Three-dimensional (3D) heat flow, dopant segregation, and interface shape during crystal growth by a gradient freeze technique in a centrifuge are analyzed by a finite volume method. The basic flow patterns for a fixed geometry (with a concave interface) at different configurations agree well with the previous report (Friedrich et al., J. Crystal Growth 167 (1996) 45). However, the self-consistent analysis allows us for the first time to further investigate the role of the Coriolis force and centrifugal acceleration on the heat and mass transfer and the interface, simultaneously. Furthermore, the rotation speed found for the weakest convection, where the Coriolis force balances the gravitational and centrifugal farces, turns out to have larger radial segregation, despite having a larger effective segregation coefficient. Rotation about the growth axis is also investigated. For this configuration, it is found that both axial and radial segregation could be reduced under certain conditions.