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Open AccessArticle

Onset of Convection in an Inclined Anisotropic Porous Layer with Internal Heat Generation

Department of Mathematics, University of Agder, Serviceboks 422, 4604 Kristiansand, Norway
Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK
Author to whom correspondence should be addressed.
Fluids 2019, 4(2), 75;
Received: 20 March 2019 / Revised: 10 April 2019 / Accepted: 11 April 2019 / Published: 16 April 2019
(This article belongs to the Special Issue Convective Instability in Porous Media, Volume II)
PDF [1014 KB, uploaded 16 April 2019]


The onset of convection in an inclined porous layer which is heated internally by a uniform distribution of heat sources is considered. We investigate the combined effects of inclination, anisotropy and internal heat generation on the linear instability of the basic parallel flow. When the Rayleigh number is sufficiently large, instability occurs and a convective motion is set up. It turns out that the preferred motion at convection onset depends quite strongly on the anisotropy ratio, ξ , and the inclination angle. When ξ < 1 the preferred motion is in the form of longitudinal rolls for all inclinations. When ξ > 1 transverse rolls are preferred for small inclinations but, at high inclinations, longitudinal rolls are preferred. At intermediate inclinations the preferred roll orientation varies smoothly between these two extremes. View Full-Text
Keywords: porous media; convection; onset; inclination; heat generation; anisotropy porous media; convection; onset; inclination; heat generation; anisotropy

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Storesletten, L.; Rees, D.A.S. Onset of Convection in an Inclined Anisotropic Porous Layer with Internal Heat Generation. Fluids 2019, 4, 75.

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