On double-diffusive convection and cross diffusion effects on a horizontal wavy surface in a porous medium
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RESEARCH
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On double-diffusive convection and cross diffusion effects on a horizontal wavy surface in a porous medium M Narayana1 , P Sibanda1* , SS Motsa1 and PG Siddheshwar2 *
Correspondence: [email protected] 1 School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01 Scottsville, Pietermaritzburg, 3209, South Africa Full list of author information is available at the end of the article
Abstract An analysis of double diffusive convection induced by a uniformly heated and salted horizontal wavy surface in a porous medium is presented. The wavy surface is first transformed into a smooth surface via a suitable coordinate transformation and the transformed nonsimilar coupled nonlinear parabolic equations are solved using the Keller box method. The local and average Nusselt and Sherwood numbers are given as functions of the streamwise coordinate and the effects of various physical parameters are discussed in detail. The effects of the Lewis number, buoyancy ratio, and wavy geometry on the dynamics of the flow are studied. It was found, among other observations, that the combined effect of Dufour and Soret parameters is to reduce both heat and mass transfer. MSC: 34B15; 65N30; 76M20 Keywords: double diffusive convection; nonsimilar solutions; porous medium; Keller box method
1 Introduction The study of double-diffusive convection has received considerable attention during the last several decades because of its occurrence in a wide range of natural and technological settings. Double-diffusive convection is an important fluid dynamic phenomenon that involves motions driven by two different density gradients diffusing at different rates (Mojtabi and Charrier-Mojtabi []). A common example of double diffusive convection is seen in oceanography, where heat and salt concentrations exist with different gradients and diffuse at differing rates. Double diffusive convection manifests in the form of “salt-fingers” (see Stern [, ]) which are observable in laboratory settings. The input of cold fresh-water from an iceberg can affect both of these variables. Double-diffusive convection has also been cited as being important in the modeling of solar ponds (Akbarzadeh and Manins []) and magma chambers (Huppert and Sparks [], Fernando and Brandt []). Doublediffusive free convection is also seen in sea-wind formations, where upward convection is also modified by Coriolis forces. This is of particular interest in oceans where the Earth’s rotation plays a dominant role in many of the motions observed. In engineering applications, double diffusive convection is commonly visualized in the formation of microstructures during the cooling of molten metals, and fluid flows around shrouded heat-dissipation fins. Typical technological motivations for the study of doublediffusive convection range from such diverse fields as the migration of moisture through © 2012 Narayana et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/lic
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