Hydromagnetic Instabilities in a Nonuniformly Rotating Layer of an Electrically Conducting Nanofluid

The stability of magnetized flows of a nonuniformly rotating layer of an electrically conducting nanofluid is investigated with regard to the effects of Brownian diffusion and thermophoresis. In the absence of a temperature gradient, new types of magnetorotational instability (MRI) are considered in axial, azimuthal, and helical magnetic fields in thin layers of a nanofluid. The increments and development regions of these instabilities are obtained depending on the angular velocity profile (Rossby number Ro) and the radial wavenumber k. In the presence of temperature and nanoparticle concentration gradients, stationary regimes of nonuniformly rotating convection in axial and helical magnetic fields are studied. Expressions are obtained for the critical Rayleigh numbers Ra-st, and neutral stability curves are plotted depending on the angular velocity profile, the profile of the external azimuthal magnetic field (the magnetic Rossby number Rb), and the radial wavenumber k. Conditions for stabilization and destabilization of stationary convection in axial and helical magnetic fields are found.