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。

To understand the characteristics of the Czochralski (Cz) furnace for the single-crystal growth of silicon, a set of global analyses of momentum, heat and mass transfer in small Cz furnaces (crucible diameter: 7.2cm, crystal diameter: 3.5cm, operated in a 10 Torr argon flow environment) is carried out using the finite-element method. The global analysis assumes a pseudosteady axisymmetric state with laminar flow, equilibrium relations at the melt/silica interface and vapor-liquid chemical equilibrium at the melt/gas interface, as well as the segregation coefficient of unity at the melt/crystal interface. Convective and conductive heat transfers, radiative heat transfer between diffuse surfaces and the Navier-Stokes equations for gas and melt phases are all combined and solved together. Thus, the velocities and temperatures obtained are used to calculate the oxygen concentrations. The global analysis code is effectively used to discuss the influences of the Marangoni effect and a gas guide (or a heat shield) placed between the crucible and the crystal. The results indicate that the gas guide reduces the heater power and changes the melt flow pattern and oxygen transport. The melt flow pattern is strongly dependent on the Marangoni effect and gas flow near the surface, and changes the oxygen concentration significantly. This analysis reveals the importance and effectiveness of global analysis.

Linear stability theory is used to analyze the stability of the basic state solution of Marangoni convection in a liquid bridge with liquid encapsulation. By processing the linear disturbance equations numerically, stability analysis can be evolved to a complex general eigenvalue problem. Inverse iteration algorithm combined with LZ algorithm is employed to solve the complex generalized eigenvalue problem. The results show that the stability of the system can be enhanced greatly by choosing reasonable matching parameters of the two fluid layers. The preferred mode of instability is axial wave number α=2, 3 and 4, which means that the system is more sensitive to the disturbance with larger wave lengths.

The present paper is devoted to the investigation of the effect of liquid encapsulation on the Marangoni convection in its inner columnar liquid layer under a microgravity condition. The asymptotic solution of the mathematic model established in the paper was obtained for the immiscible axisymmetric coaxial liquid columns contained between planar faces. Numerical simulation based on the asymptotic solution was carried out. The main influence factors on the process were discussed in detail. It is found that proper selection of the related parameters will result in a remarkable reduction of the Marangoni convective flow. Copyright.

A mathematical model describing the thermocapillary convection in two immiscible coaxial liquid columns is proposed. An approximate analytical solution is obtained by asymptotical way. The results of numerical simulation show that effective reduction of ther-mocapillary convection in the inner liquid layer can be reached by properly selecting the encapsulation which has a reasonable match relation with the encapsulated fluid.

A set of numerical analyses for momentum and heat transfer for a 3 in. (0.075m) diameter Liquid Encapsulant Czochralski (LEC) growth of single-crystal GaAs with or without an axial magnetic field was carried out using the finite-element method. The analyses assume a pseudosteady axisymmetric state with laminar flows. Convective and conductive heat transfers, radiative heat transfer between diffuse surfaces and the Navier-Stokes equations for both melt and encapsulant and electric current stream function equations for melt and crystal are considered together and solved simultaneously. The effect of the thickness of encapsulant, the imposed magnetic field strength as well as the rotation rate of crystal and crucible on the flow and heat transfer were investigated.