The following equation describes the temperature distribution in a flat rectangular metal plate. The temperature on three sides is held constant at T$1,$ and at T$2$ 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$)=($T$2$T$1)$w$($x$,$y$)+$T$1$

$2$ X$\backslash$infty $2$ n$\backslash$pi x sinh$($n$\backslash$pi y$/$L$)$ w$($x$,$ y$)=\backslash$pi n sin L sinh$($n$\backslash$pi W$/$L$)$n$=$odd ThegivendataforthisproblemareT$1=70$F$,$T$2=200$F$,$andW $=$L$=2$ft$.$

Using a spacing of $0\mathrm{.}2$ 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 $1\%.)$