Magneto hydrodynamics stability of swirling flows with heat transfer in a cylindrical container

Abstract

Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.

In the present work, a study of the mixed convection flow of low Prandtl number fluid ( Pr = 0.015) confined in a cylindrical container having an aspect ratio equal to 2 , with and without magnetic fields, has been considered. The finite volumes method has been used to resolve the equations of continuity, momentum (or Navier-Stokes), energy and electric potential. In the absence of magnetic field, the numerical results obtained show the appearance of oscillatory instabilities for the values of the critical Reynolds number Recr = 2575, 924, 802 and 606, corresponding respectively to the values of the Richardson number Ri = 0 , 0.5, 1.0 and 2.0. However, in the presence of the vertical magnetic field, the fluid continues its stable flow until the values of Reynolds number greater than those predictable to have oscillatory instabilities. Stability diagrams have been established according to the numerical results of this investigation. These diagrams put in evidence the dependence of the critical Reynolds number and critical frequency of oscillations with the increase of the Hartmann number for various values of the Richardson number. In conclusion, the stabilizing technique of the mixed convection flows of fluids having low Prandtl number (semiconductors) by the application of an external magnetic field is practically reliable.