Use the finite difference form of the heat equation, energy balance method in order to make a nodal network discretizing the geometry, and then generate a system of equations. This system of equations...

Use the finite difference form of the heat equation, energy balance method in order to make a nodal network discretizing the geometry, and then generate a system of equations. This system of equations can be written as a matrix [A] [T] = [C]. [T] will be a column vector (i.e. 1d) of the temperatures of all the nodes within the system. [A] is the coefficient matrix linking the temperature solution vector [T] to the right hand side vector [C] Use some numerical method in order to evaluate [T]. In this problem, Gauss-Seidel iteration is the best choice to solve for [T], but for a small enough matrix you could probably use just matrix division in matlab if you need to. 3) Make contour plots of temperature for each case. You will have to re-arrange the column vector of [T] in order to understand T(x,y).