A bar of rectangular cross$-$section is subjected to prescribed boundary conditions as shown below. Using numerical technique with a grid spacing of $0\mathrm{.}05$ m $,$ determine the temperature distribution and the heat transfer rate from the bar to the fluid. Use the attached summary of nodal finite$-$difference equations.

Assume steady state, $2-$D conduction, constant properties, and that $\backslash (\backslash$Delta x$=\backslash$Delta y$=0\mathrm{.}05$ m $\backslash ).$ Note the adiabat corresponding to the system symmetry. The finite difference equation for interior nodes, plane surface with convection, and adiabatic surface are shown in the attached.