The onset of double-diffusive convection in a nanofluid saturated porous layer: Cross-diffusion effects

The onset of double-diffusive convection in a horizontal porous layer saturated with a nanofluid with the Soret and Dufour effects is studied using both linear and nonlinear stability analyses in a three-dimensional way. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis, and the modified Darcy model is used for the porous medium that includes the time derivative term to describe the momentum transport. The thermal energy equation includes the diffusion and cross-diffusion terms. The linear theory depends on the normal mode technique, and the nonlinear analysis depends on the minimal representation of double Fourier series. The effects of the Soret and Dufour parameters, solutal Rayleigh number, viscosity ratio, and conductivity ratio on the stationary and oscillatory convections are presented graphically. It is found that for the stationary mode, the Soret and Dufour parameters, viscosity ratio, and thermal conductivity ratio have a stabilizing effect, while the solutal Rayleigh number destabilizes the system. For the oscillatory mode, the Soret and Dufour parameters, viscosity ratio, and Vadász number have a stabilizing effect, while the solutal Rayleigh number and the thermal conductivity ratio destabilize the system. We also study the effects of time on transient Nusselt number, which is found to be oscillatory when the time is small. However, when the time becomes very large, all three transient Nusselt number values approach the steady-state values.