An Integrated Model for Czochralski Melt Growth of Optical Crystals

2003 ◽  
Author(s):  
S. P. Song ◽  
B. Q. Li ◽  
K. G. Lynn
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Optical Thickness ◽  
Flow Profile ◽  
Interface Shape ◽  
Melt Flow ◽  
Melt Growth ◽  
Oxide Melt ◽  
Temperature Distributions ◽  
Optical Crystals

This article presents the phenomena of melt flow, heat transfer, and solidification in Czochralski (CZ) melt growth processes of optical crystals, with emphasis on the effect of internal radiative heat transfer on the temperature distributions in oxide melt and crystal, melt convection, and melt-crystal interface shape. An integrated numerical model has been developed for simulating the physical phenomena in generic CZ furnaces, which includes the models for electromagnetic induction in crucible, surface exchange radiation in furnace, internal radiation in semi-transparent oxide melt and crystal, Marangoni convection in the melt, and solidification. Each developed model compares well with available analytical solutions. Numerical simulations were carried out for the prediction of fluid flow and heat transfer in furnaces. The simulation results show that the variation in optical properties of melt and crystal strongly impact their temperature distributions. It also affects the melt flow profile and intensity. The interface shape becomes more deeply convex toward the melt, as the optical thickness of the melt increases. However, the optical thickness of the crystal exhibits a minor impact on the interface shape. The results also show that the natural convection is dominated in the melt and the Marangoni flow enforces the natural convection.

Studies on Heat Transfer From a Vertical Cylinder, With or Without Fins, Embedded in a Solid Phase Change Medium

1985 ◽  
Vol 107 (1) ◽  
pp. 44-51 ◽  
Author(s):  
B. Kalhori ◽  
S. Ramadhyani
Keyword(s):  
Heat Transfer ◽  
Experimental Investigation ◽  
Natural Convection ◽  
Solid Phase ◽  
Vertical Cylinder ◽  
Interface Shape ◽  
Fusion Temperature ◽  
Total Heat Transfer ◽  
Solid Liquid Interface ◽  
Solid Liquid

An experimental investigation of melting and cyclic melting and freezing around a vertical cylinder is reported. The studies encompass two cases: a plain vertical cylinder, and a vertical cylinder with fins. In the melting studies, the total heat transfer from the cylinder was measured as a function of time. In addition, measurements have been made of the solid-liquid interface shape after various melting times. In these studies, the solid phase was initially isothermal and either at its fusion temperature or subcooled below the fusion point. The experiments reveal the important influence of natural convection in the liquid phase in both unfinned and finned situations. Subcooling of the solid phase is observed to strongly inhibit heat transfer in the unfinned situation. In the experiment on cyclic melting and freezing, subcooling of the solid phase is once again found to have an important effect on the unfinned situation. Heat transfer from the finned cylinder is much less affected by solid-phase subcooling. All the experiments were performed with 99 percent pure n-eicosane paraffin.

Thermal Stress Analysis During the Czochralski Melt Growth of Optical Crystals

2005 ◽  
Author(s):  
F. Xu ◽  
B. Li
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Thermal Stress ◽  
Stress Analysis ◽  
Boundary Element ◽  
Gadolinium Gallium Garnet ◽  
Melt Growth ◽  
Optical Crystals ◽  
Element Method

This paper presents a finite element method for studying Czochralski melt growth of optical crystals with an emphasis on thermal and stress analyses of axisymmetric problems. A heat transfer analysis is performed to determine the temperature distribution in the crystal. The heat transfer problem is solved with a mixed computational model including the hybrid finite/boundary element for electromagnetism, the Galerkin finite element method for transport equations, the Galerkin boundary element method for external surface energy exchanges and the discontinuous finite element method for internal radiation. The temperature results are directly input as loads to determine the stresses caused by the temperature loading. Thermal stress analyses of a Gadolinium gallium garnet (Gd3Ga5O12) crystal are performed in the cases of the [100] pulling direction. Then, we can evaluate the crystal quality based on the thermal stress analysis. Three real operating cases for Gadolinium gallium garnet crystal growth processes are studied with the method presented in this paper.

