An analytical study of linear and nonlinear double diffusive convection in a fluid saturated anisotropic porous layer with Soret effect

The double diffusive convection in a horizontal anisotropic porous layer saturated with a Boussinesq fluid, which is heated and salted from below in the presence of Soret coefficient is studied analytically using both linear and nonlinear stability analyses. The normal mode technique is used in the linear stability analysis while a weak nonlinear analysis based on a minimal representation of double Fourier series method is used in the nonlinear analysis. The generalized Darcy model including the time derivative term is employed for the momentum equation. The critical Rayleigh number, wavenumber for stationary and oscillatory modes and frequency of oscillations are obtained analytically using linear theory. The effect of anisotropy parameters, solute Rayleigh number, Soret parameter and Lewis number on the stationary, oscillatory, finite amplitude convection and heat and mass transfer are shown graphically.