On the stability of Rayleigh Bénard-convection in a porous medium saturated by a nanofluid

In this article, we investigate the problem of stability in a nanofluid saturated horizontal porous layer heated from below. The porous layer is assumed to be sparsely packed to allow the use of the Darcy–Brinkman model in the equation of conservation of linear momentum. We employ a Boussinesq approximation that includes the density of nanoparticles in the base fluid and retain the nonlinear term neglected in most of the recent studies under the assumption of a dilute nanoparticle concentration. The thermophoresis and Brownian motion effects of nanoparticles are included in the concentration equation. The analysis is performed using the energy method for both bottom- and top-heavy suspension of nanoparticles. In the case of a top-heavy arrangement, the energy analysis yields the bounds that coincide with linear stability bounds. The case of a bottom-heavy arrangement has a region in which subcritical instabilities may exist.