Problem #$3(30$ pts$)$

As shown in the figure below, a T shaped bar $)=(28\frac{W}{m}*K$ in inverted position is attached to a surface maintained at $200C.$ The two sides of the bottom portion of the T bar and the top surface are insulated while the rest of the sides are subjected to a convective environment with $h=30\frac{W}{m^2}*K$ and ambient temperature of $10C.$ The mesh size is uniform for the vertical 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 the finite difference formulation for node #$10.$