On Stability Analysis of Soret Convection Within a Horizontal Porous Layer

Stability analysis using Galerkin and finite element methods
  • M. Bourich
  • M. Mamou
  • M. Hasnaoui
  • A. Amahmid
Conference paper
Part of the NATO Science Series book series (NAII, volume 134)


The Soret effect, which describes the diffusion of solute along a temperature gradient, within a horizontal layer heated from below has attracted considerable interest in pattern formation and hysteresis phenomena. In such convective configuration, negative Soret coefficient, which causes the heavier component to migrate towards the hot wall, induces a variety of pattern formation phenomena. Multiple steady/oscillatory states, subcritical flows, standing/travelling waves and Hopf bifurcations are some examples of these phenomena that have been observed experimentally and predicted numerically. A literature review showed that great interest is paid to porous or fluid binary infinite horizontal layer with stress-free boundaries. However, in practical situations, experiments are usually conducted within a finite aspect ratio layer, with non-slip boundaries. Since this type of problem remains intractable analytically and difficult to tackle with the classical analytical methods, it has received less attention. The motivation of the present study is driven by the fact that, in practical situations, the temperature is usually varying along the heated or cooled walls. Therefore, the constant flux boundary conditions are the best approach to study the convective phenomena related to industrial or natural problems. In a laboratory, it is easy to heat a wall with a constant heat flux. However, cooling with constant heat flux could be achieved when the wall materials are poorly heat conductive.


Rayleigh Number Hopf Bifurcation Linear Stability Analysis Critical Rayleigh Number Constant Heat Flux 
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  1. [1]
    Ahlers, G. and Lücke, M. (1987). Some properties of an eight-mode Lorenz model for convection in binary fluids. Phys. Rev. A, 35, 470–3.CrossRefGoogle Scholar
  2. [2]
    Batiste, O., Mercader, I., Net, M. and Knobloch, E. (1999). Onset of oscillatory fluid convection in finite containers. Phys. Rev. E, 59, 6730–41.CrossRefGoogle Scholar
  3. [3]
    Bourich, M., Hasnaoui, M., Amahmid, A. and Mamou, M. (2002). Soret driven thermosolutal convection in a shallow porous enclosure. Int. Comm. Heat Mass Transfer, 29, 717–28.CrossRefGoogle Scholar
  4. [4]
    Gilver, R. C. and Altobelli, S. A. (1994). A determination of the effective viscosity for the Brinkman-Forchheimer flow model. J. Fluid Mech., 258, 355–70.CrossRefGoogle Scholar
  5. [5]
    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, Chapter 1. Pergamon, Oxford.Google Scholar
  6. [6]
    Mamou, M., Vasseur, P. and Hasnaoui, M. (2001). On numerical stability analysis of double-diffusive convection in confined enclosures. J. Fluid Mech., 433, 209–50.zbMATHGoogle Scholar
  7. [7]
    Platten, J. K. and Legros, J. C. (1984). Convection in liquids. Springer-Verlag, Berlin.Google Scholar
  8. [8]
    Schópf, W. (1992). Convection onset for binary mixture in a porous medium and in a narrow cell: a comparison. J. Fluid Mech., 245, 263–78. 235-245.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • M. Bourich
    • 1
  • M. Mamou
    • 2
  • M. Hasnaoui
    • 1
  • A. Amahmid
    • 1
  1. 1.Faculty of Sciences Semlalia Physics DepartmentMarrakeshMorocco
  2. 2.Institute for Aerospace Research National Research Council CanadaOttawaCanada

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