Abstract
Double-diffusive convection in a horizontal layer of nanofluid in a porous medium is studied. The couple-stress fluid model is considered to describe the rheological behavior of the nanofluid and for porous medium Darcy model is employed. The model applied for couple stress nanofluid incorporates the effect of Brownian motion and thermophoresis. We have assumed that the nanoparticle concentration flux is zero on the boundaries which neutralizes the possibility of oscillatory convection and only stationary convection occurs. The dispersion relation describing the effect of various parameters is derived by applying perturbation theory, normal mode analysis method and linear stability theory. The impact of various physical parameters, like the couple stress parameter, medium porosity, solutal Rayleigh Number, thermo-nanofluid Lewis number, thermo-solutal Lewis number, Soret parameter and Dufour parameter have been examined on the stationary convection. It is observed that the couple stress parameter, thermo-nanofluid Lewis number, thermo-solutal Lewis number, Soret parameter and Dufour parameter have stabilizing effects on the stationary convection whereas the solutal Rayleigh number and Dufour parameter have very small effect on the system.
Highlights
The onset of double-diffusive convection in nanofluid finds applications in the fields of chemical science, food processing, engineering and nuclear industries, geophysics, bioengineering and cancer therapy, movement of biological fluid, oceanography [1,2,3,4,5,6,7,8,9]
Keeping in view of various applications of couple stress and nanofluid as mentioned above, our main aim in the present paper is to study the effect of cross-diffusion and couple stress parameter on the onset of convection in a horizontal layer of nanofluid saturating a porous medium
Equation (32) is the dispersion relation representing the effect of couple-stress parameter, medium porosity, thermosolutal Lewis number, thermo-nanofluid Lewis number, solutal Rayleigh Number, nanoparticle Rayleigh number, kinematic modified diffusivity ratio, Soret and Dufour parameteron double-diffusive convection in a layer of couple stress nanofluid saturating a porous medium
Summary
The onset of double-diffusive convection in nanofluid finds applications in the fields of chemical science, food processing, engineering and nuclear industries, geophysics, bioengineering and cancer therapy, movement of biological fluid, oceanography [1,2,3,4,5,6,7,8,9]. Keeping in view of various applications of couple stress and nanofluid as mentioned above, our main aim in the present paper is to study the effect of cross-diffusion and couple stress parameter on the onset of convection in a horizontal layer of nanofluid saturating a porous medium. This problem is of triple-diffusion type as it contains heat, the nanoparticles and the solute. ∇T .∇T ρ cDTC ∇ 2C , where c, cp , k and DTC be the fluid specific (at constant pressure), the heat capacity of the material constituting nanoparticles, the thermal conductivity of the porous medium and the diffusivity of Dufour type, respectively. Substituting Eq (24) into Eqs. (23) and (19)-(22), we obtain the following eigenvalue problem
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