Governing Equations for Laminar Flows Through Porous Media

A new look at viscous dissipation
  • D. B. Ingham
Conference paper
Part of the NATO Science Series book series (NAII, volume 134)

Abstract

We mean by a porous medium a material consisting of a solid matrix with an interconnected void and the solid matrix can be either rigid (the usual configuration) or it undergoes small deformation. The interconnectedness of the void (pores) allows the flow of one, or more, fluids through the material. In the simplest situation, i.e. ‘single-phase flow’, the void is saturated by a single fluid, whereas in ‘two-phase flow’ two fluids share the void space. Examples of natural porous media are sandstone, wood, limestone, etc.

Keywords

Heat Transfer Representative Elementary Volume Viscous Dissipation Mixed Convect Darcy Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Al Hadhrami, A. K., Elliott, L. and Ingham, D. B. (2002). Combined free and forced convection in vertical channels of porous media. Transport in Porous Media, 49, 265–89.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Al Hadhrami, A. K., Elliott, L. and Ingham, D. B. (2003). A new model for viscous dissipation in porous media across a range of permeability values. Transport in Porous Media. In press.Google Scholar
  3. [3]
    Bories, S. A. (1987). Natural convection in porous media. In Advances in transport phenomena in porous media (ed. J. Bear and M. Y. Corapcioglu), pp. 77-141. Martinus Nijhoff, The Netherlands.Google Scholar
  4. [4]
    Brinkman, H. C. (1947). A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A, 1, 27–34.CrossRefGoogle Scholar
  5. [5]
    Brinkman, H. C. (1947). On the permeability of media consisting of closely packed porous particles. Appl. Sci. Res. A, 1, 81–6.CrossRefGoogle Scholar
  6. [6]
    Chandrasekhara, B. C. and Nagaraju, P. (1988). Composite heat transfer in the case of steady laminar flow of a gray fluid with small optical density past a horizontal plate embedded in a saturated porous medium. Wärme-und Stoffübertr., 23, 343–52.CrossRefGoogle Scholar
  7. [7]
    Chandrasekhara, B. C. and Nagaraju, P. (1993). Composite heat transfer in a variable porosity medium bounded by an infinite flat plate. Wärme-und Stoffübertr., 28, 449–56.CrossRefGoogle Scholar
  8. [8]
    Darcy, H. P. C. (1856). Les fontaines publiques de la ville de Dijon. Victor Delmont, Paris.Google Scholar
  9. [9]
    Hossain, M. and Pop, I. (1997). Radiation effect on Darcy free convective flow along an inclined surface placed in a porous media. Heat Mass Transfer, 30, 149–53.CrossRefGoogle Scholar
  10. [10]
    Howie, L. E. (2002). Convection in ordered and disordered porous layers. In Transport phenomena in porous media II (ed. D. B. Ingham and I. Pop), pp. 155-76. Pergamon, Oxford.Google Scholar
  11. [11]
    Ingham, D. B. and Pop, I. (ed.) (1998). Transport phenomena in porous media. Pergamon, Oxford.Google Scholar
  12. [12]
    Ingham, D. B. and Pop, I. (ed.) (2002). Transport phenomena in porous media II. Pergamon, Oxford.Google Scholar
  13. [13]
    Joseph, D. D., Nield, D. A. and Papanicolaou, G. (1982). Nonlinear equation governing flow in a saturated porous medium. Water Resources Res., 18, 1049–52 and 19, 591.CrossRefGoogle Scholar
  14. [14]
    Kaviany, M. (1995). Principles of heat transfer in porous media (2nd edn). Springer-Verlag, New York.Google Scholar
  15. [15]
    Kladias, N. and Prasad, V. (1989). Convective instabilities in horizontal porous layers heated from below: effects of grain size and properties. ASME HTD, 107, 369–79.Google Scholar
  16. [16]
    Kladias, N. and Prasad, V. (1989). Natural convection in horizontal porous layers: effects of Darcy and Prandtl numbers. ASME J. Heat Transfer, 111, 926–35.CrossRefGoogle Scholar
  17. [17]
