Linear and nonlinear double-diffusive convection in a saturated anisotropic porous layer with Soret effect and internal heat source

Double-diffusive convection in an anisotropic porous layer heated and salted from below with an internal heat source and Soret effect is studied analytically using both linear and nonlinear stability analyses. The generalized Darcy model including the time derivative term is employed for the momentum equation. The critical Rayleigh number and wavenumber for stationary and oscillatory modes and frequency of oscillations are obtained analytically using linear theory. The effects of the anisotropy parameters, concentration Rayleigh number, internal heat source, Soret parameter, Vadasz number and Lewis number on the stationary, oscillatory, and heat and mass transfer are shown graphically. Heat and mass transfer have been obtained in terms of the Nusselt number and Sherwood number.