Consider steady two$-$dimensional heat conduction in a square cross section $(3cm3cm,k=40\frac{W}{m}*K)$ with constant prescribed temperature of $250C$ and $450C$ at the top and bottom surfaces, respectively. The left surface is exposed to a constant heat flux of $2000\frac{W}{m^2},$ while the right surface is in contact with a convective environment $)=(35\frac{W}{m^2}*(K)$ at $15C.$ Using a uniform mesh size of $x=y,$ determine

$($a$)$ finite difference equations and

$($b$)$ the nodal temperatures using the Gauss$-$Seidel iteration method.