Influence of the Hall current on the convective and magnetorotational instability in a thin layer of an electrically conductive nanofluid

Abstract

This study investigates the combined influence of the Hall current and the axial magnetic field on the criterion for the onset of convection in a nonuniformly rotating layer of electrically conductive nanofluids taking into account the effects of Brownian diffusion and thermophoresis. The analytical and numerical computations are presented for water-based nanofluids with alumina nanoparticles. In the absence of a temperature gradient, a new type of magnetorotational instability in an axial magnetic field in a thin layer of a nanofluid is considered. The growth rate and regions of development of this instability are numerically obtained depending on the angular velocity profile (the Rossby number Ro) and the radial wavenumber k. In the presence of temperature and nanoparticle concentration gradients, the stationary regime of nonuniformly rotating magnetoconvection is studied. The exact analytical expression for critical Rayleigh number Rast is obtained in terms of various nondimensional parameters. The results indicate that the increase in the Lewis number, the modified diffusivity ratio, and the concentration Rayleigh number is to accelerate the onset of convection. The increase in the Hall current parameter can delay or enhance the onset of convective instability. Rotation profiles with negative Rossby numbers lower the threshold for the development of thermal instability and stimulate the onset of convection. The conditions for stabilization and destabilization of stationary convection in an axial magnetic field are determined. The results are represented graphically and verified numerically.