A numerical simulation study on fluid velocity field in melt was reported in this paper by using Finite Differential Method (FDM) during the growth of Nd:YAG crystals by Cz (Czochralski) method. First

the mathematical model of Nd:YAG crystal growth was given out. The momentum conservation equation of melt

the continuity equation of melt

the heat conservation equation of melt

the mass conservation of melt

the heat conservation equation of crystal and the heat conservation equation of crucible were included in the model. Then

the dimensionless equations were given for solving the equations by the numerical method. Finally

the boundary conditions were given and the equations were solved by FDM. The simulation program was given by above method and then the changes of fluid velocity field in melt were described by simulation program. The effects of processing conditions on fluid velocity field in melt were analyzed. The effects of simulation time

the effects of crystal rotation speed during the crystal growth

the effects of the crystal diameter and the effects of the crucible size were considered. The results of simulation indicated: 1. The forced convection in the melt is weaker than the natural convection during the process of simulation

so that it can’t be shown in the figure of fluid velocity field

and the forced convection will become weaker and weaker with the simulation time increased. 2. As the rotation speed of crystal is increased

the natural convection in the melt will become stronger and stronger

and the effective area of natural convection will become bigger than it is in initial cases. 3. The natural convection in the melt will become weaker when either the diameter of crystal or the ratio of the crucible diameter to its depth is increased. Although the above method is employed to simulate the fluid velocity field during the crystal growth of Nd:YAG

it can also be used to simulate some other single crystal growth by Cz method

such as the growth of silicon single crystal

the GaAs single crystal and the GGG single crystal and so on. It is essential to adapt the parameters of the equations and the simulation program to the new materials.