A simplified model for the so-called ACRT(accelerated crucible rotation technique) Bridgman crystal growth was considered in order to investigate the principal effects of the periodic variation of angular velocity. Numerical solutions were obtained for Ro=0.5, Ra=4.236*10$_{6}$ and E=2.176*10$^{-3}$ . The effects of spin-up process combined with natural convection was investigated as a preliminary study. The spin-up time scale for the present problem was a little larger than that observed for homogeneous spin-up problems. Numerical results reveal that over a time scale of (H$^{2}$/.nu..omega.$_{f}$)$^{1}$2/ the forced convection due to the formation of Ekman layer predominates. When the state of rigid body rotation is attained, natural convection due to buoyancy emerges as the main driving force and them the steady-state is approached asymptotically. Based on our preliminary results with simple spin-up, several fundamental features associated with variation of rotation speed are successfully identified. When a periodic variation of angular velocity was imposed, the system response was also periodic. Due to effect of mixing, the heat transfer was enlarged. From the analysis of time-averaged Nusselt number along the bottom surface the effect of a periodic variation of angular velocity on the interface location could be indirectly identified.d.