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Global nonlinear stability for a triply diffusive convection in a porous layer

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Abstract

A triply convective-diffusive fluid mixture saturating a porous horizontal layer in the Darcy–Oberbeck–Boussinesq scheme is studied. The nonlinear stability analysis of the conduction solution is performed when the layer is heated from below and salted from above by one salt and below by another salt. Denoting by P i , (i = 1, 2), the salts Prandtl numbers, it is shown that in the cases {P 1 = 1; P 2 = 1; P 1 = P 2} do not exist subcritical instabilities and the thermal Rayleigh critical number of global stability in a simple closed form is given. The methodology used and the results obtained appear to be new in the existing literature and useful for the applications.

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Authors and Affiliations

  1. Department of Mathematics and Applications “R.Caccioppoli”, University of Naples Federico II, Via Cinzia, 80126, Napoli, Italy

    Salvatore Rionero

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  1. Salvatore Rionero
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Correspondence to Salvatore Rionero.

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Communicated by Oliver Kastner.

Dedicated to Professor Ingo Müller for his 75th birthday.

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Rionero, S. Global nonlinear stability for a triply diffusive convection in a porous layer. Continuum Mech. Thermodyn. 24, 629–641 (2012). https://doi.org/10.1007/s00161-011-0219-4

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  • DOI: https://doi.org/10.1007/s00161-011-0219-4

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