Nonlinear Peristaltic Transport through a Porous Medium in an Inclined Planar Channel

In order to determine the characteristics of the peristaltic transport of the gravity flow through a porous medium, the motion of an incompressible, viscous fluid in an inclined planar channel filled with a homogenous porous medium and having walls that are transversely displaced by an infinite, harmonic traveling wave of large wavelength was analyzed using a perturbation expansion in terms of a variant wave number. We obtain an explicit form for the velocity field and a relation between the pressure rise and flow rate in terms of Reynolds number, wave number, permeability parameter, inclined angle, and the occlusion. The effects of the various parameters entering into the problem are discussed numerically and with the help of graphs.