A fluid flows in the positive x-direction through a long flat duct of length , width W, and thickness , where ≫ W ≫ . The duct has porous walls at y = 0 and y = , so that a constant cross flow can be maintained, with y = 0, a constant, everywhere. Flows of this type are important in connection with separation processes using the sweep-diffusion effect. By carefully controlling the cross flow, one can concentrate the larger constituents (molecules, dust particles, etc.) near the upper wall.

a. Find the velocity profile, v.(y), by taking the coordinate system with y =0 at the midplane of the slit with the porous walls located at y±B.
b. Calculate the mass flow rate in x-direction.
c. Show that the mass flow rate obtained in section (b) is simplified to mass flow rate for laminar flow in slit when v= 0.
d. According to your calculations in part (b) and (c), does the cross flow in y-direction change the mass flow rate in x-direction? Why (explain it)?