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Flow with convective acceleration through a porous medium

Journal of Engineering Mathematics volume 10, pages 41–54 (1976)Cite this article

Summary

The flow streaming into a porous and permeable medium with arbitrary but smooth wall surface is considered on the basis of the Euler equation (in the pure fluid region) and a generalized Darcy's law in which the convective acceleration is taken into account. The asymptotic behavior of the flow for small permeability of the medium is investigated. It is shown that the flow in the porous medium is irrotational except in the boundary layer next to the surface. The velocity distribution in the boundary layer is given in a universal form. Proper boundary conditions connecting the potential flow in the pure fluid region and the potential flow in the porous medium are obtained when the boundary layer is neglected.

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References

  1. C. N. Davies,Air Filtration, Academic Press, London (1973).

    Google Scholar 

  2. J. Bear,Dynamics of fluids in porous media, American Elsevier Pub. Co., New York (1972).

    Google Scholar 

  3. G. Hamel, Über Grundwasserströmung,Z. angew. Math. Mech. 14 (1934) 129–157.

    Google Scholar 

  4. C. S. Yih,Dynamics of Nonhomogeneous Fluids, Macmillan Co., New York (1965).

    Google Scholar 

  5. P. A. C. Raats, The role of inertia in the hydrodynamics of porous media,Arch. Rational Mech. Anal. 44 (1972) 267–280.

    Google Scholar 

  6. K. Yamamoto and Z. Yoshida, Flow through a porous wall with convective acceleration,J. Phys. Soc. Japan 37 (1974) 774–779.

    Google Scholar 

  7. A. E. Scheidegger,The physics of flow through porous media, Univ. Toronto Pr. (1957).

  8. G. I. Taylor, A model for the boundary condition of a porous material, Part 1,J. Fluid Mech. 49 (1971) 319–326.

    Google Scholar 

  9. T. S. Lundgren, Slow flow through stationary random beds and suspensions of spheres,J. Fluid Mech. 51 (1972) 273–299.

    Google Scholar 

  10. C. K. W. Tam, The drag on a cloud of spherical particles in low Reynolds number flow,J. Fluid Mech. 38 (1969) 537–546.

    Google Scholar 

  11. E. A. Mason, A. P. Malinauskas and R. B. Evans III, Flow and diffusion of gases in porous media,J. Chem. Phys. 46 (1967) 3199–3216.

    Google Scholar 

  12. L. D. Landau and E. M. Lifshitz,Fluid mechanics, Pergamon Pr., New York (1959).

    Google Scholar 

  13. C. E. Weatherburn,Differential geometry of three dimensions, Cambridge Univ. Pr. (1927).

  14. J. Happel and H. Brenner,Low Reynolds number hydrodynamics, Prentice-Hall Inc. (1965).

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Author notes

  1. N. Iwamura

    Present address: Mitsubishi Heavy Industry Co., Japan

Authors and Affiliations

  1. Physics Department, Eindhoven University of Technology, Eindhoven, The Netherlands

    K. Yamamoto

  2. Department of Aeronautical Engineering, Kyoto University, Kyoto, Japan

    N. Iwamura

Authors
  1. K. Yamamoto
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  2. N. Iwamura
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Additional information

On leave from Department of Aeronautical Engineering, Kyoto University, Kyoto, Japan.

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Yamamoto, K., Iwamura, N. Flow with convective acceleration through a porous medium. J Eng Math 10, 41–54 (1976). https://doi.org/10.1007/BF01535425

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  • DOI: https://doi.org/10.1007/BF01535425

Keywords

  • Boundary Condition
  • Permeability
  • Boundary Layer
  • Porous Medium
  • Asymptotic Behavior