$5-81$ As shown in Fig. P$5-81$ a T shaped bar $\backslash (($k$=28\backslash$mathrm$\{$~W$\}/\backslash$mathrm$\{$m$\}\backslash$cdot $\backslash$mathrm$\{$K$\})\backslash )$ in inverted position is attached to a surface maintained at $\backslash (200^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The two sides of the bottom portion of the T bar are insulated while the rest of the sides are subjected to a convective environment with $\backslash ($ h$=30\backslash$mathrm$\{$~W$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash$cdot $\backslash$mathrm$\{$~K$\}\backslash )$ and ambient temperature of $\backslash (10^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The mesh size is uniform for the long portion of the bar while it is doubled in x direction for the bottom portion of the T bar. Assuming steady state conditions and no internal heat generation determine $($a$)$ the finite difference formulation for each node and $($b$)$ the nodal temperatures. Hint: Take advantage of symmetry.