The effect of a weak heterogeneity of a porous medium on natural convection

C. Braester, Peter Vadasz

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Abstract

Analytical solutions for rectangular weak heterogeneous porous domains heated from below, consistent with a basic motionless solution, are obtained by applying the weak nonlinear theory. The amplitude of the convection is obtained from an ordinary non-homogeneous differential equation, with a forcing term representative of the medium heterogeneity with respect to the effective thermal conductivity. A smooth transition through the critical Rayleigh number is obtained, thus removing a bifurcation which usually appears in homogeneous domains with perfect boundaries, at the critical value of the Rayleigh number. Within a certain range of slightly supercritical Rayleigh numbers, a symmetric thermal conductivity function is shown to reinforce a symmetrical flow while antisymmetric functions favour an antisymmetric flow. Weak heterogeneity with respect to permeability plays a relatively passive role and does not affect the solutions at the leading order. Weak heterogeneity with respect to the effective thermal conductivity does have a significant effect on the resulting flow pattern. -from Authors

Original languageEnglish (US)
Pages (from-to)345-362
Number of pages18
JournalJournal of Fluid Mechanics
Volume254
StatePublished - 1993
Externally publishedYes

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ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Engineering(all)

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