Research of heat transfer and magnetohydrodynamics in the flow of liquid between two coaxial cylinders

Background. Studies of viscous fluid flow between rotating cylinders (known as the Couette flow), both experimental and theoretical, are still relevant and are widely used in technical applications (heat exchangers, nuclear and chemical reactors, separators, astrophysics). This class of problems becomes more complicated when heat exchange takes place along with hydrodynamics. The complexity of such problems increases with a joint consideration of heat exchange and the flow of viscous conductive fluid between cylinders rotating with different angular velocities. Further research is needed to study and better understand such complex processes, which will serve to clarify the mathematical models of heat exchange and magnetohydrodynamics. The paper considers heat exchange and magnetohydrodynamics of fluid (for a given velocity field) between two rotating coaxial cylinders. The purpose of the work is to study the influence of angular velocities of cylinder rotation, Joule heat dissipation, internal heat sources/sinks, cylindrical layer thickness and magnetic Reynolds number on the temperature and magnetic induction fields of liquid in the cylindrical layer. Materials and methods. In dimensionless form, the problem of heat exchange and flow of electrically conductive liquid between two rotating cylinders is solved numerically in a cylindrical coordinate system. The control volume method (Patankar method) is used to solve the problem. Results. The influence of the velocity field, internal heat sources/sinks, Joule heat dissipation, cylindrical layer thickness on the temperature fields, radial and angular components of the magnetic induction of an electrically conducting liquid between two coaxial rotating cylinders is investigated. It is found that changing the direction of rotation of the cylinders leads to a change in the type of extremum of the angular component of magnetic induction. Reducing the magnetic Reynolds number increases the intensity of heat exchange in the liquid. Conclusions. The results obtained can be used both in the study of thermal and magnetohydrodynamics processes and in the design of power and chemical devices, separators, instruments and installations.