Bi-stability Bifurcation in Convection Double Diffusion Through a Shallow Horizontal Layer Saturated with a Complex Fluid

Abstract

The onset of non-linear convection in a porous layer saturated by a shear-thinning liquid is studied. The Carreau-Yasuda model is utilized for modeling the behavior of the working medium. Constant fluxes of heat and mass are defined on the horizontal surfaces of the cavity, while the vertical sides are assumed adiabatic. The parallel flow approximation and the finite difference approach are used to conduct the investigation analytically and numerically, respectively. The linear stability inspection of the convective and diffusive circumstances is carried out by taking into account an infinitesimal perturbation. The theory of linear stability is employed to determine the critical Rayleigh number for the motion from the rest state, Hopf bifurcation, and the transition from the stationary to oscillatory convection. Overall, the Carreau-Yasuda rheological parameters have a significant impact on the thresholds of convection. The most interesting findings of this study is highlighting the existence of a bi-stability phenomenon, i.e., the existence of two steady-state solutions, which was not observed before in non-Newtonian fluids convection.