复杂结构辐射换热工程应用及数值计算
|
摘要
本文针对渗金属锯条的双层辉光离子渗金属工艺过程和提拉法晶体生长过程中提出的质量控制问题,研究了复杂结构辐射换热数值计算及其在上述两个工艺过程中产品质量控制与提高方面的应用。
复杂结构的辐射换热计算所遇到的主要问题是:结构复杂导致计算量巨大;辐射角系数的计算因遮挡或数值计算误差而难以满足对称性和完整性,从而导致辐射换热计算不准确。本文从基本的辐射换热关系式出发,用误差传递的思想研究了角系数的计算误差对辐射换热计算的影响,表明对角系数施加完整性约束可以大大提高辐射换热计算的准确性。在对前人的角系数修正方法进行分析的基础上,对于遮挡是产生角系数计算误差的主要原因的渗金属炉内料筐温度场的工程计算,提出了一种更加简单的角系数修正方法,即将偏离完整性的角系数的计算误差分配给自身表面,该方法与文献中报道的将上述误差均匀分配给各非零角系数的方法相比,使得辐射换热计算的准确性大大提高,辐射能量的计算偏差可保证在10%以内,可以满足工程计算的需要。
在对渗金属炉内的换热进行分析之后,建立了表面间以辐射换热方式耦合在一起的具有内热源的多个平板的导热的物理模型,进行了二维和三维数值分析,研究了辅助阴极、辐射屏、料筐几何结构、材料发射率和辅助辐射板等因素对渗金属炉内料筐温度分布的影响。指出:辅助阴极具有重新分配炉内的热源分布和隔热保温的双重作用,合理添加辅助阴极对改善料筐内温度场的均匀性具有重要的作用;在渗金属炉的顶部减少辐射屏层数,可以在保证竖直方向满足工艺要求的同时改善水平方向的温度场的均匀性;料筐的几何结构对温度场有重要影响,锯条背之间的距离以60毫米为好;减少料筐材料的发射率有利于局部控制料筐温度。本文还提出了应用辅助辐射板局部控制料筐温度分布的方法。用热点偶测量了炉内的温度,为数值计算提供了参考。
本文完善了提拉法晶体生长的整体模型,在模型中加入了辐射换热的计算,研究了晶体生长过程中产生混合对流的各种因素以及辐射换热对相变面形状的影响。指出,混合对流对相变面变凸(有利于提高晶体质量)有重要的作用,本文提出了在利用混合对流改变相变面形状的基础上应用局部控制辐射换热(即在三相交界附近添加辐射环)来进一步控制相变面形状的方法。
This dissertation is concerned with thermal radiation heat transfer in plasma surface alloying process and Czochralski crystal growth. The numerical method of the diffusive-gray enclosure radiation heat transfer in complex geometry was studied, and its application was introduced into these two processes to improve the quality of handsaw and single crystal.The complex geometry always makes the thermal radiation calculation extremely expensive and difficult to satisfy the important physical constraints of reciprocity and closure in computation of the view factor. Uncertainty analysis method was applied to diffuse-gray enclosure radiation problems in this paper. Analyses of the effect of uncertainties in view factors on the radiation heat transfer show that strict enforcement of view factor closure constraint can greatly reduce the sensitivity of the results to the errors in view factors. Based on the review of several view factors rectification algorithms, a simple rectification scheme was adopted to rectify the uncertainties of view factors resulting from obstructions in an enclosure. It was found that this rectification scheme is superior to the others for the reduction of heat flux sensitive to uncertainties in view factors, and the energy conservation can be matched very well.Two and three dimensional mathematical models were developed to simulate the radiation heat transfer in the plasma surface alloying process. The effects of the supplementary cathode, shield, configuration of the frame, emissivities and auxiliary plates on the temperature distribution were numerically studied. It points out: a rational arrangement of supplementary cathode can greatly uniformize the handsaw temperature duo to its double actions of redistributing heat source and reducing thermal radiation;less shield layers at the top of the furnace leads to more uniform horizontal temperature distribution. The horizontal plate between two rows of handsaws can enhance the radiative heat transfer at the center place, and therefore can reduce the temperature difference along both horizontal and vertical directions. The temperature in the frame was measured by thermal couples. The results show that the three-dimensional simulation are reasonable.The global model of CZ crystal growth considering the diffusive-gray enclosure radiation heat transfer was developed in this paper. The effects of the combined convection of the melt and radiative heat transfer on the shape of melt-crystal interface were numerically analyzed. A new method of controlling the melt-crystal interface by changing the local radiative heat transfer is presented.
