Problem $2$

Consider steady state two dimensional heat transfer in a plate $($with unit depth$)$ which is given in the figure. The measured temperatures on the left, top and bottom walls are shown in the schematic. The righ wall of the plate is insulated. The thermal conductivity of the body is $k=10\frac{W}{mK},$ and there is no heat generation within the plate. To obtain the temperature on the plate using finite difference method, a mesh size of $x=y=1\mathrm{.}0cm$ is used.

a$).$ Use the energy balance method to derive the finite difference equations for node $1,2,3.($Must show derivation process for all three nodes$)$

b$).$ Fill in the table below use Gauss$-$Seidel iteration. Assume all nodes are initialized at $300C$

$\backslash$table$[[$Iteration$,T_1,T_2,T_3$