Rayleigh–Bénard Instability of an Ellis Fluid Saturated Porous Channel with an Isoflux Boundary

Abstract

The onset of the thermal instability is investigated in a porous channel with plane parallel boundaries saturated by a non–Newtonian shear–thinning fluid and subject to a horizontal throughflow. The Ellis model is adopted to describe the fluid rheology. Both horizontal boundaries are assumed to be impermeable. A uniform heat flux is supplied through the lower boundary, while the upper boundary is kept at a uniform temperature. Such an asymmetric setup of the thermal boundary conditions is analysed via a numerical solution of the linear stability eigenvalue problem. The linear stability analysis is developed for three–dimensional normal modes of perturbation showing that the transverse modes are the most unstable. The destabilising effect of the non–Newtonian shear–thinning character of the fluid is also demonstrated as compared to the behaviour displayed, for the same flow configuration, by a Newtonian fluid.

Exploration of rheological behavior of an Ellis fluid on the onset of thermosolutal porous convection

“…The threshold conditions for the instability were obtained both theoretically and numerically and found that the instability sets in as oscillatory convection. Brandão et al (2021) extended the work of Celli et al (2021) by assuming a uniform heat flux at the lower boundary and a uniform temperature at the upper boundary. As a result, the stability eigenvalue problem is solved numerically and the destabilising effect of the Ellis fluid rheology is demonstrated.…”