Stability of quasi-equilibrium states and supercritical regimes of thermal vibrational convection of a Williamson fluid in zero gravity conditions

Abstract

Abstract In this paper we investigate a linear stability of quasi-equilibrium states and supercritical regimes of thermal vibrational convection of a Williamson fluid between two rigid parallel plates, maintained at constant different temperatures in zero gravity conditions. Calculations are made for different angles of inclination of the vibration axis relative to the layer. It has been found that, as in the case of a Newtonian fluid, most dangerous are the hydrodynamic monotonic perturbations. Enhancement of viscoplastic properties of a fluid has a destabilizing effect at all angles of inclination of the vibration axis. An increase in the Prandtl number stabilizes the quasi-equilibrium states of the pseudoplastic fluids. In the viscoplastic limit, the critical value of the modified Rayleigh number, which determines the quasi-equilibrium stability threshold, does not depend on the Prandtl number and rheological parameters. The critical value of the perturbation wave number for pseudo- and viscoplastic fluids depends only on the angle of inclination of the vibration axis. The type of the convection excitation and the structure of the supercritical convective flows under longitudinal vibrations have been studied on the basis of full nonlinear equations of thermal vibrational convection. It has been found that the supercritical bifurcation takes place.