    Kladias, N. and Prasad, V. (1990). Flow transitions in buoyancy-induced non-Darcy convection in a porous medium heated from below. ASME J. Heat Transfer, 112, 675–84.CrossRefGoogle Scholar
  18. [18]
    Lage, J. L. (1998). The fundamental theory of flow through permeable media from Darcy to turbulence. In Transport phenomena in porous media (ed. D. B. Ingham and I. Pop), pp. 1-30. Pergamon, Oxford.Google Scholar
  19. [19]
    Mansour, M. A. (1997). Forced convection radiation interaction heat transfer in boundary layer over a flat plate submersed in a porous medium. Appl. Mech. Eng., 2, 405–13.MATHGoogle Scholar
  20. [20]
    Masuoka, T. and Takatsu, Y. (2002). Turbulence characteristics in porous media. In Transport phenomena in porous m,edia II(ed. D. B. Ingham and I. Pop), pp. 231-56. Pergamon, Oxford.Google Scholar
  21. [21]
    Nield, D. A. (1991). Estimation of the stagnant thermal conductivity of saturated porous media. Int. J. Heat Mass Transfer, 34, 1575–6.CrossRefGoogle Scholar
  22. [22]
    Nield, D. A. (1999). Modelling the effects of a magnetic field or rotation on flow in a porous medium. Momentum equation and anisotropic permeability analogy. Int. J. Heat Mass Transfer, 42, 3715–18.MATHCrossRefGoogle Scholar
  23. [23]
    Nield, D. A. (2000). Resolution of a paradox involving viscous dissipation and nonlinear drag in porous medium. Transport in Porous Media, 41, 349–57.MathSciNetCrossRefGoogle Scholar
  24. [24]
    Nield, D. A. (2002). Modelling fluid flow in saturated porous media and at interfaces. In Transport phenomena in porous media II (ed. D. B. Ingham and I. Pop), pp. 1-19. Pergamon, Oxford.Google Scholar
  25. [25]
    Nield, D. A. and Bejan, A. (1999). Convection in porous media (2nd edn). Springer, New York.Google Scholar
  26. [26]
    Pop, I. and Ingham, D. B. (2001). Convective heat transfer: mathematical and computational modelling of viscous fluids and porous media. Pergamon, Oxford.Google Scholar
  27. [27]
    Raptis, A. and Perdikis, C. (1987). Hydromagnetic free-convective flow through porous media. In Encyclopedia of fluid mechanics and modelling (ed. N. P. Cheremisinoff), pp. 239-62, Chapter 8. Gulf Publishing, Houston.Google Scholar
  28. [28]
    Shenoy, A. V. (1992). Darcy natural, forced and mixed convection heat transfer from an isothermal vertical flat plate embedded in a porous medium saturated with an elastic fluid of constant viscosity. Int. J. Eng. Sci., 30, 455 67.Google Scholar
  29. [29]
    Shenoy, A. V. (1993). Darcy-Forchheimer natural, forced and mixed convection heat transfer in non-Newtonian power-law fluid-saturated porous media. Transport in Porous Media, 11, 219–41.CrossRefGoogle Scholar
  30. [30]
    Shenoy, A. V. (1994). Non-Newtonian fluid heat transfer in porous media. Adv. Heat Transfer, 24, 101–90.CrossRefGoogle Scholar
  31. [31]
    Vadasz, P. (1998). Free convection in rotating porous media. In Transport phenomena in porous media (ed. D. B. Ingham and I. Pop), pp. 285-312. Pergamon, Oxford.Google Scholar
  32. [32]
    Vadasz, P. (1999). Flow in rotating porous media. In Fluid transport in porous media (ed. P. du Plessis), Chapter 4. Computational Mechanics Publications, Southampton.Google Scholar
  33. [33]
    Wang, M. and Bejan, A. (1987). Heat transfer correlation for Bénard convection in a saturated porous layer. Int. Comm. Heat Mass Transfer, 14, 617–26.CrossRefGoogle Scholar
  34. [34]
    Ward, J. C. (1964). Turbulent flow in porous media. J. Hydraul. Div. Amer. Soc. Civ. Eng., 90, 1–12.Google Scholar
  35. [35]
    Yih, K. A. (1999). Radiation effect on natural convection over a vertical cylinder embedded in porous media. Int. Comm. Heat Mass Transfer, 26, 259–67.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • D. B. Ingham
    • 1
  1. 1.Department of Applied MathematicsUniversity of LeedsLeedsUK

Personalised recommendations