An air-water vapor mixture flows upward through a vertical copper tube \(25.4-\mathrm{mm}\) OD, \(1.65-\mathrm{mm}\) wall thickness, which is surrounded by flowing cold water. As a result, water vapor condenses and flows as a liquid film down the inside of the tube. At one point in the condenser, the average velocity of the gas is \(10 \mathrm{~m} / \mathrm{s}\), its bulk-average temperature is \(339 \mathrm{~K}\), the pressure is \(1 \mathrm{~atm}\), and the bulk-average partial pressure of water vapor is \(0.24 \mathrm{~atm}\). The film of condensed liquid is such that its heat-transfer coefficient is \(6.0 \mathrm{~kW} / \mathrm{m}^{2} \cdot \mathrm{K}\). The cooling water is at a bulkaverage temperature of \(297 \mathrm{~K}\) and has a heat-transfer coefficient of \(0.57 \mathrm{~kW} / \mathrm{m}^{2} \cdot \mathrm{K}\). Calculate the local rate of condensation of water from the airstream. For the gas mixture, \(C_{p}=1.145 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}, \mathrm{Sc}=0.6, \mathrm{Pr}=0.7\), and \(\mu=175 \mu \mathrm{P}\). For the water vapor, \(C_{p}=1.88 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\). The thermal conductivity of copper is \(0.381 \mathrm{~kW} / \mathrm{m} \cdot \mathrm{K}\).