A mass transfer operation is preceded by laminar flow of a gaseous species B through a circular tube that is sufficiently long to achieve a fully developed velocity profile. Once the fully developed condition is reached, the gas enters a section of the tube that is wetted with a liquid film (A). The film maintains a uniform vapor density p_A,s along the tube surface.

(a) Write the differential equation and boundary conditions that govern the species A mass density distribution,
p_A(x, r), for x > 0.
(b) What is the heat transfer analog to this problem? From this analog, write an expression for the average Sherwood number associated with mass exchange over the region 0 ≤ x ≤ L. 

(c) Beginning with application of conservation of species to a differential control volume of extent π t²_o dx, derive an expression (Equation 8.86) that may be used to determine the mean vapor density p_A,m,o at x = L.
(d) Consider conditions for which species B is air at 25°C and 1 atm and the liquid film consists of water, also at 25°C. The flow rate is m = 2.5 X 10^–4 kg/s, and the tube diameter is D = 10 mm. What is the mean vapor density at the tube outlet if L = 1m?

Transcribed Image Text:

€ Species B Liquid film, Pa L Species A & B PAMO