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Fluids 2017, 2(3), 44; doi:10.3390/fluids2030044

Thermal Convection in a Rotating Anisotropic Fluid Saturated Darcy Porous Medium

Department of Mathematics, Faculty of Science, University of Basrah, Basrah 61004, Iraq
Received: 8 April 2017 / Revised: 11 August 2017 / Accepted: 15 August 2017 / Published: 21 August 2017
(This article belongs to the Special Issue Convective Instability in Porous Media)
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Abstract

The stability of the thermal convection in a fluid-saturated rotating anisotropic porous material is investigated. We take into account the rotation of a layer of saturated porous medium about an axis orthogonal to the planes bounding the layer. The permeability is allowed to be an anisotropic tensor. In particular, we restrict our attention to the case where the permeability in the vertical direction is different to that in the horizontal plane. The linear instability and nonlinear stability analysis, in the case where the inertial term vanishes, are performed. It is shown, by using an energy method, that the nonlinear critical Rayleigh numbers coincide with those of the linear analysis. The results reveal that the system becomes more stable when the rotation is present. View Full-Text
Keywords: thermal convection; nonlinear stability; anisotropy; rotation; linear instability thermal convection; nonlinear stability; anisotropy; rotation; linear instability
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Haddad, S. Thermal Convection in a Rotating Anisotropic Fluid Saturated Darcy Porous Medium. Fluids 2017, 2, 44.

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