Abstract
The onset of convection in a horizontal porous layer is investigated theoretically. The permeability of the porous medium is a continuous periodic function of the horizontal x coordinate. Floquet theory has been employed to determine the favoured two-dimensional mode of convection. For a wide range of periods of the permeability variation, a matrix eigenvalue technique with eighth order accuracy has been employed to find the critical Darcy- Rayleigh number. This is supplemented by a multiple-scales analysis of the large-period limit, and a brief consideration of the anisotropic limit for very short periods.
Original language | English |
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Pages (from-to) | 187-205 |
Number of pages | 19 |
Journal | Transport in Porous Media |
Volume | 77 |
Issue number | 2 |
DOIs | |
Publication status | Published - Mar 2009 |
Keywords
- Nonuniform permeability
- Floquet theory
- Linear stability theory
- Free convection
- Multiple scales