Consider steady two dimensional heat transfer in a square cross section (3cm x 3cm) with the prescribed temperatures at the top, right, bottom, and left surfaces to be 100, 200, 300, and 500 celcius respecively. Using a unifrom mesh size deltaX = deltaY, determine the finite difference equations and the nodal temperatures with the Gauss-Seidel iterative method.
The cross section looks like a tic tac toe board with the top left corner of the middle square is node 1, node 2 is top left, node 3 is bottom left and node four is bottom right of the middle square.