Thermal convection in a Brinkman porous medium saturated with couple-stress nanofluid: a Galerkin weighted residual approach for different conducting boundaries

Abstract

The thermal instability of a couple-stress nanofluid saturated by a porous media is studied in this article. For the porous medium, the Darcy–Brinkman model is used. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. Three cases of free-free, rigid-rigid and rigid-free boundaries are considered. For this problem, oscillatory convection is ruled out. By using the one-term Galerkin method and normal mode analysis, we solve the eigenvalue problem with Rayleigh number as an eigenvalue. The effects of Darcy number, couple-stress parameter, porosity parameter, modified diffusivity ratio, Lewis number and concentration Rayleigh number are examined analytically and graphically for stationary convection.