Computer simulation based on an efficient finite volume/Newton method is conducted to study the heat transfer, fluid flow. and interface shapes due to induction heating in a vertical zone melting (VZM) processing. Different heating configurations and convection modes are considered for the zone melting of GaAs in an ampule. It is found that the electromagnetic stirring that is dominant in the melt zone leads to a severe deformation of the interface shapes. With the same applied coil current, the coil shape does not affect much the zone shape and convection. With the increasing current frequency, the skin depth of the induced eddy current decreases, leading to a weaker convection and less concave interfaces, and the power consumption decreases as well. The calculated results for the skin depth and the power deposition are consistent with the scaling law obtained by a simple model. Also, the control of a propel zone shape by modifying the thermal environment and ampule material is discussed.