Skip to main content
SpringerLink
Log in

A New Model for Viscous Dissipation in Porous Media Across a Range of Permeability Values

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

In this paper a unified mathematical theory for the viscous dissipation term in the governing Brinkman equation is derived. This term has, unlike other models, the correct asymptotic behaviour in both the fully Darcy and Newtonian fluid flow limits.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Al-Hadhrami, A. K., Elliott, L. and Ingham, D. B.: 2002, Combined free and forced convection in vertical channels of porous media, Transport Porous Med. 49, 265–289.

    Google Scholar 

  • Beckett, P. M.: 1980, Combined natural and forced convection between parallel vertical walls, SIAM J. Appl. Math. 39, 372–384.

    Google Scholar 

  • Beckett, P. M. and Friend, I. E.: 1984, Combined natural and forced convection between parallel walls: developing flow at high Rayleigh numbers, Int. J. Heat Mass Transfer 27, 611–621.

    Google Scholar 

  • Brinkman, H. C.: 1974a, A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles, Appl. Sci. Res. A 1, 27–34.

    Google Scholar 

  • Brinkman, H. C.: 1974b, On the permeability of media consisting of closely packed porous particles, Appl. Sci. Res. A 1, 81–86.

    Google Scholar 

  • Ingham, D. B. and Pop, I.: 1998, Transport Phenomena in Porous Media, Pergamon, Elsevier Science, Oxford.

  • Ingham, D. B. and Pop, I.: 2002, Transport Phenomena in Porous Media, Pergamon, Elsevier Science, Oxford.

  • Ingham, D. B., Pop, I. and Cheng, P.: 1990, Combined free and forced convection in a porous medium between two vertical walls with viscous dissipation, Transport in Porous Media 5, 381–398.

    Google Scholar 

  • Nield, D. A.: 2000, Resolution of a paradox involving viscous dissipation and nonlinear drag in porous medium, Transport in Porous Media 41, 349–357.

    Google Scholar 

  • Nield, D. A.: 2002, in: D. B. Ingham and I. Pop (eds), Transport Phenomena in Porous Media, Pergamon, Elsevier Science, Oxford.

  • Nield, D. A. and Bejan, A.: 1999, Convection in Porous Media, 2nd edn., Springer-Verlag, New York.

    Google Scholar 

  • Pop, I. and Ingham, D. B.: 2001, Convective Heat Transfer, Pergamon, Elsevier Science, Oxford.

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, U.K

    A. K. Al-Hadhrami, L. Elliott & D. B. Ingham

Authors
  1. A. K. Al-Hadhrami
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Elliott
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. B. Ingham
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Al-Hadhrami, A.K., Elliott, L. & Ingham, D.B. A New Model for Viscous Dissipation in Porous Media Across a Range of Permeability Values. Transport in Porous Media 53, 117–122 (2003). https://doi.org/10.1023/A:1023557332542

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1023557332542

Search

Navigation