哈兹列特连铸铝合金板带凝固传热的数值模拟
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摘要
哈兹列特双带连铸连轧工艺具有流程短,能耗低,成本低,效率高等优点,引起了世界范围内铝合金板带生产企业越来越多的关注。高效率和环境友好型的连铸连轧工艺逐渐成为铝合金板带生产工业发展的一个主要趋势。直冷铸锭热轧工艺是常规的铝板带生产工艺,它是一种多工序工艺,其工序包括熔化(合金化)、直冷铸造、锯头、铣面、预热和热轧(含热粗轧和热精轧),所生产的热轧卷经过冷轧后才能达到最终的厚度。双辊铸轧工艺的工序包括熔炼(合金化)、铸轧和卷曲。铸轧带坯需冷轧方能达到最终厚度,而采用哈兹列特双带连铸工艺时铸造之后接在线热连轧,其热轧带较铸轧带坯要薄,所需的冷轧工作量自然要少。
哈兹列特连铸板坯的质量对终轧产品的性能有很大的影响。而哈兹列特双带凝固传热的数值模拟研究对提高连铸坯的表面质量、机械性能,改善微观组织非常重要,而且对哈兹列特利用余热进行热连轧节能非常有帮助。因此哈兹列特双带凝固传热的数值模拟研究非常有必要。
本文运用有限元法对哈兹列特连铸坯的凝固传热过程进行了数值模拟,在适当的假设条件下,建立了哈兹列特连铸过程的二维传热数学模型,并用热焓法建立了适用于固相、液相和固液两相区的统一能量方程。用热阻串联模型描述并计算了哈兹列特复杂的气隙层的传热,求解了哈兹列特连铸坯的凝固传热过程的两维稳态温度场,给出了连铸坯表面、中心以及连铸机出口处断面的温度分布,研究了不同过热度,连铸速度,双带涂层对哈兹列特连铸坯温度场的影响。数值计算结果表明：
(1)该传热模型比较全面的反映了哈兹列特连铸传热过程温度的变化、两相区和液芯长度的变化、坯壳的生长过程；
(2)连铸速度、双带涂层对两相区长度和铸坯温度变化,尤其是连铸机出口断面温度,有较大的影响,而过热温度则对坯壳形成位置有明显的影响；
(3)连铸速度、过热温度和双带涂层对连铸坯中心和表面的温差影响不大,它主要受双带冷却强度影响。
Hazelett twin-belt continuous casting and rolling process is absorbing more and more attention of aluminum alloy plate and strip producers of the world for its advantages, such as short procedure, low energy consumption, low production cost and high productivity. Environment-friendly and high productivity continuous casting and rolling process is becoming main trend of aluminum alloy plate and strip processes. The conventional DC casting/hot mill process route include melting and alloying, DC casting, sawing, surface milling, rolling ingot preheating, and hot rolling(both roughing and finishing). The hot rolled strip is subsequently cold rolled to finish gauge. With twin-roll casting, the steps include melting and alloying, casting and coiling. The strip is subsequently cold rolled to finish gauge. In the twin-belt process, casting is followed by in-line hot rolling to produce a hot rolled strip that is thinner than twin-roll cast strip, requiring less subsequent cold rolling.
The quality of Hazelett twin-belt continuous casting has big influence on the property of finished hot-rolled aluminum strip. The numerical simulation study on solidification and heat transfer of the twin-belt continuous casting is important to improve the surface quality, microstructure, and mechanical property of continuous casting aluminum strip and very helpful to take advantage of the heat in the as-cast strip to save energy and reduce the environmental impact, which is the biggest advantage of the Hazelett process. So it is very necessary to do some numerical simulation research on solidification and heat-transfer of Hazelett twin-belt continuous casting process.
