A long bar of rectangular cross section, \(0.2 \mathrm{~m} \times 0.3\mathrm{~m}\) on a side and having a thermal conductivity of \(15 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), is subjected to the boundary conditions shown.

Two of the sides are maintained at a uniform temperature of \(200^{\circ} \mathrm{C}\). One of the sides is adiabatic, and the remaining side is subjected to a convection process with \(T_{\infty}=30^{\circ} \mathrm{C}\) and \(h=60 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Using an appropriate numerical technique with a grid spacing of \(0.05 \mathrm{~m}\), determine the temperature distribution in the bar and the heat transfer rate between the bar and the fluid per unit length of the bar.

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Insulated Uniform temperature, T=200C Th Uniform temperature, T=200C