$1)$ Consider the wall shown to the right, thickness and width L$.$ The left and right sides of the wall are perfectly insulated and the top and bottom surfaces are exposed to two different environments with known temperatures and h values. The thermal conductivity of the wall is also known.

a$)$ Assuming steady state condition, and negligible radiation effects, represent the geometry using a finite element analysis approach using a total of $4$ nodes. The area represented by your nodes should be the minimum area that still fully represents the geometry. That is$,$ you should take advantage of any symmetries to reduce the area represented. $(8$ pts$)$