Effect of an Inclined Magnetic Field on Soret-Dufour Driven Double-Diffusive Convection in a Horizontal Binary Mixture Destabilized by Uniform Heat and Mass from Below

Abstract

This paper is dedicated to deal with thermosolutal natural convection within an enclosure submitted to destabilizing heat and mass fluxes and confining an electrically conducting binary mixture. The cavity is bathed in an external magnetic field and Soret and Dufour effects are considered. An approximate analytical solution is derived, valid in the limit of a shallow enclosure and confirmed numerically by using a finite difference method. The results show the existence of six regions in \(\left( {{\text{Du}}{\kern 1pt} --{\kern 1pt} {\text{Sr}}} \right)\) plane describing different flow behaviours. The critical Hartman number and critical inclination of magnetic field, which lead to the suppression of convective flows are calculated analytically vs. the control parameters. The obtained results illustrate a significant impact of the combined effects of the inclined magnetic field (via its intensity and inclination) and the Soret and Dufour parameters on different thresholds of convection and the resulting heat and mass transfer. Moreover, the increase in the inclination of the magnetic field in the range \({{0 < \theta < \frac{\pi }{2}} \mathord{\left/ {\vphantom {{0 < \theta < \frac{\pi }{2}} {\left( {\frac{\pi }{2} < \theta < \pi } \right)}}} \right. \kern-0em} {\left( {\frac{\pi }{2} < \theta < \pi } \right)}}\) has a stabilizing/(destabilizing) effect with respect to stationary and sub-critical convections, regardless of the Hartmann number.