$1)$ Within Python and using the finite difference method, generate a temperature contour using a $\backslash (20\backslash$times $20\backslash )$ set of nodes $($including the nodes on the top and left boundaries$).$ Use the nodal equations provided to create a system of equations for the plate. Instead of the plate being $1$ meter by $1$ meter, make the dimensions $20$ meters by $20$ meters, and use a $\backslash (\backslash$Delta $\backslash$mathrm$\{$x$\}\backslash )$ of $1$ meter. Use a conduction heat transfer coefficient $(\backslash ($ k $\backslash ))$ of $\backslash (10\backslash$mathrm$\{$~W$\}/\backslash$left$(\backslash$mathrm$\{$m$\}^\{\backslash$star$\}\backslash$mathrm$\{$C$\}\backslash$right$.\backslash ))$

$2)$ The average temperature of the plate should be no more than $210$ degrees Celsius. Implement a while loop into your code to iterate by increasing the convection heat transfer coefficient $($h$)$ until this average temperature requirement is satisfied. Begin with a convection heat transfer coefficient of $\backslash (10\backslash$mathrm$\{$~W$\}/\backslash$left$(\backslash$mathrm$\{$m$\}^\{\backslash$wedge$\}2^\{\backslash$star$\}\backslash$mathrm$\{$C$\}\backslash$right$)\backslash )$ and increase the heat transfer coefficient by $5$ each iteration.