Consider the device shown below that will be used to humidity an air stream. In the current process, air containing 1.0 mol% water vapor (species A) at 40°C and 1.0 atm enters the tube of 3.0 cm inner diameter at a velocity of 300 cm/s. A water adsorbent material saturated with liquid water lines the inner surface of the tube. Water evaporates from this liner material as air passes over it. There is no diffusion resistance of water vapor

through the liner material itself. The process is maintained at 40°C. The saturation vapor pressure of water is 55.4 mmHg at 40°C, At this temperature and 1.0 atm, the viscosity of air is 1:91 × 10^-4 g/cm s and the density of air is 1:13× 10^-3 g/cm³.

a. What is the Schmidt number for this process?

b. Develop a model, in final integrated form, to predict the concentration of water vapor exiting the tube.

c. The thickness of the adsorbent material lining the inner surface of the tube is 1.0 mm and it initially contains 0.6 g of water per cm³. If the tube is 8.0 m long and the humidification occurs at 40°C and 1.0 atm system pressure, determine how long this process can operate before the liquid water is depleted. You will need to determine the outlet concentration of water vapor and then perform an overall material balance to estimate the net overall rate of water vapor transferred.