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On the convection in a porous medium with inclined temperature gradient and vertical throughflow. Part I. Normal modes

Brevdo, L. and Ruderman, M.S. (2009) On the convection in a porous medium with inclined temperature gradient and vertical throughflow. Part I. Normal modes. Transport in Porous Media, 80 (1). pp. 137-151. ISSN 0169-3913

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Abstract

In this analysis, we apply the methods of the theory of linear absolute and convective instabilities to studying the destabilization of transverse modes in a model of convection in an extended horizontal layer of a saturated porous medium with inclined temperature gradient and vertical throughflow. In this first part of the analysis, normal modes are treated and neutral curves are obtained for a variety of values of the horizontal Rayleigh number, R h, and the Péclet number, Q v. The computations are performed by using a high-precision pseudo-spectral Chebyshev-collocation method. Our results compare well with the results found in the literature for the critical values of the vertical Rayleigh number. It is shown that the horizontal temperature gradient effect, inducing a Hadley circulation, is stabilizing for any fixed value of the throughflow velocity. The throughflow effect is stabilizing, for each of the values of R h = 0, 10, 20, 30. For higher values of R h = 40, 50, 60 considered, the influence of increasing throughflow on the stability is mixed. For a vanishing horizontal temperature gradient the critical normal mode is non-oscillatory, for all the values of throughflow. In all the cases of a non-zero horizontal temperature gradient and a non-zero throughflow considered, the critical normal mode is oscillatory, and the oscillatory frequency is an increasing function of both R h and Q v.

Item Type: Article
Keywords: Saturated porous layer; Darcy flow ; Inclined temperature gradient; Vertical throughflow; Stability of transverse modes
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
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Depositing User: Mrs Megan Hobbs
Date Deposited: 29 Mar 2010 14:17
Last Modified: 07 Jun 2010 11:09
Published Version: http://dx.doi.org/10.1007/s11242-009-9348-7
Status: Published
Publisher: Springer
Identification Number: 10.1007/s11242-009-9348-7
URI: http://eprints.whiterose.ac.uk/id/eprint/10518

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