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ISSN 在线: 2151-562X

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DOI: 10.1615/SpecialTopicsRevPorousMedia.2020029302
pages 525-537

MOTION OF A POROUS SPHERICAL SHELL IN A SPHERICAL CONTAINER

Vineet Kumar Verma
Department of Mathematics and Astronomy, University of Lucknow, Lucknow, India
Hariom Verma
Department of Mathematics and Astronomy University of Lucknow, Lucknow, INDIA-226007

ABSTRACT

In this paper slow motion of a porous spherical shell with radially varying permeability in a spherical container at the instant it passes through the center of the spherical container is discussed. The container is filled by a viscous incompressible fluid. Flow outside the porous spherical shell is governed by the Stokes equation and inside the spherical shell by the Brinkman equation. The boundary conditions used at the surface of the porous spherical shell are the continuity of velocity and stress and the no-slip condition is used on qn impermeable sphere. Exact solution of the problem is obtained and relevant quantities such as stream lines, velocity, pressure, wall correction factor, and drag on surface of the spherical shell are obtained. The influence of the permeability parameter on the flow has been discussed and exhibited graphically. We found that decrease in permeability of the porous shell caused increase in drag and wall correction factor. In the limit case obtained results reduce to the well known classical results.

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