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Transport in Porous Media

, Volume 68, Issue 2, pp 249–263 | Cite as

Effects of Hall current on f lows of a Burgers’ fluid through a porous medium

  • T. Hayat
  • M. Husain
  • M. KhanEmail author
Original Paper

Abstract

This paper generalizes the analysis of four magnetohydrodynamic (MHD) flow problems of an Oldroyd-B fluid discussed by Asghar et al. [Int. J. Non-linear Mech. 40, 589–601 (2005)] into three directions: (i) to discuss the problems in a porous medium using modified Darcy’s law (ii) to see the influence of Hall current (iii) to determine the effect of rheological parameter of Burgers’ fluid. Analytical solutions of velocity distribution valid at large and small times are given in each problem. Comparison has been provided for Oldroyd-B and Burgers’ fluids through graphs. The physical interpretation is also included.

Keywords

Burgers’ fluid Hall current Porous medium 

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References

  1. Alishayev M.G. (1974) Proceedings of moscow pedagogy institute (in Russian). Hydromechanics 3, 166–174Google Scholar
  2. Asghar S., Khan M., Hayat T. (2005) Magnetohydrodynamic transient flows of a non-Newtonian fluid. Int. J. Non-linear Mech. 40, 589–601CrossRefGoogle Scholar
  3. Auriault T.L., Geindreau C., Boutin C. (2005) Filtration law in porous media with poor separation of scales. Transp. Porous Med 60, 89–108CrossRefGoogle Scholar
  4. Capuani F., Frenkel D., Lowe C.P. (2003) Velocity fluctuations and dispersion in a simple porous medium. Phys. Rev. E 67, 0563061–0563068CrossRefGoogle Scholar
  5. Khaled A.R.A., Vafai K. (2003) The role of porous media in modeling flow and heat transfer in biological tissues. Int. J. Heat Mass Transfer 46, 4989–5004CrossRefGoogle Scholar
  6. Khuzhayorov B., Auriault J.L., Royer P. (2000) Derivation of macroscopic filtration law for transient linear viscoelastic fluid in porous media. Int. J. Eng. Sci. 38, 487–504CrossRefGoogle Scholar
  7. Kim M.C., Lee S.B., Kim S. et al. (2003) Thermal instability of viscoelastic fluids in a porous media. Int. J. Heat Mass Transfer 46, 5065–5072CrossRefGoogle Scholar
  8. Krishnan J.M., Rajagopal K.R. (2003) Review of the uses and modeling of bitumen from ancient to modern times, Appl. Mech. Rev. 56, 149–214CrossRefGoogle Scholar
  9. Levy T. (1983) Fluid flow through an array of fixed particles. Int. J. Eng. Sci. 21, 11–23CrossRefGoogle Scholar
  10. Masuoka T., Takatsu Y. (2002) Turbulence characteristic in porous media. In: Derek B.I., Pop I. (eds). Transport Phenomena in Porous Media, vol. II. Elsevier Sci. Ltd, Boston, pp. 231–256Google Scholar
  11. Ravindran P., Krishnan J.M., Rajagopal K.R. (2004) A note on the flow of a Burgers’ fluid in an orthogonal rheometer. Int. J. Eng. Sci. 42, 1973–1985CrossRefGoogle Scholar
  12. Sahimi M. (1995) Flow and Transport in Porous Media and Fractured Rock From Classical Methods to Modern Approaches. VCH, WeinheimGoogle Scholar
  13. Slattery J.C. (1999) Advanced Transport Phenomena. Cambridge University Press, CambridgeGoogle Scholar
  14. Sutton G.W., Sherman A. (1965) Engineering Magnetohydrodynamics. McGraw Hill, New YorkGoogle Scholar
  15. Tan W.C., Masuoka T. (2005a) Stokes’ first problem for a second grade fluid in a porous half-space with heated boundary. Int. J. Non-linear Mech. 40, 515–522CrossRefGoogle Scholar
  16. Tan W.C., Masuoka T. (2005b) Stokes’ first problem for an Oldroyd-B fluid in a porous half space. Phys. Fluids 17, 023101–023107CrossRefGoogle Scholar
  17. Vafai K., Tien C.L. (1981) Boundary and inertia effects on flow and heat transfer in porous media. Int. J. Heat Mass Transfer 24, 195–203CrossRefGoogle Scholar
  18. Wiegel F.W. (1980) Fluid Flow Through Porous Macromolecular Systems. Springer-Verlag, BerlinGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan

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