In this paper, a two-dimensional heat-transfer model which considers a generalized energy equation that is valid for the solid, liquid, and mushy zones in the Hazelett continuous cast was developed to simulate the solidification and heat transfer of twin-belt continuous casting of aluminum alloy slab by the finite element method under some assumptions. The heat transfer of Hazelett caster mold interface was described by an overall thermal resistance model. The steady state temperature field during the continuous casting was computed and the temperature distribution of slab surface, center and continuous casting exit was also computed when casting was close to steady state. the influence of process parameters such as casting speed, superheat and belt coat on temperature distribution was investigated. The result of calculation indicated as follows:
(1) The Hazelett heat-transfer model built in this paper reflects mushy zone evolution, the length of liquid core and slab temperature distribution for the heat transformation process completely during Hazelett twin-belt continuous casting.
(2) Continuous casting speed and twin-belt coat have big influence on temperature field, especially twin-belt caster exit temperature, super heat has much influence on the formation position of shell
(3) Process parameters such as continuous casting speed, super heat, twin-belt coat have little influence on the temperature difference between center and surface of Hazelett casted slab, which is mainly influenced by twin-belt cooling condition
哈兹列特连铸板坯的质量对终轧产品的性能有很大的影响。而哈兹列特双带凝固传热的数值模拟研究对提高连铸坯的表面质量、机械性能,改善微观组织非常重要,而且对哈兹列特利用余热进行热连轧节能非常有帮助。因此哈兹列特双带凝固传热的数值模拟研究非常有必要。
本文运用有限元法对哈兹列特连铸坯的凝固传热过程进行了数值模拟,在适当的假设条件下,建立了哈兹列特连铸过程的二维传热数学模型,并用热焓法建立了适用于固相、液相和固液两相区的统一能量方程。用热阻串联模型描述并计算了哈兹列特复杂的气隙层的传热,求解了哈兹列特连铸坯的凝固传热过程的两维稳态温度场,给出了连铸坯表面、中心以及连铸机出口处断面的温度分布,研究了不同过热度,连铸速度,双带涂层对哈兹列特连铸坯温度场的影响。数值计算结果表明：
(1)该传热模型比较全面的反映了哈兹列特连铸传热过程温度的变化、两相区和液芯长度的变化、坯壳的生长过程；
(2)连铸速度、双带涂层对两相区长度和铸坯温度变化,尤其是连铸机出口断面温度,有较大的影响,而过热温度则对坯壳形成位置有明显的影响；
(3)连铸速度、过热温度和双带涂层对连铸坯中心和表面的温差影响不大,它主要受双带冷却强度影响。
Hazelett twin-belt continuous casting and rolling process is absorbing more and more attention of aluminum alloy plate and strip producers of the world for its advantages, such as short procedure, low energy consumption, low production cost and high productivity. Environment-friendly and high productivity continuous casting and rolling process is becoming main trend of aluminum alloy plate and strip processes. The conventional DC casting/hot mill process route include melting and alloying, DC casting, sawing, surface milling, rolling ingot preheating, and hot rolling(both roughing and finishing). The hot rolled strip is subsequently cold rolled to finish gauge. With twin-roll casting, the steps include melting and alloying, casting and coiling. The strip is subsequently cold rolled to finish gauge. In the twin-belt process, casting is followed by in-line hot rolling to produce a hot rolled strip that is thinner than twin-roll cast strip, requiring less subsequent cold rolling.
The quality of Hazelett twin-belt continuous casting has big influence on the property of finished hot-rolled aluminum strip. The numerical simulation study on solidification and heat transfer of the twin-belt continuous casting is important to improve the surface quality, microstructure, and mechanical property of continuous casting aluminum strip and very helpful to take advantage of the heat in the as-cast strip to save energy and reduce the environmental impact, which is the biggest advantage of the Hazelett process. So it is very necessary to do some numerical simulation research on solidification and heat-transfer of Hazelett twin-belt continuous casting process.
