A flue passing hot exhaust gases has a square cross section, \(300 \mathrm{~mm}\) to a side. The walls are constructed of refractory brick \(150 \mathrm{~mm}\) thick with a thermal conductivity of \(0.85 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) and thermal diffusivity of \(\alpha=5.5 \times 10^{-7} \mathrm{~m}^{2} / \mathrm{s}\). Initially with no flue gases flowing, the walls are at a uniform temperature of \(25^{\circ} \mathrm{C}\). The interior surface is suddenly exposed to hot gases at \(350^{\circ} \mathrm{C}\) with a convection coefficient of \(100 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), while the exterior surface experiences convection with air at \(25^{\circ} \mathrm{C}\) and a convection coefficient of \(5 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Using the implicit, finitedifference method with a grid spacing of \(50 \mathrm{~mm}\) and a time increment of \(1 \mathrm{~h}\), find the temperature distribution in the wall and the rate of heat loss by convection from the exterior of the flue at 5, 10, 50, and \(100 \mathrm{~h}\) after introduction of the flue gases.