Thermosolutal Marangoni boundary layer magnetohydrodynamic flow with the Soret and Dufour effects past a vertical flat plate

A numerical study of laminar magnetohydrodynamic thermosolutal Marangoni convection along a vertical surface in the presence of the Soret and Dufour effects has been performed. The diffusion-thermo implies that the heat transfer is induced by concentration gradient, and thermo-diffusion implies that the mass diffusion is induced by thermal gradient. In conformity to actuality, it is assumed that the surface tension varies linearly with both the temperature and concentration and that both interface temperature and concentration are quadratic functions of the interface arc length x. The general governing partial differential equations are converted into nonlinear ordinary differential equations using unique similarity transformations. The aim of this study is to investigate the effects of Hartmann number (0 ≤ M ≤ 5), thermosolutal surface tension ratio (0 ≤ R ≤ 5), Soret parameter (0.1 ≤ Sr ≤ 2), Dufour parameter (0.03 ≤ Du ≤ 0.6), Prandtl number (0.72 ≤ Pr ≤ 10) and Schmidt number (0.3 ≤ Sc ≤ 3) on the fluid velocity heat and mass transfer. It is found that, both of temperature and concentration gradient at the wall increases as the thermosolutal surface tension ratio increases. Also, the increase in Prandtl number results in an enhancement in the heat transfer at the wall.