scholarly journals NATURAL CONVECTION IN RECTANGULAR CAVITIES WITH DIFFERENT ASPECT RATIOS

2011 ◽  
Vol 10 (1-2) ◽  
pp. 44
Author(s):  
R. M. Nogueira ◽  
M. A. Martins ◽  
F. Ampessan
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Flow Behavior ◽  
Heated Wall ◽  
Flow Profile ◽  
Height Ratio ◽  
Dimensionless Variable ◽  
Aspect Ratios ◽  
Wide Range

Natural convection in closed cavities has been extensively studied in recent decades. This spontaneous method of heat transfer has a wide range of applications in engineering. In the present work, natural convection was numerically analyzed in a rectangular cavity heated on one of the sides and cooled on the opposite side. Temperatures of the heated wall and of the cooled wall were assumed to be constant. The objective of these studies was to determine the effects of the aspect ratio and the Rayleigh number on flow behavior and heat transfer in the cavity. In the simulations, the Rayleigh number drastically influenced the flow profile and heat transfer inside de cavity, as well as the thickness of the thermal boundary layer. It was also verified that the Nusselt number is strongly dependent on the L/D (Length/Height) ratio, and that this dimensionless variable increases with the increase of the W/L. The simulation of natural convection problems in the CFD Studio satisfactorily described the studied situations.

scholarly journals Heat Transfer Analysis of Viscous Incompressible Fluid by Combined Natural Convection and Radiation in an Open Cavity

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
M. Saleem ◽  
M. A. Hossain ◽  
Suvash C. Saha ◽  
Y. T. Gu
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Optical Thickness ◽  
Radiative Heat Transfer ◽  
Transfer Rate ◽  
Radiative Heat ◽  
Radiation Heat Transfer ◽  
Open Cavity ◽  
Heat Transfer Analysis

The effect of radiation on natural convection of Newtonian fluid contained in an open cavity is investigated in this study. The governing partial differential equations are solved numerically using the Alternate Direct Implicit method together with the Successive Overrelaxation method. The study is focused on studying the flow pattern and the convective and radiative heat transfer rates are studied for different values of radiation parameters, namely, the optical thickness of the fluid, scattering albedo, and the Planck number. It was found that, in the optically thin limit, an increase in the optical thickness of the fluid raises the temperature and radiation heat transfer of the fluid. However, a further increase in the optical thickness decreases the radiative heat transfer rate due to increase in the energy level of the fluid, which ultimately reduces the total heat transfer rate within the fluid.

A Novel Method for Melt Flow Control and Inclusion Suppression in Optical Crystal Growth

2007 ◽  
Author(s):  
Haisheng Fang ◽  
Lili Zheng ◽  
Hui Zhang ◽  
Yong Hong ◽  
Qun Deng
Keyword(s):  
Crystal Growth ◽  
Natural Convection ◽  
Flow Control ◽  
Melting Temperature ◽  
Constant Temperature ◽  
Czochralski Growth ◽  
Interface Shape ◽  
Melt Flow ◽  
Solidification Interface ◽  
Crystal Rotation

Optical and laser crystals grown by Czochralski technique from a solute-rich melt usually suffer defects of melt inclusion or bubble core, which severely affects optical, thermal and mechanical properties of the material. The main purpose of this paper is to study the inclusion mechanisms and to minimize such defects. Two types of mechanisms possibly responsible for inclusion defects are presented. In the current investigation, Czochralski grown optical single crystals are examined to recognize the effects of crystal rotation and natural convection on the melt flow pattern and solidification interface shape. It is established that increasing the rotation rate of crystal or reducing natural convection in the melt will cause the solid-liquid interface change from the convex shape to concave and high concentration of the species may be pushed away from the solidification interface. Simulations were performed to establish the relationships between Gr/Re2 and growth interface shape change, and between Gr/Re2 and stagnant point location were established. A disk submerged into the melt was used to reduce natural convection by reducing the melt height. The idea was similar to the submerged baffle or submerged heater used in Bridgeman crystal growth. The effect of submerged baffle on enhancement of crystal rotation effect was demonstrated. Simulation results showed that the melt flow near the solidification interface depended strongly on the baffle location, which was not surprised. The idea of submerged heater was also examined in Czochralski growth. Different from a constant temperature close to the melting temperature used in Bridgman growth, the submerged heater temperature should be selected on a higher temperature between the melting temperature and crucible temperature. The value depended strongly on the ratio between crystal and crucible diameters. It was proved that a constant temperature was not the best choice in Czochralski growth. In fact, an optimized temperature profile could be found in numerical simulations for melt flow control and inclusion suppression.

