Stability of thermovibrational convection of pseudoplastic fluid in plane vertical layer

Based on equations for thermal vibrational convection, the structure of the plane-parallel convective flow in a vertical layer of Williamson’s fluid is investigated. The layer is subjected to high frequency linear polarized vibrations directed along the layer. It is shown that with the growth of vibrations, the nonlinear-viscous properties of a pseudoplastic fluid stop producing the effect on the structure and intensity of its main flow, which becomes very similar to that of the Newtonian fluid. For the case of longitudinal high-frequency linear polarized vibrations, a linear stability problem is formulated and solved. This problem deals with the stability of the averaged plain parallel flow of the pseudoplastic Williamson’s fluid with respect to small periodic perturbations directed along the layer. Numerical calculations show that, as in the case of the Newtonian fluid, at small values of the Prandtl number the monotonic hydrodynamic perturbations are the most dangerous. With increasing Prandtl number, the oscillatory thermal perturbations become more dangerous. Strengthening of the pseudoplastic fluid properties leads to destabilization of the main flow relative to the both types of instabilities. The presence of vibrations, as in the case of the Newtonian fluid, causes the appearance of an additional vibration mode of instability and the relatively small values of the Graschof number corresponding to it. The influence of this vibration mode on the stability of the main flow is determined by the vibration frequency and the magnitude of a temperature gradient. Amplification of the vibration intensity leads to flow destabilization in all examined instability modes. For the given set of rheological parameters of Williamson’s fluid, there are critical values of the modified and vibration Graschof number, at which the averaged flow becomes absolutely unstable with respect to all types of the instabilities. The absolute destabilization of the main flow occurs at higher values of the vibration Graschof number compared to that for the Newtonian fluid.