A dormitory at a large university, built 50 years ago, has exterior walls constructed of \(L_{s}=30\)-mm-thick sheathing with a thermal conductivity of \(k_{s}=0.1 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). To reduce heat losses in the winter, the university decides to encapsulate the entire dormitory by applying an \(L_{i}=30-\mathrm{mm}\)-thick layer of extruded insulation characterized by \(k_{i}=0.029 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) to the exterior of the original sheathing. The extruded insulation is, in turn, covered with an \(L_{g}=5\)-mm-thick architectural glass with \(k_{g}=1.4 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). Determine the heat flux through the original and retrofitted walls when the interior and exterior air temperatures are \(T_{\infty, i}=22^{\circ} \mathrm{C}\) and \(T_{\infty, o}=0^{\circ} \mathrm{C}\), respectively. The inner and outer convection heat transfer coefficients are \(h_{i}=5 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and \(h_{o}=30 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), respectively.