We present a numberical study of the flow induced by a rotating magnetic field on a liquid metal which fills a cylindrical container. Using a low frequency approximation and assuming axisymmetry, a finite difference technique is employed for the calculation of the flow field. Two different cases are considered in order to show that using a rotating magnetic field requires a detailed knowledge of its interaction with the flow. In the first situation, which is isothermal, it is shown that increasing the field intensity leads to the occurrence of Taylor-Couette type centrifugal instabilities depending upon the aspect ratio of the cavity. In the second case, which includes a heat transfer problem, it is shown that applying a very moderate rotating field to an initially unstable thermally driven convection is able to restore the flow stability.
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