Magneto-convection in an anisotropic porous layer with Soret effect

Thermal instability in an electrically conducting two component Boussinesq fluid-saturated-porous medium has been investigated, in the presence of Soret coefficient. The porous medium is confined between two horizontal surfaces, and subjected to a constant vertical magnetic field. Flow in the porous medium is characterized by generalized Darcy model, which includes the time derivative term. Performing linear and non-linear stability analysis, the effect of magnetic field on the stability of flow through porous medium has been investigated. The normal mode method is used in linear stability analysis, while a weak non-linear analysis based on a minimal representation of double Fourier series method is used in non-linear analysis. The critical Rayleigh number, wave number for stationary and oscillatory modes, and frequency of oscillations are obtained analytically using linear theory. Effects of various parameters on stationary, oscillatory and finite amplitude convection, rate of heat and mass transfer have been obtained analytically and presented graphically.