Corsider the $2-$D configuration in which two square are nested $($a plate with a square hole in the middte$).$ The surfaces of the squares are at constant iemperature. A steady$-$state heat transfer occurs between these two surfaces due to the temperature difference.

a$)$ Divide the area between these two surfaces into grids. Use a minimum of $5$ grids for distance $L$

b$)$ Derive formulations via energy balance method. Make necessary simplifications. You may use any physical values for the configuration $($Temperaturs$,$ dimensions etc.$).$

c$)$ Salve the equarions with a seitable method and obtain the temperature fitsributions for different A$/$a dimensions. Calculate the heat trassfer between two surfaces per unit meter. Use these calcelated values to obtain a shape facter for this geometry:

$Q=SkT$

The shape fuctor should be in terms of Aa ratio. Consider at least six ratios $($you can consider more If you wish$).$

At least two rasios for $1\mathrm{.}4$

$d1$

$At$ least four ratios for $1\mathrm{.}4$

a