Numerical simulation of the Rayleigh-Benard convection under the influence of magnetic fields

Through performing numerical simulations, the three-dimensional thermally driven flows, namely the Rayleigh-Benard convection (RBC hereafter) flows, have been studied under the influence of magnetic field in the confined rectangular enclosure full of liquid metal. To validate our numerical methodologies, some of our numerical solutions are compared with the available experimental results that good agreements are found between them. Besides, the correlations between the Nusselt number (Nu hereafter) and the Rayleigh number (Ra hereafter) are also in accordance with the experimental results, whereas the Hartmann number (Ha hereafter) keeps constant. Nevertheless, in the present study, a new correlation law between Nu and varied Ha is established when Ra is fixed, this formula is more helpful when particularly considering the influence of the magnetic field. Regarding the horizontal magnetic field, it is found that the evolution of Nu versus magnetic intensity can be divided into three stages: when Ha is small, Nu increases with Ha because the three-dimensional RBC flow transits to transient-two dimensional pattern; when Ha is moderate, Nu increases with Ha because the transient-two dimensional flow is more stable that the dynamic motion of vortex cells is disappeared gradually; when Ha continues to increase, Nu still increases with Ha due to the growth in number of the convective cells. It should be noted that such transient process of the flow field can be hardly observed in the experiments, because the liquid metal is opaque, however, we are able to present the evolutions of the temperature fields as well as the flow structures with the help of numerical techniques.