In this paper, we present a three-dimensional numerical study of glass melt in a small scale circular crucible heated by two rod electrodes. Lorentz forces are imposed into the melt by applying an additional external magnetic field. The coupled non-linear conservation equations for mass, momentum, energy and electrical charge are solved with the commercial finite volume code FLUENT. We perform numerical parameter studies by varying the magnetic flux density and the electrode potential to verify the influence of the Lorentz force on the velocity and temperature distribution in the crucible. We observe that the Lorentz force leads to an overall increase of the kinetic energy. Especially below the electrodes, a region which is not affected by buoyancy, the Lorentz force increases the velocity significantly. If the Lorentz force is the dominating driving force the mean velocity is almost a linear function of the Lorentz force. For counteracting Lorentz force and buoyancy between the electrodes we find a discontinuous modification of the flow pattern during the transition from buoyancy dominated to a Lorentz force dominated flow regime and vice versa. Even more, we pass through a hysteresis and obtain two steady solutions for one set of parameters depending on the starting conditions. Furthermore, we identify regimes in which we have a significant improvement of the temperature homogenization. The results show that Lorentz forces provide a new way to influence thermally driven convection of molten glass and can lead to the improvement of mixing. (C) 2009 Elsevier Ltd. All rights reserved.