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Brinkman Flow Generated by the Rectilinear Oscillations of an Oblate Spheroid Along its Axis of Symmetry

In this paper, we consider an impervious Oblate spheroid placed in a fully saturated porous medium, where in the flow is governed by Brinkmann flow equation. We  assume that the  spheroid is performing rectilinear harmonic oscillations along the axis of symmetry with a speed u.  The flow is studied under the Stokesian approximation. The expressions for the velocity and pressure fields are obtained in terms of Legendre  functions,  associated Legendre functions and  Radial and Angular spheroidal wave functions. We obtain an expression for the drag experienced by the spheroid, and  numerically study its variation with respect to the flow parameters and display its variation  through graphs.   