复杂结构的辐射换热计算所遇到的主要问题是:结构复杂导致计算量巨大;辐射角系数的计算因遮挡或数值计算误差而难以满足对称性和完整性,从而导致辐射换热计算不准确。本文从基本的辐射换热关系式出发,用误差传递的思想研究了角系数的计算误差对辐射换热计算的影响,表明对角系数施加完整性约束可以大大提高辐射换热计算的准确性。在对前人的角系数修正方法进行分析的基础上,对于遮挡是产生角系数计算误差的主要原因的渗金属炉内料筐温度场的工程计算,提出了一种更加简单的角系数修正方法,即将偏离完整性的角系数的计算误差分配给自身表面,该方法与文献中报道的将上述误差均匀分配给各非零角系数的方法相比,使得辐射换热计算的准确性大大提高,辐射能量的计算偏差可保证在10%以内,可以满足工程计算的需要。
在对渗金属炉内的换热进行分析之后,建立了表面间以辐射换热方式耦合在一起的具有内热源的多个平板的导热的物理模型,进行了二维和三维数值分析,研究了辅助阴极、辐射屏、料筐几何结构、材料发射率和辅助辐射板等因素对渗金属炉内料筐温度分布的影响。指出:辅助阴极具有重新分配炉内的热源分布和隔热保温的双重作用,合理添加辅助阴极对改善料筐内温度场的均匀性具有重要的作用;在渗金属炉的顶部减少辐射屏层数,可以在保证竖直方向满足工艺要求的同时改善水平方向的温度场的均匀性;料筐的几何结构对温度场有重要影响,锯条背之间的距离以60毫米为好;减少料筐材料的发射率有利于局部控制料筐温度。本文还提出了应用辅助辐射板局部控制料筐温度分布的方法。用热点偶测量了炉内的温度,为数值计算提供了参考。
本文完善了提拉法晶体生长的整体模型,在模型中加入了辐射换热的计算,研究了晶体生长过程中产生混合对流的各种因素以及辐射换热对相变面形状的影响。指出,混合对流对相变面变凸(有利于提高晶体质量)有重要的作用,本文提出了在利用混合对流改变相变面形状的基础上应用局部控制辐射换热(即在三相交界附近添加辐射环)来进一步控制相变面形状的方法。
This dissertation is concerned with thermal radiation heat transfer in plasma surface alloying process and Czochralski crystal growth. The numerical method of the diffusive-gray enclosure radiation heat transfer in complex geometry was studied, and its application was introduced into these two processes to improve the quality of handsaw and single crystal.The complex geometry always makes the thermal radiation calculation extremely expensive and difficult to satisfy the important physical constraints of reciprocity and closure in computation of the view factor. Uncertainty analysis method was applied to diffuse-gray enclosure radiation problems in this paper. Analyses of the effect of uncertainties in view factors on the radiation heat transfer show that strict enforcement of view factor closure constraint can greatly reduce the sensitivity of the results to the errors in view factors. Based on the review of several view factors rectification algorithms, a simple rectification scheme was adopted to rectify the uncertainties of view factors resulting from obstructions in an enclosure. It was found that this rectification scheme is superior to the others for the reduction of heat flux sensitive to uncertainties in view factors, and the energy conservation can be matched very well.Two and three dimensional mathematical models were developed to simulate the radiation heat transfer in the plasma surface alloying process. The effects of the supplementary cathode, shield, configuration of the frame, emissivities and auxiliary plates on the temperature distribution were numerically studied. It points out: a rational arrangement of supplementary cathode can greatly uniformize the handsaw temperature duo to its double actions of redistributing heat source and reducing thermal radiation;less shield layers at the top of the furnace leads to more uniform horizontal temperature distribution. The horizontal plate between two rows of handsaws can enhance the radiative heat transfer at the center place, and therefore can reduce the temperature difference along both horizontal and vertical directions. The temperature in the frame was measured by thermal couples. The results show that the three-dimensional simulation are reasonable.The global model of CZ crystal growth considering the diffusive-gray enclosure radiation heat transfer was developed in this paper. The effects of the combined convection of the melt and radiative heat transfer on the shape of melt-crystal interface were numerically analyzed. A new method of controlling the melt-crystal interface by changing the local radiative heat transfer is presented.
