A series of three-dimensional numerical simulations was conducted to investigate the convection inside an electromagnetically levitated silicon droplet under vertical, horizontal and rotational magnetic fields, respectively. The results show that the flow is totally axisymmetric and two counter-circulating vortexes appear in the droplet with an inner-outer distribution under vertical magnetic fields. The inner vortex brings fluids from the top area to bottom area directly, which is potentially responsible for the requirement of quite strong vertical magnetic fields in the experimental measurement of thermal conductivity of molten silicon. With horizontal magnetic fields, the vortexes inside the droplet turn to an up-down distribution, which is more beneficial in the thermal conductivity measurement since it prevents the direct convective heat transfer effectively. However, the horizontal magnetic field fails to suppress the convection effectively and the flow is intense and spatially imbalanced, leading to a less stable flow state. The rotational magnetic field combines the advantages of the formers, suppresses the convection along z-axis apparently and creates an up-down distribution of vortexes simultaneously. It suggests that the rotational magnetic field shows potential interest in the measurement of thermal conductivity of melts. Besides, the rotational magnetic field would evoke forced convection in azimuthal direction, which can be better controlled by varying magnetic intensity and rotating frequency. The azimuthal flow is expected to balance the rotation of melts induced by helicity of coils in experiments and shows potential advantages in melt stirring and solidification from undercooled melts. (C) 2018 Elsevier Ltd. All rights reserved.