Magnetic Field Effect on Multiplicity of Solutions Induced by Thermosolutal Convection in a Bénard Square Porous Cavity Submitted to Horizontal Concentration Gradient

In this work, we present a numerical study of the magnetic field effect on double diffusive natural convection in a square porous cavity saturated with an electrically conducting binary mixture. The cavity is heated from below and cooled from the top, while its vertical walls are adiabatic and maintained at constant but different concentrations. The numerical results are obtained for a Lewis number Le = 10 and the following ranges for the other controlling parameters: 40 ≤ RT ≤ 1000, -0.2 ≤ N ≤ 0.2 and -0.5 ≤ Ha ≤ 0.5, where RT, N and Ha are the thermal Rayleigh number, the buoyancy ratio and the Hartmann parameter, respectively. First, the effect of the Hartmann parameter on the maintenance and disappearance of the multiple steady state solutions obtained in the case of purely thermal convection is examined. Then, the combined effect of N and Ha on the existence of these steady solutions is analyzed. It is found that the critical values of N corresponding to the transitions between the different solutions are modified by the application of a magnetic field. However, the nature of the transitions is unchanged. It is shown that the magnetic field may affect considerably the flow intensity and the heat and mass transfer in the medium.