Double-diffusive convective transport in a nanofluid-saturated porous layer with cross diffusion and variation of viscosity and conductivity

Abstract

The onset of double-diffusive nanofluid convection in a fluid-saturated horizontal porous layer is studied with thermal conductivity and viscosity dependent on the nanoparticle volume fraction. The Darcy model has been used for the porous medium, while the nanofluid incorporates the effects of Brownian motion along with thermophoresis. The nanofluid is assumed to be diluted and this enables the porous medium to be treated as a weakly heterogeneous medium with variation in the vertical direction of conductivity and viscosity. In addition, the thermal energy equation includes regular diffusion and cross diffusion terms. The linear stability analysis is based on the normal mode technique, while for nonlinear analysis, minimal representation of the truncated Fourier series representation involving only two terms has been used. It is found that for the stationary mode the Soret parameter, Dufour parameter, viscosity ratio, and conductivity ratio have a stabilizing effect, while the solutal Rayleigh number destabilizes the system. For the oscillatory mode, the Soret parameter, Dufour parameter, and viscosity ratio have a stabilizing effect while the solutal Rayleigh number and conductivity ratio destabilize the system. For steady finite amplitude motions, the heat and mass transport decreases with an increase in the values of the Dufour parameter and solutal Rayleigh number. The Soret parameter enhances the solute concentration Nusselt number while it retards the thermal Nusselt number and concentration Nusselt number. The viscosity ratio and conductivity ratio enhances the heat and mass transports. We also study the effect of time on transient Nusselt numbers which is found to be oscillatory when time is small. However, when time becomes very large, all three transient Nusselt values approach a steady value. © 2013 Wiley Periodicals, Inc.