Abstract
In this work, a large-scale instability of the hydrodynamic -effect in an obliquely rotating stratified nanofluid taking into account the effects of Brownian diffusion and particle flux under the influence of a temperature gradient (thermophoresis) is obtained. The instability is caused by the action of an external small-scale non-spiral force, which excites small-scale velocity oscillations with zero helicity and a low Reynolds number. Nonlinear equations for large-scale motions are obtained using the method of multiscale asymptotic expansions by a small parameter (Reynolds number). A linear large-scale instability of hydrodynamic -effect is investigated depending on the parameters of rotation , temperature stratification , and concentration of nanoparticles . A new effect of the generation of large-scale vortex structures in nanofluid at is associated with an increase in the concentration of nanoparticles is obtained. The maximum instability increment is reached at inclination angles for the Prandtl numbers , and for the Prandtl numbers at inclination angles . It has been found that the frequency changing of the parametric impact will make it possible to control and track the generation of large-scale vortex structures. It is shown that circularly polarized Beltrami vortices appear in nanofluid as the result of new large-scale instability development. In this paper, the saturation regime of large-scale instability in an obliquely rotating stratified nanofluid with an external small-scale non-spiral force is investigated. In the stationary regime was obtained a dynamic system of equations for large-scale perturbations of the velocity field. Numerical solutions of this system of equations are obtained, which show the existence of localized vortex structures in the form of nonlinear Beltrami waves and kinks. The velocity profile of kink tends to be constant at large Z values.
Highlights
In recent years there has been considerable attention to the problem of transfer processes in nanofluids, which describe a two-phase system consisting of a carrier medium and nanoparticles with characteristic sizes from 1 to 100 nm [1]
In [2] it was shown that the temperature gradient and rotation have a stabilizing effect, while the volume fraction of nanoparticles and the ratio of nanoparticles density to the base fluid have a destabilizing effect on the system
Unlike preceding articles [2,3,4,5] in this paper we investigated the large-scale vortex structures (LSVS) formation mechanism in a rotating layer of stratified nanofluid under the influence of an external small-scale force
Summary
VORTEX DYNAMO IN AN OBLIQUELY ROTATING STRATIFIED NANOFLUID BY SMALL-SCALE NON-HELICAL FORCES. Special attention should be paid to the processes of formation and evolution of large-scale structures that affect heat transfer in nanofluids. It was shown there that a decrease in the gravity parameter has a stabilizing effect, while an increase in the gravity parameter has a destabilizing effect on the stationary convection In this case, the critical Rayleigh number increases with an increase of the Taylor number, which indicates the suppression of the onset of convection. Unlike preceding articles [2,3,4,5] in this paper we investigated the large-scale vortex structures (LSVS) formation mechanism in a rotating layer of stratified nanofluid under the influence of an external small-scale force. Of LSVS in a Newtonian rotating and temperature stratified fluid under the action of a small-scale force with zero helicity F0rotF0 = 0 was considered in [6]. The hydrodynamic equations of a viscous incompressible rotating nanofluid in the Boussinesq approximation has the following form (see for example [2,3,4]):
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