引文
1.顾维藻,神家锐,马重芳,等.强化换热.北京:科学出版社,1990
2.钟之英,余钧,陈雪蕾.异型辐射元件综合强化辐射对流换热的研究.工程热物理学报,1991,12[3]:289-293
3. Yamada Y., Akai M. and Mori Y. Sield-and-Tube side heat transfer augmentation by the use of wall radiation in a crossflow shell-and-tube heat exchanges. ASME, J. of Heat Transfer, 1984, 106: 735～742
4. Echigo R. Effective energy conversion method between gas enthalpy and thermal radiation and application to industry furnances. Heat Transfer, 1982, 6: 361
5.胡佳,田长霖.垂直壁前置以薄层多孔材料时的自然对流与辐射传热.工程热物理学报,1986,7[2]:133～138
6.刘云龙,梁新刚,任建勋,等.微重力场中对流-辐射耦合换热系统的地面模拟.清华大学学报[自然科学版],1997,37[2]:106～109
7.洪涛.封闭空间三维湍流自然对流与辐射的复和换热:[硕士学位论文].北京:清华大学热能工程系,1993
8. Kim D. M. and Viskanta R. Effect of wall conduction and radiation on natural convection in a rectanglar cavity. Numerical heat Transfer, 1984, 7: 449～470
9. Argyris J. and Szimmat J. An analysis of temperature radiation interchange problems. Computer Methods in Applied Mechanics and Engineering, 1992, 94: 155～180
10. Atherton L. J., Derby J. J. and Brown R. A. Radiative heat transfer in Czochraiski crystal growth. Journal of Crystal Growth, 1987, 84: 57～78
11. Wu H. L.and Fricker N. An investigation of the behavior of swirling jet flames in a narrow cylinderical furnance. J. Inst. Fuel, 1976, 49: 144～151
12. Steward F. R. and Cannon P. The Calculation of radiation heat flux in a cylindrical furnace using the Monte Carlo Method. Int. J. Heat Mass Transfer, 1971, 14[2]: 245～262
13. Chang S. L. and Rhee K. T. A coordinate transformation method for the radiation heat transfer prediction in soot-laden combustion products. J. Heat Transfer, 1988, 110: 807～809
14.李万林,傅振宣.角系数计算程序方法.工程热物理学报,1982,3[1]:76～82
15.徐重,王从曾,等.锯切工具离子渗金属技术.中国专利,871043580,1987,7
16. Xu Z. Xu-Tec Process. U.S. Patent, 4731539, 1988-03-15
17. Xu Z., Fang B. H., Zheng W. N., et al. A novel plasma surface metallurgy: XUTEC process. Surface and Coatings Technology, 1990, 43/44: 1065～1073
18.徐重.双层辉光离子渗金属技术.太原工业大学学报,1993,24:30～35
19.徐重,王从曾,苏永安,等.离子渗钨钼技术在手用钢锯条上的应用研究.金属热处理,1988,3:13～19
20.双层辉光离子渗金属技术.太原大学表面工程研究所
21.“863”重大关键技术项目“双层辉光离子渗金属技术”可行性报告.太原工业大学表面工程研究所,1994,6,15
22.闵乃本.晶体生长的物理基础.上海:上海科技出版社.1982
23.卞伯绘.辐射换热的分析与计算.北京:清华大学出版社出版,1988
24. Siegel R. and Howell J. R. Thermal Radiation Heat Transfer. New York:Hemisphere and McGraw-Hill, 1981
25.杨贤荣等.辐射换热角系数手册.北京:国防工业出版社,1980
26. Flouros M., Bungart S., Leiner W. et al. Calculation of the view factors for radiantHeat exchange in a new volumetric receiver with tapered ducts. Transactions ofthe ASME, Journal of Solar Energy Engineering. 1995, 117: 58～60
27. Naraghi M. H. N.and Warna J. P. Radiation configuration factors from axisymmetric bodies to plane surfaces. Int. J. Heat Mass Transfer. 1988, 31[7]: 1537～1539
28. Treat H. Radiation view factors between the surfaces of a long rectangular duct and a centrally positioned cylinder. Heat Transfer Engineering. 1994, 15[2]: 25～31
29. Ambirajan A. and Venkateshan S. P. Accurate determination of diffuse view factors between planar surfaces. Int. J. Heat Mass Transfer, 1993, 36[8]: 2203～2208
30. Minning C. P. Calculation of shape factors between parallel ring sections sharing a common center line. AIAA Journal, 1976, 14: 813～816
31. Emery A. F., Johansson O., Lobo M., et al. A comparative study of methods for computing the diffuse radiation view factors for complex structures. Journal of Heat Transfer, 1991, 113: 413～422
32. Taniguchi H., Yang W. J., Kudo K., et al. Radiant transfer in gas filled enclosures by radiant energy absorption distribution method. In: C.L. Tien, V.P. Carey, J.K. Farrel eds. Proc 8th Int. Heat Transfer Conf. Washington: Hemisphere Pub. Co. 1986. 757～762
33. Murty C. V. S. Evaluation of radiation reception factors in a rotary kiln using amodified Monte Carlo scheme. Int. J. Heat Transfer, 1993, 36[1]: 119～132
34.李本文,陈海耿.用均匀离散射线法计算复杂几何系统的角系数.东北大学学报[自然科学版],1995,16[3]:277～281
35. Cohen M. F., Greenberg D. P., Brock P. J., et al. An efficient radiosity approachfor realistic image synthesis. IEEE CG&A, 1986, 6[3]: 26～35
36. Emery A. F., Johansson O. and Abrous A. Radiation heat transfer calculations for space structures. Paper No. AIAA-87-1522, 22nd AIAA Thermophysics Conference, 1987, June 8～10, Honolulu, HI
