Create an array of node locations for the problem

Hint: You should define your nodes so that the edge nodes sit on the boundaries of the space.

Another hint: Will need an array of at least 40x40 to get an accurate answer. This is nearly impossible to implement by brute force

One more hint: If a node sits both inside and outside of the pipe, assume the entire node is inside the pipe.

Derive the steady state finite difference equations for the 4 cases below:

Internal node at constant temperature

Internal node (no generation)

Boundary nodes at constant temperature (both edges and corners!)

Adiabatic boundary nodes (both edges and corners!)