### 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 language | English (US) |
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Pages (from-to) | 345-362 |

Number of pages | 18 |

Journal | Journal of Fluid Mechanics |

Volume | 254 |

State | Published - 1993 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Fluid Mechanics*,

*254*, 345-362.