Simultaneous heat and mass transfer: film condensation

An air-water vapor mixture flows upward through a vertical copper tube 25.4-mm OD, 1.65-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 m/s, it is bulk-average temperature is 339 K, the pressure is 1 atm, and the bulk-average partial pressure of water vapor is 0.24 atm. The film of condensed liquid is such that its heat-transfer coefficient is 6.0 kW/m^2K. The cooling water is at a bulk-average temperature of 297 K and has a heat-transfer coefficient of 0.57 kW/m^2K.

Calculate the local rate of condensation of water from the airstream. For the gas mixture, C_p = 1.145 kJ/kgK, Sc = 0.6, Pr = 0.7, and u = 175 uP. For the water vapor, C_p = 1.88 kJ/kgK. The thermal conductivity of copper is 0.381 kW/mK

Answer: 21.3 kg/m^2 h