temperature T (x, y) as a function of the xy coordinates shown is given by
where
T(x,y)=(T2T1)w(x,y)+T1
2 X\infty 2 n\pi x sinh(n\pi y/L) w(x, y)=\pi n sin L sinh(n\pi W/L) n=odd ThegivendataforthisproblemareT1=70F,T2=200F,andW =L=2ft.
Using a spacing of 0.2 for both x and y, generate a surface mesh plot and a contour plot of the temperature distribution.
(Hint: Use two nested for loops, one over x and one over y. Within the y loop, use a while loop (or use any other method that you know) to determine how many terms are required in the series to produce a temperature calculation that is accurate to within 1%.)

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