$5-67$ Consider sleady two$-$dimensional heat transfer in a long solid bar of $(a)$ square and $(b)$ rectangular cross sections as shown in the figure. The measured temperatures at selected points of the outer surfaces are as shown. The thermal conductivity of the body is $k=20\frac{W}{m}-K,$ and there is no heat generation. Using the finite difference method with a mesh size of $x=y=1\mathrm{.}0cm,$ determine the temperatures at the indicated points in the medium. Answers $(a)T_1=185C.T_2=T_3=T_4=190$@$C$

$($d$)$

$($b$)$