37. Sparrow E. M. A new and simpler formulation for radiative angle factors. ASME J. Heat Transfer, 1963, 85: 81～88
38. Mitalas G. P. and Stephenson D. G. Fortran Ⅳ programs to calculate radiant interchange factors. National Research Council of Canada, Division of Buiilding Research, Ottawa, Canada, DBR-25, 1966
39. Shapiro A. B. Computer Implementation, Accuracy, and Timing of Radiation View Factor Algorithms. Transactions of the ASME. Journal of Heat Transfer, 1985, 107: 730～732
40. Chung T. J. and Kim J. Y. Radiation viewfactors by finite elements. ASME Journal of Heat Transfer, 1982, 104: 792～795
41. Taylor R. P. and Luck R. Comparision of Reciprocity and closure enforcement methods for radiation view factors. J. Thermophysics and Transfer, 1995, 9[4]: 660～666
42. Leersum J. V. A method for determining a consistent set of radiation view factors from a set generated by a nonexact method. Int. J. Heat and Fluid Flow, 1989, 10[1]: 83～85
43. Larsen M. E. and Howell J. R. Least-squares smoothing of direct-exchange areas in zonal analysis. Journal of Heat Transfer, 1986, 108[1]: 239～242
44.关治,陈景良.数值计算方法.北京:清华大学出版社,1989
45.李志信,梁新刚,耿旭.双辉法渗金属锯条炉内温度场均匀性研究阶段工作报告.1995
46.李志信,梁新刚,耿旭.863课题进展情况汇报.1996
47.李志信,梁新刚,耿旭,等.双辉法渗金属炉内温度场的数值分析.中国工程热物理学会传热传质学年会,1996,北京
48. Tsui Y. T. and Tsou F. K. Ratio of Radial to total heat flow in circular rod. J. Heat Trans. ASME, 1963, 85: 285～286
49. Batchelor G. K. Note on a class of Solutions of the Navier-Stokes Equations Representing Steady Rotationally Symmetric Flow. Quart. J. Mech. App. Math., 1951, 4: 29～41
50. Jones A. D. W. Scaling Analysis of the Flow of a Low Prandtl Number Czochralski Melt. J. Crystal Growth, 1988, 88: 465～476
51. Nassau K. and Carruthers J.R. Non-mixing cells due to crucible rotation during Czochralski crystal growth. J. Apply Phys. 1968, 39: 5205～5214
52. Shiroki K. Simulations of Czochralski growth on crystal rotation rate influence in fixed crucibles. J. Crystal Growth, 1977, 40: 129～138
53. Lamprecht R., Schwave D., Scharmann A., et al. Experiments on buoyant, thermocapiilary and forced convection in Czochralski configuration. J. Crystal Growth, 1983, 65: 143～152
54. Jones A. D. W. An expriment model of the flow in Czochralski growth. J.Crystal Growth, 1983, 61: 235～244
55. Jones A. D. W. Spoken patterns. J. Crystal Growth, 1983, 63: 70～76
56. Munakata T, and Tanasawa I. Onset of oscillatory flow in a Czochralski growth melt and its suppression by magnetic field. J. Crystal Growth, 1990, 106: 566～576
57. Ozoe H., Toh K. and Inoue T. Transition mechanisum of flow modes in Czochralski convection. J. Crystal Growth, 1991, 110: 472～480
58. Rossby H. T. J. Fluid Mech., 1969, 36: 309
59. Verhoeven J. D. Phys. Fluids, 1969, 12: 1733
60. Krishnamurtri R. J. Fluid Mech., 1973, 60: 285
61. Choe K.S., Stefani J. A and Dettling T.B.. Effects of growth conditions on thermal profiles during Czochralski Silicon crystal growth. J. Crystal Growth, 1991, 108: 262～276
62.王健伟,万群,秦福.采用温度测量的方法对直拉法熔体流动的研究.半导体技术,1992,2[1]:62～64
63. Kakimoto K., Eguchi M., Watanabe H. Direct observation by X-ray radiography of convection of molten Silicon in the Czochralski growth method. J.Crystal Growth, 1988, 88: 365～370
64. Kakimoto K., Eguchi M., Watanabe H., et al. Natural and forced convection of molten Silicon during CZ single crystal growth. J. Crystal Growth, 1989, 94: 412～420
65. Kakimoto K., Eguchi M., Watanabe H., et al. Flow instability of molten Silicon in the CZ configuration. J. Crystal Growth, 1990, 102: 16～20
66. Masahito. Double-beam X-ray radiography system for three-dimensional flowvisualization of molten Silicon convection. J. Crystal Growth, 1993, 133: 23～28
67. Kabayashi N. and Arizumi T. Computational analysis of the flow in a crucible. J.Crystal Growth, 1975, 30: 177～184
68. Kabayashi N. Computational Simulation of the melt flow during Czochralski growth. J. Crystal Growth, 1978, 52: 425～434
69. Langlois W. E. Digital simulation of CZ bulk flow in a parameter range appropriate from liquid semiconductors. J. Crystal Growth, 1977, 42: 386～399
70. Langlois W. E. Convection in growth melts. Physico-Chem. Hydrodyn, 1981, 2: 245～261
71. Langlois W. E. Bouyancy-driven flows in crystal growth melts. Ann. Rev. Fluid Mech., 1985, 17: 191～215
