How to solve

A longitudinal fin with a square cross section has a cooling through channel $120mm60mm.$ The fin has thermal conductivity $k=(A)\frac{W}{m}K,$ length $L=160mm$ and width $w=80mm.$ A cooling liquid passes through the channel and all $4$ walls of the channel are maintained at temperature $($B$)C.$ The base of the plate is maintained at a uniform temperature $T_0=(C)C,$ while the fin outer surfaces are exposed to air at a temperature of $T_{}=(D)C$ and a convection coefficient of $h=(E)\frac{W}{m^2}K.$ The fin is shown in Figure $1.$

$($a$)$ Using the two$-$dimensional finite$-$difference method with $x=y=5mm,$ and taking advantage of symmetry, write finite$-$difference equations for fin nodes.

$($b$)$ Rewrite the equations of $($a$)$ in Gauss$-$Seidel form.

$($c$)$ Determine the temperature distribution in the fin using Gauss$-$Seidel method. Make a reasonable guess of nodal temperatures for iteration $k=0$ and complete iterations until convergence criterion reaches $0\mathrm{.}1$ K $.$

$($d$)$ Determine the total heat loss from the fin.

VALUES OF A$,$B$,$C$,$D AND E ARE $200,40,120,30$ AND $150$ respectively.