Coupled Heat and Mass Transfer By MHD Free Convection Flow along a Vertical Plate with Streamwise Temperature and Species Concentration Variations Ali J. Chamkha, 1 S.M.M. EL-Kabeir, 2,3 and A.M. Rashad 2 1 Manufacturing Engineering Department, The Public Authority for Applied Education and Training, Shuweikh, Kuwait 2 Department of Mathematics, Faculty of Science, South Valley University, Aswan, Egypt 3 Department of Mathematics, Salman bin Abdulaziz University, College of Science and Humanity Studies, Al-Kharj, Saudi Arabia The problem of steady, laminar, coupled heat and mass transfer by MHD free convective boundary-layer flow along a vertical flat plate with the combined effects of streamwise sinusoidal variations of both the surface temperature and the species concentration in the presence of Soret and Dufour effects is considered. A suitable set of dimensionless variables is used to transform the governing equations of the problem into a non-similar form. The resulting non-similar equations have the property that they reduce to various special cases previously considered in the literature. An adequate and efficient implicit, tri-diagonal finite difference scheme is employed for the numerical solution of the obtained equations. Various comparisons with previously published work are performed and the results are found to be in excellent agreement. A representative set of numerical results for the velocity, temperature, and concentra- tion profiles as well as the surface shear stress, rate of heat transfer, and the rate of mass transfer is presented graphically for various parametric conditions and is dis- cussed. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(2): 100–110, 2013; Published online 28 December 2012 in Wiley Online Library (wileyonlineli- brary.com/journal/htj). DOI 10.1002/htj.21033 Key words: heat and mass transfer, MHD, natural convection, Soret and Dufour effects, sinusoidal surface temperature and concentration 1. Introduction Coupled heat and mass transfer finds applications in a variety of engineering applications, such as the migration of moisture through the air contained in fibrous insulation, grain storage installations, filtration, and chemical catalytic reactors, and in processes such as spreading of chemical pollutants in plants and diffusion of medicine in blood veins. Free convection flow of an incompress- ible viscous fluid past an infinite or semi-infinite vertical plate has been studied so long because of its technological importance. Many studies that considered combined heat and mass transfer in natural convection boundary-layer flows over heated surfaces with various geometries can be found in the monograph by Gebhart el al. [1]. Callahan and Marner [2] solved the problem of transient free © 2012 Wiley Periodicals, Inc. Heat Transfer—Asian Research, 42 (2), 2013 100