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Dynamic Properties of Thermal Convection in Porous Medium

  • Dmitry V. Lyubimov

Abstract

Thermal convection in porous media is considered in most of the works on the base of Darcy law and Boussinesq approximation. The main distinction of the Darcy-Boussinesq equations from that of the uniform fluid convection is the lower order of the velocity field spatial derivatives. This leads to the change of the boundary conditions: at the impermeable boundary one can impose only the condition of impermeability (and not the no-slip condition). The second distinction is of less importance: the inertial terms are absent in the equation of motion. This should prevent the appearance of the oscillatory states. The similar situation takes place in the uniform fluid when the value of the Prandtl number is high enough.

Keywords

Porous Medium Rayleigh Number Phase Portrait Thermal Convection Principal Eigenvalue 
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References

  1. 1.
    D. V. Lyubimov, On the convective flows in the porous medium heated from below, Journal of Applied Mechanics and Technical Physics, 2:131 (1975) (in Russian).Google Scholar
  2. 2.
    V. I. Yudovich, Co-symmetry, degeneracy of the operator equations solutions, onset of the filtration convection, Mathematical notes, 49:142 (1991) (in Russian).CrossRefGoogle Scholar
  3. 3.
    A. F. Glukhov, D. V. Lyubimov and G. F. Putin, Convective motions in a porous medium near the equilibrium instability threshold, Sov. Phys. Dokl., 23:22 (1978)Google Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Dmitry V. Lyubimov
    • 1
  1. 1.Theoretical Physics DepartmentPerm State UniversityPermRussia

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