This paper presents numerical solutions for the steady, axisymmetric melt motions in a simplified model of the floating-zone process with a needle-eye induction coil. With only buoyant and thermocapillary convections, there are two meridional circulations, and the stronger, outer circulation involves an undesirable radially inward flow near the crystal-melt interface. Adding crystal rotation alone can only decrease the magnitudes of the meridional circulations. Adding a rotating magnetic field alone has the undesirable effect of increasing the magnitude and extent of the radially inward flow near the crystal-melt interface. Combining a rotating magnetic field in one azimuthal direction with crystal rotation in the opposite azimuthal direction overwhelms the buoyant and thermocapillary convections and produces the desired radially outward flow over the entire crystal-melt interface. The magnitude of this radially outward flow is easily controlled by changing either the angular velocity of the crystal rotation or the strength of the rotating magnetic field.