(Solved): Problem 5: Consider a long bar of rectangular cross section ( \( 60 \mathrm{~mm} \) by \( 90 \mathr ...

Problem 5: Consider a long bar of rectangular cross section ( \( 60 \mathrm{~mm} \) by \( 90 \mathrm{~mm} \) on a side) and of thermal conductivity \( 1 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K} \). The top surface is exposed to a convection process with air at \( 100^{\circ} \mathrm{C} \) and a convection heat transfer coefficient of \( 100 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K} \), while the remaining surfaces are maintained at \( 50^{\circ} \mathrm{C} \). Using a grid spacing of \( 30 \mathrm{~mm} \), determine the temperatures at nodes 1,2 , and 3 shown in Figure below.