In this paper, a two-dimensional heat-transfer model which considers a generalized energy equation that is valid for the solid, liquid, and mushy zones in the Hazelett continuous cast was developed to simulate the solidification and heat transfer of twin-belt continuous casting of aluminum alloy slab by the finite element method under some assumptions. The heat transfer of Hazelett caster mold interface was described by an overall thermal resistance model. The steady state temperature field during the continuous casting was computed and the temperature distribution of slab surface, center and continuous casting exit was also computed when casting was close to steady state. the influence of process parameters such as casting speed, superheat and belt coat on temperature distribution was investigated. The result of calculation indicated as follows:
(1) The Hazelett heat-transfer model built in this paper reflects mushy zone evolution, the length of liquid core and slab temperature distribution for the heat transformation process completely during Hazelett twin-belt continuous casting.
(2) Continuous casting speed and twin-belt coat have big influence on temperature field, especially twin-belt caster exit temperature, super heat has much influence on the formation position of shell
(3) Process parameters such as continuous casting speed, super heat, twin-belt coat have little influence on the temperature difference between center and surface of Hazelett casted slab, which is mainly influenced by twin-belt cooling condition
引文
[1]王戈,王祝堂.2007年中国铝加工工业述评[J].轻合金加工技术,2008,36(7)：1-5
[2]刘静安,尹晓辉.我国铝轧制工业的发展现状及与国际先进水平的差距(续)[J].有色金属加工,2008,37(2)：1-3
[3]张文竹,王祝堂.中国铝加工工业现状及发展趋势[J].中国金属通报,2006,6(24)：6-9
[4]程磊,谢水生,黄国杰.中国铝板带箔轧制工业的发展[J].轻合金加工技术,2007,35(11)：12-17
[5]苏鸿英,世界铝板带箔的生产工艺技术和装备现状[J].世界有色金属,2001,36(10)：12-18
[6]王祝堂,易敏.中国铝加工生产与市场一览[J].轻合金加工技术,2004,32(10)：1-5
[7]李宗耀.我国铝加工的生产技术与工艺装备现状及发展趋势[J].中国铝业,1999,18(9)：3-6
[8]钟掘.我国铝业发展的重大技术创新[J].2007铝型材技术(国际论坛文集),2007,中国·广州
[9]卢焕瑞.铝加工业节能问题[J].有色金属加工,2004,33(2)：12-15
[10]刘蒙,柴西林.中国铝工业炉节能减排分析及展望[J].冶金设备,2010,181(3)：67-72
[11]崔凤岐,王祝堂.中国、美国铝加工材产能地区分布结构[J].轻合金加工技术,2006,34(2)：1-4
[12]赵世庆.对我国铝加工产业发展战略的浅见与建议[J].铝加工,2006,168(3)：1-6
[13]翁利民.新形势下宏观政策对我国铝加工的影响[J].有色金属加工,2009,38(3)：6-9
[14]王祝堂,陈冬一,王仕越.最新变形铝及铝合金国际四位数字体系牌号及化学成分[J].轻合金加工技术,2008,36(10)：34-41
[15]肖亚庆主编.铝加工技术实用手册[M].北京：冶金工业出版社,2005
[16]中国航空材料编委会主编.中国航空材料手册[M].北京：冶金工业出版社,2005
[17]Hufnggel W. key to aluminum alloys, Designations Compositions Trade Names of Aluminum Materials 1st additional. Published by the Aluminum-Zentrale,1982
[18]Hatch J E. Aluminum Properties and Physical Metallurgy. ASM Metals Park,1984138
[19]Mondolfo L T. Aluminum Alloy Structure and Properties, Butterworths, London-Boston
