A hot, 0.5-m-diameter, 35 -mm-thick aluminum alloy disk is quenched from an initial temperature of \(T_{i}=\) \(400^{\circ} \mathrm{C}\) in a large oil bath of temperature \(T_{\infty}=35^{\circ} \mathrm{C}\). As it is quenched, the disk rests horizontally on the bottom of the well-insulated bath container. Use the results of Section 5.3.3 to determine the time needed to reduce the disk temperature to \(100^{\circ} \mathrm{C}\). The metal properties are \(ho=1000 \mathrm{~kg} / \mathrm{m}^{3}, k=185 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), and \(c=775 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\).