Thermo-Convective Flow of a Yield-Stress Fluid Between Two Horizontal Plates for Rayleigh Numbers Greater Than the Critical Value

Abstract

In this paper, two-dimensional unsteady simulations of yield-stress fluids in the Poiseuille–Rayleigh–Bénard flow between two horizontal plates were performed. The laminar flow of these fluids is characterized by the existence of high- and low-viscous zones. The thermal and hydrodynamic behaviors were studied in the case where the convective instability was developed, and the high-viscous zones were minimized. The commercial computational fluid dynamics (CFD) package fluent was adopted to perform the different simulations. The average Nusselt number over time of the two plates was chosen to characterize the thermal transport, while the average of the maximum vertical velocity component over time in the horizontal mid-plane described the hydrodynamics of the flow. It was found that the fluid behaved according to a range of viscosities with the same order of magnitude as the plastic viscosity. The effect of the dimensionless numbers on the flow showed that the yield-stress fluid could mimic a Newtonian behavior in the pre-described conditions. Although, the fluid still held the non-Newtonian character distinguished by the dependency on the Bingham number Bn. This returned to the increase of the apparent viscosity with Bn which contributed to the weakening of the convective streams, and consequently, reduced convective thermal transport.