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Effect of anisotropic permeability on Darcy's law

✍ Scribed by L. E. Payne; J. F. Rodrigues; B. Straughan

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 105 KB
Volume: 24
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.228

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✦ Synopsis

Abstract

The concept of structural stability is discussed and briefly reviewed within the context of fluid flow in porous media. Then the equations for non‐Boussinesq (penetrative) convection in a porous medium with anisotropic permeability are analysed. It is shown, by deriving truly a priori estimates, that the solution exists in the natural functional framework and depends continuously on changes in the permeability. Since under appropriate circumstances the onset of thermal convection may be via Hopf bifurcation rather than stationary convection, such a priori continuous dependence estimates are of much value. Copyright © 2001 John Wiley & Sons, Ltd.

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