A Revised Work on the Rayleigh-Bénard Instability of Nanofluid in a Porous Medium Layer

Abstract

To reveal the mechanism of the enhanced heat transfer in nanofluids, Buongiorno (ASME J. Heat Transfer, vol. 128, 2006, pp. 240–250) developed a convective transport model by considering the slip mechanisms of nanoparticles migration. By now, many extended researches are based on his model. Among them, the study on porous medium flow pioneered by Nield & Kuznetsov (Int. J. Heat & Mass Transfer, vol. 52, 2009, pp.5796–5801) has received much attention. Their work employed the Darcy model and Buongiorno’s model to investigate the thermal instability in a horizontal porous medium layer saturated by a nanofluid. Through a sophisticated analysis, they obtained an approximate formula capable of predicting the stability threshold. However, a potential contradiction exists in their analysis owing to an improper assumption about the thermophoretic coefficient, which may lead to an unphysical result. To date, much of current works still adopted this improper assumption in various extended problems. To resolve this contradiction, the present study revises their work by considering the dependence of thermophoretic coefficient on the volume fraction of nanoparticles. A nonlinear basic-state solution of concentration is obtained and then used to implement the linear stability analysis. In comparison with Nield’s formula, the present result shows that the threshold of instability shifts to a lower concentration by more than one order of magnitude. The mechanism causing the shift is discussed and the novelty of the present study is stressed.