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darcy law

Mathematical Modelling of Natural Phenomena (1)

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Convective Instability of Reaction Fronts in Porous Media
K. Allali, A. Ducrot, A. Taik, V. Volpert
Journal:

Mathematical Modelling of Natural Phenomena / Volume 2 / Issue 2 / 2007

Published online by Cambridge University Press:

15 June 2008, pp. 20-39

Print publication:

2007
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We study the influence of natural convection on stability of reaction fronts in porous media. The model consists of the heat equation, of the equation for the depth of conversion and of the equations of motion under the Darcy law. Linear stability analysis of the problem is fulfilled, the stability boundary is found. Direct numerical simulations are performed and compared with the linear stability analysis.