Abstract
Peristaltic pumping by a sinusoidal traveling wave in the porous walls of a two-dimensional channel filled with a viscous incompressible conducting fluid under the effect of transverse magnetic field is investigated theoretically and graphically. It has been considered that the fluid entering the flow region through one plate at the same rate as it is leaving through the other plate. This rate called the porosity of the boundaries and denoted by
V. A perturbation solution is obtained, which satisfies the momentum equation for the case in which the amplitude ratio is small. It has been noticed that the mean axial velocity and the reversal flow decrease by increasing the magnetic parameter. The mean axial velocity and the reversal flow decrease by increasing
V until the upper quarter of the channel they increase by increasing
V. Also the fluid motion is non-symmetric. Numerical results are reported for various of the physical parameters of interest.