Interaction of peristaltic flow with pulsatile fluid through a porous medium

The interaction of purely periodic mean flow with a peristaltic induced flow is investigated within the framework of a two-dimensional analogue. The mathematical model considers a viscous incompressible fluid flow through a porous medium between infinite parallel walls on which a sinusoidal traveling wave is imposed. A perturbation solution to the complete set of Navier-Stokes equations is found for the case in which the frequency of the traveling wave and that of the imposed pressure gradient are equal. The ratio of the traveling wave amplitude to channel width is assumed to be small. For this case a first-order steady flow is found to exist, as contrasted to a second-order effect in the absence of the imposed periodic pressure gradient and the effect of the permeability parameter and the various parameters including in the problem are discussed numerically.