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On cross-diffusion effects on flow over a vertical surface using a linearization method

Precious Sibanda*, Ahmed Abdalmgid Khidir and Faiz Gadelmola Awad

Author Affiliations

School of Mathematics, Statistics & Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg 3209, South Africa

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Boundary Value Problems 2012, 2012:25  doi:10.1186/1687-2770-2012-25

Published: 24 February 2012


In this article, we explore the use of a non-perturbation linearization method to solve the coupled highly nonlinear system of equations due to flow over a vertical surface subject to a magnetic field. The linearization method is used in combination with an asymptotic expansion technique. The effects of Dufour, Soret and magnetic filed parameters are investigated. The velocity, temperature and concentration distributions as well as the skin-friction, heat and mass transfer coefficients have been obtained and discussed for various physical parametric values. The accuracy of the solutions has been tested using a local non-similarity method. The results show that the non-perturbation technique is an accurate numerical algorithm that converges rapidly and may serve as a viable alternative to finite difference and finite element methods for solving nonlinear boundary value problems.

Mathematics Subject Classification (2000): 76D05; 74S30; 76E06; 76M25.

cross-diffusion; free convection; linearization method; incompressible flow; magneto-hydrodynamics (MHD)