A mathematical model describing the axisymmetric thermocapillary convection in three immiscible coaxial liquid columns held between two planar faces with individual constant temperature is proposed in the present paper. An approximate analytical solution is obtained by asymptotical way. The expected control of the thermocapillary convection can be realized by choosing reasonable matching parameters.

Numerical simulation of flow and heat transfer for a 3 in. (0.075m) diameter liquid encapsulant full float zone (LEFZ) growth of single-crystal GaAs was conducted using the finite-element method. Convective and conductive heat transfers, radiative heat transfer between diffuse surfaces and the Navier–Stokes equations for both melt and encapsulant as well as the interface position are all combined and solved simultaneously. The effect of the thickness of encapsulant, rotation rate of crystal and feed rod on the flow and heat transfer as well as on the growing and melting interface shape were investigated.

In order to understand the basic characteristics of the gas-phase mass-transfer coefficient (kg) in a small silicon Czochralski (Cz) furnace, a very crude model was proposed and the results were correlated by the Sherwood number as a function of Reynolds number. It was confirmed that by installing a gas guide in the hot zone, the mass transfer coefficient was significantly enhanced. A set of global analyses of small Cz furnaces was conducted with different values of diffusivity of SiO in the gas phase (DSiO) and of oxygen in the melt phase (DO) in order to elucidate which rate process controls the average oxygen concentration ([O]ave) in the grown crystal. These simulations revealed that in these small Cz furnaces, [O]ave is dependent on the gas phase mass transfer rate and melt flow patterns. A decrease in DSiO causes an increase in [O]ave. An increase in DO tends to increase [O]ave slightly in most cases.

A set of numerical simulation of the effect of the gas shearing flow over a silicon melt free surface on Marangoni convection under microgravity condition was conducted by using finite element method. For given gas channel width, Marangoni number and aspect ratio a remarkable reduction of Marangoni convection in silicon liquid bridge can be achieved by choosing the optimal gas velocity in accordance with the correlation proposed in the paper. The effectiveness of the reduction of the gas flow under different conditions shows that, in some cases, Marangoni convection reduction of 99% can be realized by this non-contaminating method.

采用有限元法对LEC法生长的3英寸GaAs单晶中的热应力进行求解。假设晶体为轴对称的各向同性线弹性体。主要讨论了不同液封厚度、轴向磁场强度以及晶体转速下的流动和传热所对应的晶体中的热应力分布，同时也考察了界面形状对应力的影响。