Thermal instability of a horizontal nanofluid layer in a porous medium with high porosity

The stability analysis of a porous medium layer saturated by a nanofluid was pioneered by Nield and Kuznetsov (Thermal instability in a porous medium layer saturated by a nanofluid, Int. J. Heat Mass Transfer, 2009; 52:5796-5801), which substantially raises interest in the research of nanofluids due to its fundamental importance in the understanding of the mechanisms behind the heat transfer enhancement. Their study commenced with the Rayleigh-Benard problem by employing the Buongiorno model for nanofluids and the Darcy and/or the Brinkman models for porous media. However, the thermophoretic diffusion coefficients were considered to be constant in the calculation of the diffusive mass flux of nanoparticles, which may lead to a negative particle concentration occurring at the lower boundary before the onset of convection. This paper tries to revise the analysis (using the Brinkman model) by considering the dependence of thermophoretic diffusion coefficient on the volume fraction of nanoparticles. Following regular mathematical manipulation, we obtain a nonlinear basic-state concentration that can eliminate the potential contradiction occurring in previous analyses. Comparison is made to reveal the difference between the present result and previous analyses. The present results show that the stability threshold is shifted to a lower value and the system is unconditionally unstable for a common nanofluid. To gain a deeper insight into the instability characteristics, the dispersion diagrams of growing disturbances are depicted for various parameters conditions. A series of accurate numerical results is provided to benefit the research on the field of nanofluids.

Automated summary

This paper analyzes the stability of a porous medium layer saturated by a nanofluid and proposes a revision to previous analyses by considering the dependence of thermophoretic diffusion coefficient on the volume fraction of nanoparticles. The results show a shift in the stability threshold and the system is unconditionally unstable for a common nanofluid. The dispersion diagrams of growing disturbances are provided to gain deeper insights into the instability characteristics.