Creeping flow past a porous approximately spherical shell: stress jump boundary condition

D. Srinivascaharya, M. Krishna Prasad

Abstract


The creeping flow of an incompressible viscous liquid past a porous approximately spherical shell is considered. The flow in the free fluid region outside the shell and in the cavity region of the shell is governed by the Navier–Stokes equations. The flow within the porous annular region of the shell is governed by Brinkman’s model. The boundary conditions used at the interface are continuity of the velocity, continuity of the pressure and Ochoa-Tapia and Whitaker’s stress jump condition. An exact solution for the problem and an expression for the drag on the porous approximately spherical shell are obtained. The drag is evaluated numerically for several values of the parameters governing the flow.

doi:10.1017/S144618111100071X

Keywords


porous approximately spherical shell; Stokes flow; Brinkman equation; stress jump coefficient



DOI: http://dx.doi.org/10.21914/anziamj.v52i0.4081



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.