72. Crochet M. J., Wouters P. J., Geyling F. T., et al. Finite-element simulation of Czochralski bulk flow. J. Crystal Growth, 1983, 65: 153～165
73.邬小波.提拉法晶体生长过程的数值分析及模拟实验:[清华大学博士论文].北京:清华大学工程力学系,1994
74. Fontaine J. P., Extrement G. P., Chevrier V., et al. Experimental and theoreticaltreatments of the Czochraski growth of Bil2GeO20. J. Crystal Growth, 1994, 139:67～80
75. Sabhapathy P. and Salcodean M. E. Numerical analysis of heat transfer in LECgrowth ofGaAs. J. Crystal Growth, 1989, 97: 125-1～35
76. Mihelcic M. and Wingerath K. Three-dimensional simulations of the Czochralskibulk flow in a stationary transverse field and in a vertical magnetic field: effects on the asymmetry of the flow and temperature distribution in the Si melt. J. Crystal Growth, 1987, 82: 318～326
77. Neumann G. Three-dimensional numericalsimulationof buoyancy-driven convection in vertical cylinders heat from below. J. Fluid Mech., 1990, 214: 559～578
78. Kakimoto K., Watanabe M., Eguchi M., et al. Flow instability of the melt during Czochralski Si crystal growth: dependence on growth conditions: a numerical simulation study. J. Crystal Growth, 1994, 139: 197～205
79. Derby J. J., Brown R. A., Geyling F. T., et al. A thermal-capillary model for Liquid-Encapsulated Czochraski crystal growth. J. Electrochem Sot., 1985, 132[2]: 470～482
80. Derby J. J. and Brown R. A. Thermal-capillary analysis of Czochralski and LiquidEncapsulated Czochralski crystal growth. J. Crystal Growth, 1986, 74: 605～624
81. Derby J. J. and Brown R. A., On the quasi-steady assumption in modellingCzochralski crystal growth. J.Crystal Growth, 1988, 87: 251～260
82. Derby J. J. and Brown R. A. On the dynamics of Czochralski crystal growth. J.Crystal Growth, 1987, 83: 137～151
83. Atherton L. J., Derby J. J. and Brown R. A. Radiative heat exchange in Czochralski crystal growth. J. Crystal Growth, 1987, 84: 57～78
84. Derby J. J., Atherton L. J., Thomas P. D., et al,Finite element methods for analysis of the dynamics and control of Czochralski crystal growth, J. Sci. Computing,1988, 2: 297
85. Sackinger P.K., Brown R. A. and Derby J. J. Axisymmtric convection in a complete thermal-capillary for Czochralski crystal growth, Int. J. Num. Meths. Fluids, 1989, 9: 453～492
86. Derby J. J. and Xiao Q. Some effects of crystal rotation on large-scale thermlcapillary model, J. Crystal Growth, 1991, 113: 575～586
87. Kinney T. A., Bornside D. E. and Brown R. A. Quantitative assessment of an integrated hydrodynamic thermal-capillary model for larger diameter Czochralski growth of Silicon: comprison of predicted temperature field with experiment. J. Crystal Growth, 1993, 26: 413～434
88. Kaobayashi S. and Miyahara S. Turbulent heat transfer through the melt in Silicon Czochralski growth. J. Crystal Growth, 1991, 109: 149～154
89. Kinney T. A. and Brown R. A. Application of turbulence modeling to the integrated hydrodynamic thermal-capillary model of Czochralski crystal growth of Silicon. J. Crystal Growth, 1993, 132: 551～574
90. Hurle D. T. Analytical representation of the shape of the meniscus in Czochralski growth. J. Crystal Growth, 1983, 63: 13～17
91.Pantakar S.V.传热与流动的数值计算,张政译.北京:科学出版社,1984
92.陶文诠.数值传热学.西安:西安交通大学出版社,1988
93. Geng, X., Wu X. B. and Guo Z.Y. Numerical simulation of combined flow inCzochralski crystal growth. J. crystal growth [to be published]
94. Rupp R., Muller G. and Neumann G. Three dimensional time dependent modelling of the marangoni convection in zone melting configurations for GaAs. J. Crystal Growth, 1989, 97: 34～41
95. Okano Y. and Fukuda T. Numerical study on CZ growth of Oxide single crystals. J. Crystal Growth, 1991, 109: 94-98
96. Kopetsch H. Numerical simulation of the interface inversion in CZ growth of Oxide crystals. J. Crystal Growth, 1990, 102: 505-528
97. Yi K. W., Chung H. T., Lee H. W., et al. The effects of pulling rates on the shape of crystal/melt interface in Si single crystal growth by the Czochralski method. J. Crystal Growth, 1993, 132: 451-460
98. Wu X.B., Geng X., Guo Z.Y.. Foundamental study of crystal/melt interface shape change in Czochralski crystal growth. J. Crystal Growth, 1996, 169: 786-794
99. Srivastava, R. K., Ramachandra P. A. and Dudukovic M. P. Simulation of jet cooling effects on Czochralski crystal growth. J. Crystal Growth, 1986, 76:395-407
