Influence of Magnetic Field on Fingering Instability in a Porous Medium with Cross-Diffusion Effect: a Thermal Non-equilibrium Approach

The purpose of this paper is to investigate the thermal instability problem under the influence of three diffusing components on fluid saturated horizontal porous media under local thermal non-equilibrium effect. These three components are vertical magnetic field, solute and heat. We considered an electrically conducting two components fluid and anisotropic porous medium. The physical system is heated and salted from above. Flow in the porous medium is characterized by Darcy model, whereas the fluid and solid phases are not in local thermodynamic equilibrium (LTNE). Linear stability analysis is used to calculate critical Darcy-Rayleigh number and corresponding wave number for onset of stationary convection. The study is based on mainly four controlling parameters, Darcy-Chandrasekhar number (Q), dimensionless inter-phase heat transfer coefficient (H), Soret (Sr) and Dufour (Du) cross-diffusion parameters, among several. We illustrated the effects of these parameters on thermal instability and found parameters may have stabilizing or destabilizing effects, thus may advance or delay the onset of convection. Various comparative studies are also presented between different cases and conditions, such as for anisotropic and isotropic cases, cross-diffusion and without cross-diffusion cases and for different values of Sr and Du.