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Three-Dimensional Simulations for Convection Problem in Anisotropic Porous Media with Nonhomogeneous Porosity, Thermal Diffusivity, and Variable Gravity Effects

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Abstract

A convection problem in anisotropic and inhomogeneous porous media has been analyzed. In particular, the effect of variable permeability, thermal diffusivity, and variable gravity with respect to the vertical direction, has been studied. A linear and nonlinear stability analysis of the conduction solution has been performed. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using a three- dimensional simulation. Our results show that the linear threshold accurately predicts on the onset of instability in the basic steady state. However, the required time to arrive at the basic steady state increases significantly as the Rayleigh number tends to the linear threshold.

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Acknowledgments

This work was supported by the Iraqi Ministry of Higher Education and Scientific Research. The author acknowledges the comments and suggestions of Prof. B. Straughan which led to improvements in the manuscript. Also, the author would like to thank three anonymous referees for their pointed remarks that have led to improvements in the manuscript.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Durham, Durham , DH1 3LE, UK

    A. J. Harfash

  2. Department of Mathematics, College of Sciences, University of Basrah, Basra, Iraq

    A. J. Harfash

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  1. A. J. Harfash
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Correspondence to A. J. Harfash.

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Harfash, A.J. Three-Dimensional Simulations for Convection Problem in Anisotropic Porous Media with Nonhomogeneous Porosity, Thermal Diffusivity, and Variable Gravity Effects. Transp Porous Med 102, 43–57 (2014). https://doi.org/10.1007/s11242-013-0260-9

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  • DOI: https://doi.org/10.1007/s11242-013-0260-9

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