Chapter 8, Problem 8.129P

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 ${\rho }_{\text{A,s}}$ , along the tube surface.

(a) Write the differential equation and boundary conditions that govern the species A mass density distribution, ${\rho }_A\left(x,r\right),\text{for}x>0$ .
(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 $0\le x\le L$ .
(c) Beginning with application of conservation of species to a differential control volume of extent $\pi r_o^{2}dx$ , derive an expression (Equation 8.86) that may be used to determine the mean vapor density ${\rho }_{A,m,o}\text{at}x=L$ .
(d) Consider conditions for which species B is air at $\text{25}°\text{C}$ and $\text{1 atm}$ and the liquid him consists of water,also at $\text{25}°\text{C}$ . The flow rate is $\stackrel{\dot{}}{m}=2.5\times {10}^{-4}\text{kg/s}$ , and the tube diameter is $D=10\text{mm}$ . What is the mean vapor density at the tube outlet if $L=1\text{mm}$ ?