Oscillating Magnetohydrodynamic Stokes Flow between Porous Plates with Spatiotemporally Periodic Reabsorption

Abstract

The study addresses the oscillating magnetohydrodynamic (MHD) Stokes flow between two parallel plates with periodic reabsorption both spatially and temporally. Two cases are distinguished by applying either (1) transverse or (2) parallel external magnetic field. Analytical solutions of velocity and pressure are derived for both cases and the effect of Womersley and Hartmann number, and the absorption coefficient is examined. The study generalizes existing literature on analytic MHD Stokes flow solutions accounting for periodic boundary conditions both in time and space. The non-oscillating non-MHD Stokes flow in a porous channel (available in the literature) is proven to be a limit of the analytic solution introduced here. The MHD effects are noticeable in flows oscillating with low or moderate frequency but are barely detectable in high-frequency flows even in the presence of strong magnetic fields.