Within Python and using the finite difference method, generate a temperature contour using a $2020$ 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 $x$ of $1$ meter. Use a conduction heat transfer coefficient $($k$)$ of $10\frac{W}{m^{**}C}$

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 $10\frac{W}{m^2{?}^{***}C}$ and increase the heat transfer coefficient by $5$ each iteration.