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Acta Mech 204, 120 (2009)
DOI 10.1007/s00707-008-0036-4
Received: 19 September 2007 / Revised: 12 January 2008 / Published online: 16 July 2008 Springer-Verlag 2008
Abstract We examine the effect of local thermal non-equilibrium on double diffusive convection in a uid-saturated sparsely packed porous layer heated from below and cooled from above, using both linear and nonlinear stability analyses. The Brinkman model is employed as the momentum equation. A two-eld model that represents the uid and solid phase temperature elds separately is used for the energy equation. The onset criterion for stationary, oscillatory and nite amplitude convection is derived analytically. It is found that a small inter-phase heat transfer coefcient has signicant effect on the stability of the system. There is a competition between the processes of thermal and solute diffusion that causes the convection to set in through either oscillatory or nite amplitude mode rather than stationary. The effect of solute Rayleigh number, porosity modied conductivity ratio, Lewis number, ratio of diffusivities, Vadasz number and Darcy number on the stability of the system is investigated. The nonlinear theory based on the truncated representation of Fourier series method predicts the occurrence of subcritical instability in the form of nite amplitude motions. The effect of thermal non-equilibrium on heat and mass transfer is also brought out.
1 Introduction
The problem of double diffusive convection in porous media has attracted considerable interest during the last few years because of its wide range of applications, from the solidication of binary mixtures to the migration of solutes in water-saturated soils. Other examples include geophysical systems, electro-chemistry and the migration of moisture through air contained in brous insulation. Early studies on the phenomena of double diffusive convection in porous media are mainly concerned with problem of convective instability in a horizontal layer heated and salted from below. During the last 2 decades, there has been a great upsurge of interest in determining the effect of extensions to Darcys law since many practical applications involve media for which Darcys law is inadequate. A comprehensive review of the literature concerning double diffusive natural convection in a uid-saturated porous medium may be found in the book by Nield and Bejan [1]. Useful review articles on double diffusive convection in porous media include those by...