Abstract
In this paper we study the problem of Rayleigh–Bénard convection in a porous medium. Assuming that the viscosity depends on both the temperature and pressure and that it is analytic in these variables we show that the Rayleigh–Bénard equations for flow in a porous media satisfy the idea of exchange of stabilities. We also show that the static conduction solution is linearly stable if and only if the Rayleigh number is less than or equal to a critical Rayleigh number. Finally, we show that a measure of the thermal energy of the fluid decays exponentially which in turn implies that the L2 norm of the perturbed temperature and velocity also decay exponentially.
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Rajagopal, K.R., Saccomandi, G. & Vergori, L. Stability analysis of Rayleigh–Bénard convection in a porous medium. Z. Angew. Math. Phys. 62, 149–160 (2011). https://doi.org/10.1007/s00033-010-0062-7
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DOI: https://doi.org/10.1007/s00033-010-0062-7