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Journal of Porous Media

Impact factor: 1.035

ISSN Print: 1091-028X
ISSN Online: 1934-0508

Journal of Porous Media

DOI: 10.1615/JPorMedia.v9.i8.40
pages 745-767

Viscous Flow Past a Spherical Void in Porous Media: Effect of Stress Jump Boundary Condition

G. P. Raja Sekhar
Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721302
M. K. Partha
Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India
P.V.S.N. Murthy
Department of Mathematics, Indian Institute of Technology, Kharagpur, West Bengal, 721302, India


The effect of the spherical void of characteristic size R0 in porous media in an undisturbed uniform flow U is investigated analytically. The flow inside the void is governed by Stokes equation, and the flow in the porous region is governed by Brinkman equation. The stress jump boundary condition proposed by Ochoa-Tapia and Whitaker (Int. J. Heat Mass Transfer, 38, pp. 2636−2655, 1995) for the tangential stresses at the porous liquid interface along with the continuity of velocity components and normal stress is used. The flow field is computed by matching the boundary conditions at the porous fluid interface. It is found that the effect of the void increases with the decrease of permeability. The effect of the stress jump coefficient and porosity on some of the physical quantities, such as volume flow coming inside the void, is analyzed.