A thin-walled, uninsulated 0.4-m-diameter duct is used to route chilled air at \(0.07 \mathrm{~kg} / \mathrm{s}\) through the attic of a large commercial building. The attic air is at \(37^{\circ} \mathrm{C}\), and natural circulation provides a convection coefficient of \(4 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) at the outer surface of the duct. If chilled air enters a 16-m-long duct at \(7^{\circ} \mathrm{C}\), what is its exit temperature and the rate of heat gain? Properties of the chilled air may be evaluated at an assumed average temperature of \(300 \mathrm{~K}\).