2.钟之英,余钧,陈雪蕾.异型辐射元件综合强化辐射对流换热的研究.工程热物理学报,1991,12[3]:289-293
3. Yamada Y., Akai M. and Mori Y. Sield-and-Tube side heat transfer augmentation by the use of wall radiation in a crossflow shell-and-tube heat exchanges. ASME, J. of Heat Transfer, 1984, 106: 735～742
4. Echigo R. Effective energy conversion method between gas enthalpy and thermal radiation and application to industry furnances. Heat Transfer, 1982, 6: 361
5.胡佳,田长霖.垂直壁前置以薄层多孔材料时的自然对流与辐射传热.工程热物理学报,1986,7[2]:133～138
6.刘云龙,梁新刚,任建勋,等.微重力场中对流-辐射耦合换热系统的地面模拟.清华大学学报[自然科学版],1997,37[2]:106～109
7.洪涛.封闭空间三维湍流自然对流与辐射的复和换热:[硕士学位论文].北京:清华大学热能工程系,1993
8. Kim D. M. and Viskanta R. Effect of wall conduction and radiation on natural convection in a rectanglar cavity. Numerical heat Transfer, 1984, 7: 449～470
9. Argyris J. and Szimmat J. An analysis of temperature radiation interchange problems. Computer Methods in Applied Mechanics and Engineering, 1992, 94: 155～180
10. Atherton L. J., Derby J. J. and Brown R. A. Radiative heat transfer in Czochraiski crystal growth. Journal of Crystal Growth, 1987, 84: 57～78
11. Wu H. L.and Fricker N. An investigation of the behavior of swirling jet flames in a narrow cylinderical furnance. J. Inst. Fuel, 1976, 49: 144～151
12. Steward F. R. and Cannon P. The Calculation of radiation heat flux in a cylindrical furnace using the Monte Carlo Method. Int. J. Heat Mass Transfer, 1971, 14[2]: 245～262
13. Chang S. L. and Rhee K. T. A coordinate transformation method for the radiation heat transfer prediction in soot-laden combustion products. J. Heat Transfer, 1988, 110: 807～809
14.李万林,傅振宣.角系数计算程序方法.工程热物理学报,1982,3[1]:76～82
15.徐重,王从曾,等.锯切工具离子渗金属技术.中国专利,871043580,1987,7
16. Xu Z. Xu-Tec Process. U.S. Patent, 4731539, 1988-03-15
17. Xu Z., Fang B. H., Zheng W. N., et al. A novel plasma surface metallurgy: XUTEC process. Surface and Coatings Technology, 1990, 43/44: 1065～1073
18.徐重.双层辉光离子渗金属技术.太原工业大学学报,1993,24:30～35
19.徐重,王从曾,苏永安,等.离子渗钨钼技术在手用钢锯条上的应用研究.金属热处理,1988,3:13～19
20.双层辉光离子渗金属技术.太原大学表面工程研究所
21.“863”重大关键技术项目“双层辉光离子渗金属技术”可行性报告.太原工业大学表面工程研究所,1994,6,15
22.闵乃本.晶体生长的物理基础.上海:上海科技出版社.1982
23.卞伯绘.辐射换热的分析与计算.北京:清华大学出版社出版,1988
24. Siegel R. and Howell J. R. Thermal Radiation Heat Transfer. New York:Hemisphere and McGraw-Hill, 1981
25.杨贤荣等.辐射换热角系数手册.北京:国防工业出版社,1980
26. Flouros M., Bungart S., Leiner W. et al. Calculation of the view factors for radiantHeat exchange in a new volumetric receiver with tapered ducts. Transactions ofthe ASME, Journal of Solar Energy Engineering. 1995, 117: 58～60
27. Naraghi M. H. N.and Warna J. P. Radiation configuration factors from axisymmetric bodies to plane surfaces. Int. J. Heat Mass Transfer. 1988, 31[7]: 1537～1539
28. Treat H. Radiation view factors between the surfaces of a long rectangular duct and a centrally positioned cylinder. Heat Transfer Engineering. 1994, 15[2]: 25～31
29. Ambirajan A. and Venkateshan S. P. Accurate determination of diffuse view factors between planar surfaces. Int. J. Heat Mass Transfer, 1993, 36[8]: 2203～2208
30. Minning C. P. Calculation of shape factors between parallel ring sections sharing a common center line. AIAA Journal, 1976, 14: 813～816
31. Emery A. F., Johansson O., Lobo M., et al. A comparative study of methods for computing the diffuse radiation view factors for complex structures. Journal of Heat Transfer, 1991, 113: 413～422
32. Taniguchi H., Yang W. J., Kudo K., et al. Radiant transfer in gas filled enclosures by radiant energy absorption distribution method. In: C.L. Tien, V.P. Carey, J.K. Farrel eds. Proc 8th Int. Heat Transfer Conf. Washington: Hemisphere Pub. Co. 1986. 757～762
33. Murty C. V. S. Evaluation of radiation reception factors in a rotary kiln using amodified Monte Carlo scheme. Int. J. Heat Transfer, 1993, 36[1]: 119～132
34.李本文,陈海耿.用均匀离散射线法计算复杂几何系统的角系数.东北大学学报[自然科学版],1995,16[3]:277～281
35. Cohen M. F., Greenberg D. P., Brock P. J., et al. An efficient radiosity approachfor realistic image synthesis. IEEE CG&A, 1986, 6[3]: 26～35
36. Emery A. F., Johansson O. and Abrous A. Radiation heat transfer calculations for space structures. Paper No. AIAA-87-1522, 22nd AIAA Thermophysics Conference, 1987, June 8～10, Honolulu, HI
37. Sparrow E. M. A new and simpler formulation for radiative angle factors. ASME J. Heat Transfer, 1963, 85: 81～88