An experimental and analytical study of natural convection with appreciable thermal radiation effects

1972 ◽  
Vol 52 (1) ◽  
pp. 57-95 ◽  
Author(s):  
T. Audunson ◽  
B. Gebhart
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Natural Convection ◽  
Thermal Radiation ◽  
Convective Heat ◽  
Radiation Effects ◽  
Experimental Results ◽  
Fluid Medium ◽  
Temperature Distributions

An experimental and theoretical investigation has been carried out to determine the effect of thermal radiation on a natural convection boundary layer formed adjacent to a vertical flat surface with uniform heat flux input. In the experiment, the gases air, argon and ammonia were used as the fluid medium, thus permitting the observation of radiation effects in non-abosrbing and absorbing media. Experimental results were obtained for three different wall emittances at ambient pressures ranging from 2 to 8 atmospheres in air and argon and from 2 to 7 atmospheres in ammonia. An interferometer was used to measure the temperature distributions in the boundary layer and to evaluate the conductive (convective) heat flux from the surface into the fluid medium. The experimental temperature distributions and heat-transfer results obtained in ammonia gas are compared to the predictions of a perturbation analysis developed by the present writers. General agreement between theory and experiment is found. The presence of a radiating gas is seen to increase the convective heat transfer by as much as 40 % for the conditions of the present experiments. The results further indicate that the temperature distributions and wall-temperature gradients are strongly affected by both variations in the surface emittance and variations in gaseous emission and absorption. For non-absorbing gases, the experimental results are found to be in general agreement with existing theory. It is also shown that the experimental temperature distributions agree very well with theoretical predictions obtained by treating the convection and radiation processes as independent and superimposed.

scholarly journals Numerical analysis of PCM melting filling a rectangular cavity with horizontal partial fins

2020 ◽  
Vol 307 ◽  
pp. 01011
Author(s):  
Tarik Bouhal ◽  
Saïf ed-Dîn Fertahi ◽  
Oussama Limouri ◽  
Younes Agrouaz ◽  
Tarik Kousksou ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Study ◽  
Melting Process ◽  
Heat Transfer Characteristics ◽  
Triangular Shape ◽  
Temperature Distributions ◽  
Exchange Area ◽  
The Right ◽  
Change Material

The present numerical study is conducted to analyze melting process within a rectangular enclosure filled by phase change material (PCM) vertically heated from one side. The right hot wall and the left cold wall are maintained at temperatures, Th=38.3 °C and Tc =28.3 °C, respectively, and it was filled by solid PCM Gallium initially at temperature Tc. The horizontal walls are insulated. A transient numerical model is developed to study the heat transfer and melting behaviours, and the natural convection is accounted. To enhance the heat transfer and the melting process of the PCM, fins with a rectangular and triangular shape are proposed. Moreover, the effects of both thermophysical properties and fins integration on the flow structure and heat transfer characteristics are investigated in detail. The melt fraction contours with the natural convection driven flow are performed and compared, as well as the temperature distributions for a Rayleigh number of around Ra= 106. It is found that the rate of the melting increases with the elevation in the values of specific heat capacity Cp as well as the thermal conductivity λ of the PCM Gallium. The results show also that the rectangular fin accelerates the PCM melting faster than the triangular fin’s shape thanks to the increased exchange area.

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