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CREEPING FLOW PAST A POROUS APPROXIMATELY SPHERICAL SHELL: STRESS JUMP BOUNDARY CONDITION

Part of: Foundations, constitutive equations, rheology

Published online by Cambridge University Press:  05 December 2011

D. SRINIVASACHARYA  and
M. KRISHNA PRASAD
D. SRINIVASACHARYA*
Affiliation:
Department of Mathematics, National Institute of Technology, Warangal – 506 004, A.P., India (email: dsc@nitw.ac.in, dsrinivasacharya@yahoo.com, kpm973.nitw@gmail.com)
M. KRISHNA PRASAD
Affiliation:
Department of Mathematics, National Institute of Technology, Warangal – 506 004, A.P., India (email: dsc@nitw.ac.in, dsrinivasacharya@yahoo.com, kpm973.nitw@gmail.com)
*
✉For correspondence; e-mail: dsrinivasacharya@yahoo.com
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Abstract

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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.

Keywords

porous approximately spherical shellStokes flowBrinkman equationstress jump coefficient

MSC classification

Secondary: 76A05: Non-Newtonian fluids
Type
Research Article
Information
The ANZIAM Journal , Volume 52 , Issue 3 , January 2011 , pp. 289 - 300
Copyright
Copyright © Australian Mathematical Society 2011

References

[1]Beavers, G. S. and Joseph, D. D., “Boundary conditions at a naturally permeable wall”, J. Fluid Mech. 30 (1967) 197–207; doi:10.1017/S0022112067001375.CrossRefGoogle Scholar
[2]Bhatt, B. S. and Sacheti, N. C., “Flow past a porous spherical shell using the Brinkman model”, J. Phys. D: Appl. Phys. 27 (1994) 37–41; doi:10.1088/0022-3727/27/1/006.CrossRefGoogle Scholar
[3]Bhattacharyya, A. and Raja Sekhar, G. P., “Stokes flow inside a porous spherical shell: stress jump boundary condition”, Z. Angew. Math. Phys. 56 (2005) 475–496; doi:10.1007/s00033-004-2115-2.CrossRefGoogle Scholar
[4]Brinkman, H. C., “A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles”, Appl. Sci. Res. 1 (1957) 27–34; doi:10.1007/BF02120313.CrossRefGoogle Scholar
[5]Debye, P. and Bueche, A. M., “Intrinsic viscosity, diffusion, and sedimentation rate of polymers in solution”, J. Chem. Phys. 16 (1948) 573–579; doi:10.1063/1.1746948.CrossRefGoogle Scholar
[6]Happel, H. and Brenner, J., Low Reynolds number hydrodynamics (Prentice Hall, Englewood Cliffs, NJ, 1965).Google Scholar
[7]Jones, I. P., “Low Reynolds number flow past a porous spherical shell”, Proc. Cambridge Philos. Soc. 73 (1973) 231–238; doi:10.1017/S0305004100047642.CrossRefGoogle Scholar
[8]Joseph, D. D. and Tao, L. N., “The effect of permeability on the slow motion of a porous sphere in a viscous liquid”, Z. Angew. Math. Mech. 44 (1964) 361–364; doi:10.1002/zamm.19640440804.CrossRefGoogle Scholar
[9]Kuznetsov, A. V., “Analytical investigation of the fluid flow in the interface region between a porous medium and a clear fluid in channels partially filled with a porous medium”, Appl. Sci. Res. 56 (1996) 53–67; doi:10.1007/BF02282922.CrossRefGoogle Scholar
[10]Kuznetsov, A. V., “Analytical investigation of Couette flow in a composite channel partially filled with a porous medium and partially with a clear fluid”, Int. J. Heat Mass Transfer 41 (1998) 2556–2560; doi:10.1016/S0017-9310(97)00296-2.CrossRefGoogle Scholar
[11]Matsumoto, K. and Suganuma, A., “Settling velocity of a permeable model floc”, Chem. Eng. Sci. 32 (1977) 445–447; doi:10.1016/0009-2509(77)85009-4.CrossRefGoogle Scholar
[12]Neale, G., Epstein, N. and Nader, W., “Creeping flow relative to permeable spheres”, Chem. Eng. Sci. 28 (1973) 1865–1874; doi:10.1016/0009-2509(73)85070-5.CrossRefGoogle Scholar
[13]Ochoa-Tapia, J. A. and Whitaker, S., “Momentum transfer at the boundary between a porous medium and a homogeneous fluid – I. Theoretical development”, Int. J. Heat Mass Transfer 38 (1995) 2635–2646; doi:10.1016/0017-9310(94)00346-W.CrossRefGoogle Scholar
[14]Ochoa-Tapia, J. A. and Whitaker, S., “Momentum transfer at the boundary between a porous medium and a homogeneous fluid – II. Comparison with experiment”, Int. J. Heat Mass Transfer 38 (1995) 2647–2655; doi:10.1016/0017-9310(94)00347-X.CrossRefGoogle Scholar
[15]Ooms, G., Mijnlieff, P. E. and Beckers, H. L., “Frictional force exerted by a flowing fluid on a permeable particle, with particular reference to polymer coils”, J. Chem. Phys. 53 (1970) 4123–4130; doi:10.1063/1.1673911.CrossRefGoogle Scholar
[16]Qin, Y. and Kaloni, P. N., “A Cartesian-tensor solution of the Brinkman equation”, J. Eng. Math. 22 (1988) 177–188; doi:10.1007/BF02383599.Google Scholar
[17]Saffman, P. G., “On the boundary condition at the surface of a porous medium”, Stud. Appl. Math. 50 (1971) 93–101.CrossRefGoogle Scholar
[18]Srinivasacharya, D., “Flow past a porous approximate spherical shell”, Z. Angew. Math. Phys. 58 (2007) 646–658; doi:10.1007/s00033-006-6003-9.CrossRefGoogle Scholar
[19]Zlatanovski, T., “Axisymmetric creeping flow past a porous prolate spheroidal particle using the Brinkman model”, Q. J. Mech. Appl. Math. 52 (1999) 111–126; doi:10.1093/qjmam/52.1.111.CrossRefGoogle Scholar