38. Mitalas G. P. and Stephenson D. G. Fortran Ⅳ programs to calculate radiant interchange factors. National Research Council of Canada, Division of Buiilding Research, Ottawa, Canada, DBR-25, 1966
39. Shapiro A. B. Computer Implementation, Accuracy, and Timing of Radiation View Factor Algorithms. Transactions of the ASME. Journal of Heat Transfer, 1985, 107: 730～732
40. Chung T. J. and Kim J. Y. Radiation viewfactors by finite elements. ASME Journal of Heat Transfer, 1982, 104: 792～795
41. Taylor R. P. and Luck R. Comparision of Reciprocity and closure enforcement methods for radiation view factors. J. Thermophysics and Transfer, 1995, 9[4]: 660～666
42. Leersum J. V. A method for determining a consistent set of radiation view factors from a set generated by a nonexact method. Int. J. Heat and Fluid Flow, 1989, 10[1]: 83～85
43. Larsen M. E. and Howell J. R. Least-squares smoothing of direct-exchange areas in zonal analysis. Journal of Heat Transfer, 1986, 108[1]: 239～242
44.关治,陈景良.数值计算方法.北京:清华大学出版社,1989
45.李志信,梁新刚,耿旭.双辉法渗金属锯条炉内温度场均匀性研究阶段工作报告.1995
46.李志信,梁新刚,耿旭.863课题进展情况汇报.1996
47.李志信,梁新刚,耿旭,等.双辉法渗金属炉内温度场的数值分析.中国工程热物理学会传热传质学年会,1996,北京
48. Tsui Y. T. and Tsou F. K. Ratio of Radial to total heat flow in circular rod. J. Heat Trans. ASME, 1963, 85: 285～286
49. Batchelor G. K. Note on a class of Solutions of the Navier-Stokes Equations Representing Steady Rotationally Symmetric Flow. Quart. J. Mech. App. Math., 1951, 4: 29～41
50. Jones A. D. W. Scaling Analysis of the Flow of a Low Prandtl Number Czochralski Melt. J. Crystal Growth, 1988, 88: 465～476
51. Nassau K. and Carruthers J.R. Non-mixing cells due to crucible rotation during Czochralski crystal growth. J. Apply Phys. 1968, 39: 5205～5214
52. Shiroki K. Simulations of Czochralski growth on crystal rotation rate influence in fixed crucibles. J. Crystal Growth, 1977, 40: 129～138
53. Lamprecht R., Schwave D., Scharmann A., et al. Experiments on buoyant, thermocapiilary and forced convection in Czochralski configuration. J. Crystal Growth, 1983, 65: 143～152
54. Jones A. D. W. An expriment model of the flow in Czochralski growth. J.Crystal Growth, 1983, 61: 235～244
55. Jones A. D. W. Spoken patterns. J. Crystal Growth, 1983, 63: 70～76
56. Munakata T, and Tanasawa I. Onset of oscillatory flow in a Czochralski growth melt and its suppression by magnetic field. J. Crystal Growth, 1990, 106: 566～576
57. Ozoe H., Toh K. and Inoue T. Transition mechanisum of flow modes in Czochralski convection. J. Crystal Growth, 1991, 110: 472～480
58. Rossby H. T. J. Fluid Mech., 1969, 36: 309
59. Verhoeven J. D. Phys. Fluids, 1969, 12: 1733
60. Krishnamurtri R. J. Fluid Mech., 1973, 60: 285
61. Choe K.S., Stefani J. A and Dettling T.B.. Effects of growth conditions on thermal profiles during Czochralski Silicon crystal growth. J. Crystal Growth, 1991, 108: 262～276
62.王健伟,万群,秦福.采用温度测量的方法对直拉法熔体流动的研究.半导体技术,1992,2[1]:62～64
63. Kakimoto K., Eguchi M., Watanabe H. Direct observation by X-ray radiography of convection of molten Silicon in the Czochralski growth method. J.Crystal Growth, 1988, 88: 365～370
64. Kakimoto K., Eguchi M., Watanabe H., et al. Natural and forced convection of molten Silicon during CZ single crystal growth. J. Crystal Growth, 1989, 94: 412～420
65. Kakimoto K., Eguchi M., Watanabe H., et al. Flow instability of molten Silicon in the CZ configuration. J. Crystal Growth, 1990, 102: 16～20
66. Masahito. Double-beam X-ray radiography system for three-dimensional flowvisualization of molten Silicon convection. J. Crystal Growth, 1993, 133: 23～28
67. Kabayashi N. and Arizumi T. Computational analysis of the flow in a crucible. J.Crystal Growth, 1975, 30: 177～184
68. Kabayashi N. Computational Simulation of the melt flow during Czochralski growth. J. Crystal Growth, 1978, 52: 425～434
69. Langlois W. E. Digital simulation of CZ bulk flow in a parameter range appropriate from liquid semiconductors. J. Crystal Growth, 1977, 42: 386～399
70. Langlois W. E. Convection in growth melts. Physico-Chem. Hydrodyn, 1981, 2: 245～261
71. Langlois W. E. Bouyancy-driven flows in crystal growth melts. Ann. Rev. Fluid Mech., 1985, 17: 191～215
