One way to increase the flux of ionic materials through a mass transfer fin is to apply an electric field along its length as shown in Figure P8.23. The fin has a diameter, \(d\), and length, \(L\). The base of the fin is exposed to a constant concentration of \(a, c_{a}\). The tip of the fin is sealed so that the flux of \(a\) is zero there. The free-stream concentration of \(a\) is \(c_{a \infty}\) and the mass transfer coefficient is \(k_{c}\). Both the diffusivity of \(a\) and its mobility are constant throughout the fin.

a. Assuming a constant applied electric field, \(\mathcal{E}_{o}\), derive the differential equation for the concentration profile. Assume dilute solutions and that the Nernst-Einstein equation holds.

b. Determine the concentration profile within the fin.

c. How does the fin effectiveness depend upon the applied electric field?

Transcribed Image Text:

FIGURE P8.23 Cao Cac kc Dab Mab E