Using a magnetic field to reduce natural convection in a vertical cylindrical annulus

This paper presents the investigation of laminar natural convection in 3D vertical cylindrical annulus containing electrically conductive fluids under a horizontal magnetic field. The model was composed of two isothermal coaxial cylinders. Both ends of the cylinders were supposed adiabatic and all walls were assumed electrically insulated. Complex nonlinear governing equations were solved numerically by means of the finite volume method. The effects of different parameters such as the strength of the magnetic field, the radii ratio, aspect ratio, and Prandtl number on the temperature distribution, average Nusselt number, distribution of Lorentz forces as well as induced electric field were investigated. Results showed that for aspect ratios lower than about 1, the average Nusselt number increased as aspect ratio was increased. When aspect ratio was greater than about 1, the average Nusselt number decreases as aspect ratio was enlarged. Moreover, results showed that the average Nusselt number increased as radii ratio was increased. Results also revealed that a stronger magnetic field was needed to achieve pure conduction in the case of thick annulus. The presence of magnetic field induced an electric field which affected the Lorentz force. Distributions of Lorentz force and induced electric field indicated respectively the formation of Hartmann and Roberts layers. Furthermore, the average Nusselt number increased with increasing Prandtl number at all Hartmann numbers. It was also found that with increasing Hartmann number, the effect of Prandtl number on the average Nusselt number decreased. (C) 2017 Elsevier Masson SAS. All rights reserved.