[20]L. Zhuang, R. de Haan, J. Bottema, C. T. W. Lahaye and P. De Smet. Improvement in Bake Hardening Response of A1-Si-Mg Alloys[J], MaterialS Science Forum,2000 Vol.331-337:1309-1314
[21]马邦娟.铝电解与铝加工一体化发展实现共赢[J].有色金属加工,2004,33(2)：13-16
[22]肖翠萍.铝加工厂的节能新途径[J].铝加工,2005,37(6)：18-21
[23]陈策,王京海.铝合金热轧技术的发展[J].轻合金加工技术,2002,27(4)：25-28
[24]秋海滨,张明.铝铝合金双辊铸轧-热连轧方法.2008年全国铝合金熔炼技术交流会集,2008
[25]林敦熹.双辊快速连续铸轧超薄带坯技术进展[J].轻合金加工技术,2001,29(10)：14-17
[26]王祝堂.世纪回首铝带坯连铸连轧技术[J].轻合金加工技术,2001,29(5)：21-25
[27]马道章.哈兹列特工艺在铝板带连铸连轧应用中若干问题的探讨[J].铝加工,2005,162：18-24
[28]刘小玲,马道章.浅谈哈兹列特连铸技术在我国铝板带生产上的应用[J].上海有色属,2004,25(2)：77-82
[29]马道章.美国哈兹列特有色连铸技术的最新进展[J].上海有色金属,1999,20(1)：64-75
[30]Hazelett Strip-casting Corporation. Method of and molten metal feeder for continuous casting [P]. World Intellectual Property Organization:Wo 2006/089419A1,2006-08-31
[31]Hazelett Strip-casting Corporation. Method and apparatus for continuous casting of metal under controlled load conditions [P]. UK patent application:GB 2 086 281 A
[32]Hazelett Strip-casting Corporation. Steam preheating and endless flexible casting belt in a continuous casting machine [P]. UK patent application:GB 2 085 779 A
[33]Hazelett Strip-casting Corporation. Non-rotating, levitating, cylindrical air-pillow apparatus and method for supporting and guiding an endless flexible casiting belt into the entrance of a continuous metal-casting machine [P]. World Intellectual Property Organization:Wo 01/08835A1,2001-08-02
[34]Hazelett Strip-casting Corporation. Magnetized finned backup rollers for guiding and stabilizing an endless casting belt [P]. Canadian intellectual property office:CA 2 259 604 2005.7.6
[35]Hazelett Strip-casting Corporation. Improvements in or relating to coated metal casting-surfaces [P]. Patent specification:1 450 778
[36]Hazelett Strip-casting Corporation. Surface texturing of casting belts of continuous casting machines [P]. World Intellectual Property Organization:Wo 2005/032743,2005-04-14
[37]胡汉起主编.金属凝固原理[M].北京：机械工业出版社,1987
[38]胡宾宾,潘复生.铝合金铸锭凝固及热变形微观组织的预测与模拟现状[J].材料导报,2007,21(5)：349-353
[39]怀刚,李梅娥.基于有限差分网格的凝固模拟后处理研究[J].铸造,2005,52(5)：350-352
[40]王迎春,朱立光.连铸凝固传热全过程数值模拟与控制[J].特种铸造及有色合金,2005,25(9)：532-534
[41]严波,李欣.连铸结晶器内钢液凝固热传导有限元方法[J].重庆大学学报,2004,27(4)：114-117
[42]赵鑫,温泽峰.铸件凝固过程中温度场的数值模拟[J].西南交通大学学报,2006,41(1)：16-20
[43]B. Farouk, D. Apelian, A Numerical and Experimental Study of the Solidification Rate in a Twin-belt Caster[J]. Metallurgical and Materials Transactions, vol 23B,1992
[44]A. G.Gerber, A. C. M.Sousa. A Parametric Study of the Hazelett thin-slab Casting Process [J]. Materials Processing Technology,49(1995),41-56.
[45]Pedro G, Q. Netto, A Technique For the Evaluation of Instantaneous Heat Flux For the Horizontal Strip Casting Aluminum Alloys [J]. ISIJ International, Vol.41(2001).
