The moisture in hot, humid, stagnant air surrounding a cold-water pipeline continually diffuses to the cold surface where it condenses. The condensed water forms a liquid film around the pipe, and then continuously drops off the pipe to the ground below. At a distance of 10 cm from the surface of the pipe, the moisture content of the air is constant. Close to the pipe, the moisture content of the air approaches the vapor pressure of water evaluated at the temperature of the pipe.
a. Draw a picture of the physical system, select the coordinate system that best describes the transfer process, and state at least five reasonable assumptions of the mass-transfer aspects of the water condensation process.
b. What is the simplified form of the general differential equation for mass transfer in terms of the flux of water vapor, NA?
c. What is the simplified differential form of Fick’s equation for water vapor, NA?
d. What is the simplified form of the general differential equation for mass transfer in terms of the concentration of water vapor, cA?