Stability of Thermovibrational Convection of a Pseudoplastic Fluid in a Plane Vertical Layer
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Based on the thermovibrational convection equations, we have investigated the structure of the averaged plane-parallel convective flow in a plane vertical layer of Williamson fluid executing high-frequency linearly polarized vibrations along the layer. We show that as the vibrations are intensified, the nonlinear viscous properties of a pseudoplastic fluid cease to affect the structure and intensity of its main flow, and it becomes similar to a flow of ordinary Newtonian fluid. The linear problem of stability of an averaged plane-parallel flow of pseudoplastic Williamson fluid has been formulated and solved for the case of longitudinal high-frequency linearly polarized vibrations for small periodic perturbations along the layer. Numerical calculations have shown that, as in a Newtonian fluid, the monotonic hydrodynamic perturbations are most dangerous at low Prandtl numbers. As the Prandtl number increases, the thermal instability modes begin to exert an undesirable effect. An enhancement of pseudoplastic fluid properties leads to destabilization of the main flow for both types of perturbations. Similarly to a Newtonian fluid, an additional vibrational instability mode to which small Grashof numbers correspond appears in the presence of vibrations. The influence of this vibrational mode on the stability of the main flow is determined by the vibration frequency and the temperature gradient. An intensification of the vibrations destabilizes the flow for all of the investigated instability modes. For a given set of rheological parameters of the Williamson model, there are critical values of the modified and vibrational Grashof numbers at which the averaged flow completely loses its stability with respect to the types of perturbations under consideration. Absolute destabilization of the main flow in a pseudoplastic fluid occurs at higher values of the vibrational Grashof number than those in a Newtonian fluid.
Key wordsnon-Newtonian fluid thermovibrational convection high-frequency vibrations stability vertical layer
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- 1.Gershuni, G.Z. and Zhukhovitskii, E.M., On two types of instability of convective motion between parallel vertical planes, Izv. Vyssh. Uchebn. Zaved., Ser. Fiz., 1958, no. 4, pp. 43–47.Google Scholar
- 4.Gershuni, G.Z., Zhukhovitskii, E.M., and Nepomnyashchy, A.A., Ustoichivost’ konvektivnykh techenii (Stability of Convective Flows), Moscow: Nauka, 1989.Google Scholar
- 13.Lyubimova, T.P., On steady solutions of the equations of convection of visco-plastic fluid heated from below with temperature-dependent rheological parameters, Izv. Akad. Nauk BSSR, Fiz.-Mat. Nauki, 1986, no. 1, pp. 91–96.Google Scholar
- 14.Perminov, A.V. and Shulepova, E.V., Influence of high-frequency vibrations on convective motion of non-newtonian fluid, Nauch.-Tekh. Vedom. SPbGPU, Fiz.-Mat. Nauki, 2011, vol. 3, no. 129, pp. 169–175.Google Scholar
- 18.Gershuni, G.Z. and Lyubimov, D.V., Thermal Vibrational Convection, New York: Wiley, 1998.Google Scholar
- 20.Sharifulin, A.N., Wave instability of free-convective motion in a vibration field, in Nestatsionarnye protsessy v zhidkostyakh i tverdykh telakh (Unsteady Processes in Liquids and Solids), Sverdlovsk: Ural. Nauch. Tsentr AN SSSR, 1983, pp. 58–62.Google Scholar
- 22.Tetel’min, V.V. and Yazev, V.A., Reologiya nefti (Oil Rheology), Moscow: Granitsa, 2009.Google Scholar
- 23.Lyubimov, D.V., Lyubimova, T.P., and Morozov, V.A., Software package for numerical investigation of linear stability of multi-dimensional flows, Bull. Perm Univ., Inform. Syst. Technol., 2001, no. 5, pp. 74–81.Google Scholar