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Resolution of a Paradox Involving Viscous Dissipation and Nonlinear Drag in a Porous Medium

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Abstract

The modelling of viscous dissipation in a porous medium saturated by an incompressible fluid is discussed, for the case of Darcy, Forchheimer and Brinkman models. An apparent paradox relating to the effect of inertial effects on viscous dissipation is resolved, and some wider aspects of resistance to flow (concerning quadratic drag and cubic drag) in a porous medium are discussed. Criteria are given for the importance or otherwise of viscous dissipation in various situations.

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References

  • Bakhmeteff, B. A. and Feodoroff, N. V.: 1937, Flow through granular beds, J. Appl. Mech. 4, A97-A104.

    Google Scholar 

  • Bejan, A.: 1995, Convection Heat Transfer, 2nd edition, Wiley, New York, pp. 523-527.

    Google Scholar 

  • Dybbs, A. and Edwards, R. V.: 1984, A new look at porous media fluid mechanics - Darcy to turbulent, In: J. Bear and Y. Corapcioglu (eds), Martinus Nijhoff Publishers, Dordrecht, pp. 199-256.

    Google Scholar 

  • Fand, R. M., Varahasamy, M. and Yamamoto, L. M.: 1994, Heat transfer by natural convection from horizontal cylinders embedded in porous media whose matrices are composed of spheres: viscous dissipation, In: G. F. Hewitt (ed.), Heat Transfer 1994, Proc. 10th IHTC, Brighton UK, Institute of Chemical Engineers, Rugby, UK, Vol. 5, pp. 237-242.

    Google Scholar 

  • Firdaouss, M., Girermond, J. L. and Le Quéré, P.: 1997, Nonlinear corrections to Darcy's law at low Reynolds numbers, J. Fluid Mech. 343, 331-350.

    Google Scholar 

  • Joseph, D. D., Nield, D. A. and Papanicolaou, G.: 1982, Nonlinear equation governing flow in a saturated porous medium, Water Resour. Res. 18, 1049-1052.

    Google Scholar 

  • Kacaç, S. and Yener, Y.: 1987, Basics of heat transfer, In: S. Kacaç, R. K. Shah and W. Aung (eds), Handbook of Single-Phase Convective Heat Transfer, Wiley, New York, Chap. 1.

    Google Scholar 

  • Kaviany, M.: 1995, Principles of Heat Transfer in Porous Media, 2nd edition, Springer-Verlag, New York.

    Google Scholar 

  • Lage, J. L.: 1998, The fundamental theory of flow through permeable media from Darcy to turbulence, In: D. B. Ingham and I. Pop (eds), Transport Phenomena in Porous Media, Elsevier Science, Oxford, pp. 1-30.

    Google Scholar 

  • Lage, J. L., Antohe, B. V. and Nield, D. A.: 1997, Two types of nonlinear pressure-drop versus flow-rate relation observed for saturated porous media, ASME J. Fluids Engng 119, 701-706.

    Google Scholar 

  • Macdonald, I. F., El-Sayed, M. S., Mow, K. and Dullien, F. A. L.: 1979, Flow through porous media - Ergun equation revisited, Ind. Engng Chem. Fund. 18, 199-208.

    Google Scholar 

  • Mei, C. C. and Auriault, J. L.: 1991, The effect of weak inertia on flow through a porous medium, J. Fluid Mech. 222, 647-663.

    Google Scholar 

  • Murthy, P. V. S. N. and Singh, P.: 1997, Effect of viscous dissipation on a non-Darcy natural convection regime, Int. J. Heat Mass Transfer 40, 1251-1260.

    Google Scholar 

  • Nakayama, A. and Pop, I.: 1989, Free convection over a non-isothermal body in a porous medium with viscous dissipation, Int. Comm. Heat Mass Transfer 16, 173-180.

    Google Scholar 

  • Nield, D. A.: 1991, The limitations of the Brinkman-Forchheimer equation in modelling flow in a saturated porous medium and at an interface, Int. J. Heat Fluid Flow 12, 269-272.

    Google Scholar 

  • Nield, D. A.: 1994, Modelling high-speed flow of an incompressible fluid in a saturated porous medium, Transport in Porous Media 14, 85-88.

    Google Scholar 

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

    Google Scholar 

  • Rasoloarijaona, M. and Auriault, J. L.: 1994, Nonlinear seepage flow through a rigid porous medium, Eur. J. Mech. B/Fluids 13, 177-195.

    Google Scholar 

  • Skjetne, E. and Auriault, J. L.: 1999, New insights on steady, non-linear flow in porous media, Eur. J. Mech. B/Fluids 18, 131-145.

    Google Scholar 

  • Takhar, H. G. and Beg, O. A.: 1997, Effects of transverse magnetic field, Prandtl number and Reynolds number on non-Darcy mixed convective flow of an incompressible viscous fluid past a porous vertical flat plate in a saturated porous medium, Int. J. Energy Res. 21, 87-100.

    Google Scholar 

  • Wodie, J. C. and Levy, T.: 1991, Correction non linéaire de la loi de Darcy, C. R. Acad. Sci. Paris, Série II, 312, 157-161.

    Google Scholar 

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  1. Department of Engineering Science, University of Auckland, Private Bag 92019, Auckland, New Zealand

    D. A. Nield

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Nield, D.A. Resolution of a Paradox Involving Viscous Dissipation and Nonlinear Drag in a Porous Medium. Transport in Porous Media 41, 349–357 (2000). https://doi.org/10.1023/A:1006636605498

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