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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

Author Affiliations

1 School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01 Scottsville, Pietermaritzburg, 3209, South Africa

2 Department of Mathematics, Bangalore University, Central College Campus, Bangalore, 560001, India

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Boundary Value Problems 2012, 2012:88  doi:10.1186/1687-2770-2012-88

Published: 6 August 2012


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.

double diffusive convection; nonsimilar solutions; porous medium; Keller box method