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Stokes Flow Past Porous Bodies of Arbitrary Shape

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Abstract

In this paper we discuss a new approach to discuss Stokes flow past porous bodies of arbitrary shape using the Darcy [1] model and Saffman [2] boundary conditions.

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References

  1. H. P. G. Darcy, Les fontaines publiques de la ville de Dijon, Paris, V. Dalmont, (1856).

  2. P. G. Saffman, On the boundary condition at the surface of a porous medium, Studies Appl. Math., 50 (1971), 93–101.

    Article  MATH  Google Scholar 

  3. Mirela Kohr, G. P. Raja Sekhar, and Wolfgang L. Wendland, Boundary integral equations for a three-dimensional Stokes-Brinkman cell model, Math. Models Methods Appl. Sci., 18(12) (2008), 2055–2085.

    Article  MathSciNet  MATH  Google Scholar 

  4. Mirela Kohr, G. P. Raja Sekhar, and Wolfgang L. Wendland, Boundary integral method for Stokes flow past a porous body, Math. Meth. Appl. Sci., 31 (2008), 1065–1097.

    Article  MathSciNet  MATH  Google Scholar 

  5. J. Richardson and H. Power, A boundary element analysis of Stokes flow past a body of arbitrary shape, Transactions on Modelling and Simulation, 10(9) (1995), 585–593, WIT Press, DOI: https://doi.org/10.2495/BE950641.

    MATH  Google Scholar 

  6. J. Richardson and H. Power, A boundary element analysis of Oseen flow past a porous body of arbitrary shape, Math. Engrg. Indust., 6(2) (1997), 99–114.

    MathSciNet  MATH  Google Scholar 

  7. D. D. Joseph, and L. N. Tao, Lubrication of a porous bearing, J. Appl. Mech, Trans ASME, Series E, 33 (1966), 753–760.

    Article  Google Scholar 

  8. G. S. Beavers, and D. D. Joseph, Boundary conditions at a naturally permeable wall, J. Fluid Mech., 30(1) (1967), 197–207.

    Article  Google Scholar 

  9. G. Neale, N. Epstein, and W. Nader, Creeping flow relative to permeable spheres, Chem. Engg. Sci., 28 (1973), 1865–1864.

    Article  Google Scholar 

  10. B. S. Padmavathi, T. Amaranath, and D. Palaniappan, Stokes flow about a porous spherical particle, Arch. Mech., 46(1–2) (1994), 191–199.

    MATH  Google Scholar 

  11. S. Haber, and R. Mauri, Boundary conditions for Darcy’s flow through porous media, Int. J. Multiphase flow, 9(5) (1983), 561–574.

    Article  MATH  Google Scholar 

  12. R. Radha, B. Sri Padmavati, and T. Amaranath, New approximate analytical solutions for creeping flow past axisymmetric rigid bodies, Mech. Res. Comm., 37 (2010), 256–260.

    Article  MATH  Google Scholar 

  13. R. Radha, B. Sri Padmavati, and T. Amaranath, A new approximate analytical solution for arbitrary Stokes flow past rigid bodies, Z. Angew. Math. Phys., 63 (2012), 1103–1117.

    Article  MathSciNet  MATH  Google Scholar 

  14. D. Choudhuri, R. Radha, and B. Sri Padmavati, Stokes flow past an arbitrary shaped body with slip-stick boundary conditions, Applied Mathematics and Computation, 219 (2013), 5367–5375.

    Article  MathSciNet  MATH  Google Scholar 

  15. Christine Bernardi, Frédéric Hecht, and Olivier Pironneau, Coupling Darcy and Stokes equations for porous media with cracks, ESAIM: Mathematical Modelling and Numerical Analysis, 39(1) (2005), 7–35.

    Article  MathSciNet  MATH  Google Scholar 

  16. R. H. Davis and H. A. Stone, Flow through beds of porous particles, Chemical Engineering Science, 48(23) (1993), 3993–4005.

    Article  Google Scholar 

  17. M. Le Bars and M. Grae Worster, Interfacial conditions between a pure fluid and a porous medium: Implications for binary alloy solidification, J. Fluid Mech., 550 (2006), 149–173.

    Article  MathSciNet  MATH  Google Scholar 

  18. J. Prakash, G. P. Raja Sekhar, and M. Kohr, Faxén’s law for arbitrary oscillatory Stokes flow past a porous sphere, Arch. Mech., 64(1) (2012), 41–63.

    MathSciNet  MATH  Google Scholar 

  19. Nan Chen, Max Gunzburger, and Xiaoming Wang, Asymptotic analysis of the differences between the Stokes-Darcy system with different interface conditions and the Stokes-Brinkman system, J. Math. Anal. Appl., 368 (2010), 658–676.

    Article  MathSciNet  MATH  Google Scholar 

  20. D. Palaniappan, S. D. Nigam, T. Amaranath, and R. Usha, Lamb’s solution of Stokes equations, a Sphere theorem, Quart. J. Mech. Appl. Math., 45(1) (1992), 47–56.

    Article  MathSciNet  MATH  Google Scholar 

  21. B. S. Padmavathi, G. P. Rajasekhar, and T. Amaranath, A note on complete general solution of Stokes equations, Quart. J. Mech. appl. Math., 50(3) (1998), 383–388.

    Article  MathSciNet  MATH  Google Scholar 

  22. A. Oberbeck, Ueber stationäre Flüssigkeitsbewegungen mit Berücksichtigung der inneren Reibung, Journal fur die reine und angewandte Mathematik, 81 (1876), 62–80.

    MathSciNet  MATH  Google Scholar 

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Acknowledgement

The authors wish to gratefully acknowledge the financial support received from UGC SAP (DSA I), India. One of the authors (BSP) also wishes to acknowledge the financial support received under the research project No. MTR/2017/000591 under MATRICS (SERB, DST, India).

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Hyderabad, Hyderabad, 500 046, India

    R. Radha & B. Sri Padmavati

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  1. R. Radha
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  2. B. Sri Padmavati
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Correspondence to R. Radha or B. Sri Padmavati.

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Radha, R., Padmavati, B.S. Stokes Flow Past Porous Bodies of Arbitrary Shape. Indian J Pure Appl Math 51, 1247–1263 (2020). https://doi.org/10.1007/s13226-020-0462-0

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  • DOI: https://doi.org/10.1007/s13226-020-0462-0

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