Linear and Nonlinear Double-Diffusive Convection in a Fluid-Saturated Porous Layer with Cross-Diffusion Effects

The double-diffusive convection in a horizontal fluid-saturated porous layer, which is heated and salted from below in the presence of Soret and Dufour effects, is studied analytically using both linear and nonlinear stability analyses. The linear analysis is based on the usual normal mode technique, while the nonlinear analysis is based on truncated representation of Fourier series. The generalized Darcy model that includes the time derivative 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 effects of solute Rayleigh number, Lewis number, normalized porosity parameter, Vadasz number, Soret and Dufour parameters on the stationary, oscillatory convection, and heat and mass transfers are shown graphically. The Vadasz number has dual effect on the threshold of the oscillatory convection. Some known results are recovered as special cases of the present problem.