Oscillatory Fluid Flow Through a Porous Medium Channel Bounded by Two Impermeable Parallel Plates

Abstract

In the absence of the inertia effects, the analytic solution to the fully developed oscillatory fluid flow through a porous medium channel bounded by two impermeable parallel plates is presented. For the limiting case when a highly viscous fluid undergoes slow pulsation in a high porosity medium, the phase lag vanishes and similar velocity profiles are observed. At the other extreme limiting situation, fluid flow near the symmetry plane has a phase lag of 90 deg from the pressure gradient wave. Moreover, the velocity profiles exhibit maxima next to the wall which is similar to the “channeling” phenomenon observed in variable-porosity studies. It is shown that the temporal average of the frictional drag over a period vanishes, indicating no net energy losses due to oscillations.