72. Crochet M. J., Wouters P. J., Geyling F. T., et al. Finite-element simulation of Czochralski bulk flow. J. Crystal Growth, 1983, 65: 153～165
73.邬小波.提拉法晶体生长过程的数值分析及模拟实验:[清华大学博士论文].北京:清华大学工程力学系,1994
74. Fontaine J. P., Extrement G. P., Chevrier V., et al. Experimental and theoreticaltreatments of the Czochraski growth of Bil2GeO20. J. Crystal Growth, 1994, 139:67～80
75. Sabhapathy P. and Salcodean M. E. Numerical analysis of heat transfer in LECgrowth ofGaAs. J. Crystal Growth, 1989, 97: 125-1～35
76. Mihelcic M. and Wingerath K. Three-dimensional simulations of the Czochralskibulk flow in a stationary transverse field and in a vertical magnetic field: effects on the asymmetry of the flow and temperature distribution in the Si melt. J. Crystal Growth, 1987, 82: 318～326
77. Neumann G. Three-dimensional numericalsimulationof buoyancy-driven convection in vertical cylinders heat from below. J. Fluid Mech., 1990, 214: 559～578
78. Kakimoto K., Watanabe M., Eguchi M., et al. Flow instability of the melt during Czochralski Si crystal growth: dependence on growth conditions: a numerical simulation study. J. Crystal Growth, 1994, 139: 197～205
79. Derby J. J., Brown R. A., Geyling F. T., et al. A thermal-capillary model for Liquid-Encapsulated Czochraski crystal growth. J. Electrochem Sot., 1985, 132[2]: 470～482
80. Derby J. J. and Brown R. A. Thermal-capillary analysis of Czochralski and LiquidEncapsulated Czochralski crystal growth. J. Crystal Growth, 1986, 74: 605～624
81. Derby J. J. and Brown R. A., On the quasi-steady assumption in modellingCzochralski crystal growth. J.Crystal Growth, 1988, 87: 251～260
82. Derby J. J. and Brown R. A. On the dynamics of Czochralski crystal growth. J.Crystal Growth, 1987, 83: 137～151
83. Atherton L. J., Derby J. J. and Brown R. A. Radiative heat exchange in Czochralski crystal growth. J. Crystal Growth, 1987, 84: 57～78
84. Derby J. J., Atherton L. J., Thomas P. D., et al,Finite element methods for analysis of the dynamics and control of Czochralski crystal growth, J. Sci. Computing,1988, 2: 297
85. Sackinger P.K., Brown R. A. and Derby J. J. Axisymmtric convection in a complete thermal-capillary for Czochralski crystal growth, Int. J. Num. Meths. Fluids, 1989, 9: 453～492
86. Derby J. J. and Xiao Q. Some effects of crystal rotation on large-scale thermlcapillary model, J. Crystal Growth, 1991, 113: 575～586
87. Kinney T. A., Bornside D. E. and Brown R. A. Quantitative assessment of an integrated hydrodynamic thermal-capillary model for larger diameter Czochralski growth of Silicon: comprison of predicted temperature field with experiment. J. Crystal Growth, 1993, 26: 413～434
88. Kaobayashi S. and Miyahara S. Turbulent heat transfer through the melt in Silicon Czochralski growth. J. Crystal Growth, 1991, 109: 149～154
89. Kinney T. A. and Brown R. A. Application of turbulence modeling to the integrated hydrodynamic thermal-capillary model of Czochralski crystal growth of Silicon. J. Crystal Growth, 1993, 132: 551～574
90. Hurle D. T. Analytical representation of the shape of the meniscus in Czochralski growth. J. Crystal Growth, 1983, 63: 13～17
91.Pantakar S.V.传热与流动的数值计算,张政译.北京:科学出版社,1984
92.陶文诠.数值传热学.西安:西安交通大学出版社,1988
93. Geng, X., Wu X. B. and Guo Z.Y. Numerical simulation of combined flow inCzochralski crystal growth. J. crystal growth [to be published]
94. Rupp R., Muller G. and Neumann G. Three dimensional time dependent modelling of the marangoni convection in zone melting configurations for GaAs. J. Crystal Growth, 1989, 97: 34～41
95. Okano Y. and Fukuda T. Numerical study on CZ growth of Oxide single crystals. J. Crystal Growth, 1991, 109: 94-98
96. Kopetsch H. Numerical simulation of the interface inversion in CZ growth of Oxide crystals. J. Crystal Growth, 1990, 102: 505-528
97. Yi K. W., Chung H. T., Lee H. W., et al. The effects of pulling rates on the shape of crystal/melt interface in Si single crystal growth by the Czochralski method. J. Crystal Growth, 1993, 132: 451-460
98. Wu X.B., Geng X., Guo Z.Y.. Foundamental study of crystal/melt interface shape change in Czochralski crystal growth. J. Crystal Growth, 1996, 169: 786-794
99. Srivastava, R. K., Ramachandra P. A. and Dudukovic M. P. Simulation of jet cooling effects on Czochralski crystal growth. J. Crystal Growth, 1986, 76:395-407