Two-dimensional numerical computations were carried out in order to clarify the effect of magnetic field on paramagnetic and diamagnetic fluids in a vertical cylindrical container with thermal and vertical magnetic field gradients under both gravitational and nongravitational fields. In both gravitational and nongravitational fields, the magnetizing force that was produced by the gradient of magnetic field could be utilized to control the heat transfer rate for paramagnetic and diamagnetic fluids. These phenomena could be successfully explained by visualizing the field of magnetizing force.