2D heat transfer -- 2

Consider the chimney geometry given (figure, left). Use the grid (resolution) given (figure, right) as the initial grid. Grid refinement will be necessary while checking for GRID SENSITIVITY. There are two solid layers (blue and brown) of different materials. Solve for the temperature variation (discrete values of the temperature at the nodes) on a horizontal plane (within the solid) at two different vertical locations, (case a) for the part surrounded entirely with the cold outside air and (case b) for the part attached to the house at one side, in contact with the inside air at room temperature, while the other three sides are surrounded with the cold outside air. The boundary conditions (BC) for the inner and outer surfaces of the chimney are:
(a) for the upper part of the chimney - inner BC: convection with the HOT FLUID; outer BC: convection with the COLD AIR
(b) for the lower part of the chimney - inner BC: convection with the HOT FLUID; outer BC: for 3 sides, convection with the COLD AIR and for 1 side, convection with INSIDE AIR (ROOM)
Make use of any symmetry that is possible. Make sure to number the nodes that you use. Your report should include (i) the finite difference equations for all types of nodes that you have used in your analysis (identifying the node numbers of that type); (ii) your computer code; (iii) solution vectors of the temperature values for cases (a) and (b). You may use any solver of your choice.