Inflection of flow transition curves by magnetic effect in annulus and consequential bifurcation map in wide ranges of Rayleigh and Hartmann numbers

Abstract

In this study, the bifurcation phenomenon of natural convection at a Prandtl number of 0.3 is analyzed for a circular magnetic field applied to an annulus of a diameter ratio of 2. Flows in the annulus have been categorized as upward and downward flows according to the flow patterns observed near the upper stagnation region of the annulus. In previous studies on the bifurcation of natural convection without magnetic effects, no bifurcation was observed at very low (<7000) or high (>45,000) Rayleigh conditions. However, the results presented here indicate the bifurcation can occur even at high Rayleigh conditions (>45,000) under specific magnetic conditions. A bifurcation map was thus created over a range of Hartmann numbers from 0 to 20 and Rayleigh numbers from 3000 to 80,000 and the inflection of the transition lines was studied. As a result, the transition Rayleigh and Hartmann numbers and the critical Rayleigh and Hartmann numbers were redefined.