Hydromagnetic and Soret driving free convection in an inclined porous cavity saturated by a conducting binary mixture

Abstract

We consider the Soret convection in an inclined rectangular Darcy porous medium filled with an electrically conductive binary fluid. The long sidewalls of the porous cavity are subject to constant gradients of heat and submitted to a uniform and constant transversal magnetic field while its short sides are adiabatic and impermeable. An approximate analytical solution to the present problem, valid in the central part of the shallow cavity, is obtained on the basis of the parallel flow approximation and validated numerically using a finite-difference method. Results are presented in terms of streamlines, isotherms, iso-concentration lines, Nusselt and Sherwood numbers and separation of species for Hartmann number varying in the range [0, 20]. A good agreement is observed between the analytical predictions and numerical simulations.