[46]秦永健,孙国雄.双带式薄板连铸数值模拟[J].东南大学学报,1995,25(2)：35-41
[47]W.D. Beanon, E.P. lncorpera. A Continuum Model for Momentum, Heat and Species Transport in Binary Solid-Liquid Phase Change Systems--Model Formulation [J], Int. J. Heat Mass Transfer, Vol 30, No6,2162—2170,1987
[48]W.D. Beanon, E.P. Incorpera, A Continuum Model for Momentum, Heat and Species Transport in Binary Solid-Liquid Phase Change Systems--Application to solidifieation in a rectangular cavity[J]. Int.J. Heat Mass Transfer, Vol 30,No.6,2171-2187,1987
[49]R.I.L. Guthrie, R.P. Tavares, Mathematical and physical modelling of steel flow and solidification in twin-roll/horizontal belt thin-strip casting machines [J]. Applied Mathematical Modelling 22(1998) 851-872
[50]Yu-Chuan Miao, Xiao-Ming Zhang, Numerical simulation of the fluid flow, heat transfer, and solidification of twin-roll strip casting [J]. Journal of Materials Processing Technology,174 (2006)7-13
[51]S.M. Wang, Y.H. Kang, Analysis of flow and heat transfer in twin-roll strip casting by finite element method [J]. Trans. ASME--J. Eng. Ind.117 (1995) 304-315
[52]Y. Kim, B. Farouk, A mathematical model for thermal analysis of thin strip casting of low carbon steel [J]. Trans. ASME--J. Eng. Ind.113 (1991) 53-58
[53]R.W. Hazelett, The present status of continuous casting between moving flexible belts, [J]. Iron Steel Eng, (1966) 105-110.
[54]徐宏,侯华,赵宇宏.铝铸件凝固模拟边界热交换系数的测定[J].中国有色金属学报2003,13(4)：881-886.
[55]杜风山,张沛,许志强.铝铸锭凝固边界热交换规律及温度场模拟[J].中国有色金属学报,2007,17(11)：1750-1754.
[56]车芳,程常桂,物性参数对连铸结晶器传热模型计算结果的影响[J].过程工程学报2010,10(1)：26-31
[57]刘旭东,朱苗勇,连铸凝固传热过程钢的热物性参数分析,第十四届全国炼钢学术议文集
[58]高思云.基于热传导反问题的材料热物性预测方法研究[D].硕士学位论文,重庆大学2005.
[59]姜华,张佳秋,铸造材料热物性参数数据库[J].第61届世界铸造会议论文集,1995
[60]张伟,周建新,凝固模拟热物性参数数据库系统的研究与开发[J].铸造技术,2004,26(11)：1072-1074
[61]王向群,刘瑞祥,铸造CAE热物性参数数据库的开发与设计[J].中国铸造装备与技术,1(2004)
[62]Jyrki M, Seppo L, Coupled Simulation of Heat of Transfer and Phase Transformation in Continuous Casting Steel [J]. ISIJ International,1996,36,183-186
[63]Lally B, Bieger L, Finite difference heat-transfer modeling for continuous casting [J]. Metal Trans B,1990,21 B(2).761-770
[64]F. Kavicka, J. Stetina, The optimization of a concasting technology by two numerical models [J]. Materials Processing Technology,185 (2007) 152-159
[65]Lei Zhang, Hou-Fa Shen, Numerical simulation on solidification and thermal stress of continuous casting billet in mold based on meshless methods [J]. Materials Science and Engineering A 466 (2007) 71-78
[66]X.Q. Kong, Application of FEM in Heat Transfer Process[J]. Science Press, Beijing,1998
[67]杨永昌,关绍康,陈斌斌,哈兹列特连铸连轧3003铝合金板带组织和性能研究[J].轻合金加技术,2010,38(10)：15-18
[68]A.G.Gerber, A.C.M.Sousa, Numerical Investigation of the Influence of Air Gaps Uponthe Solidification in a Rotary Caster [J]. Materials Processing Technology 48, (1995) 657-665
[69]Kaiho, Robert D. Pehlke. Metal-Mold Interracial Heat Transfer [J].Metallurgical Transaction B,1985, Vol 16B:585.594.
[70]竹励萍,金属型铸造凝固过程铸件/铸型界面换热系数的研究[D].硕士学位论文,天津理工大学,2009
[2]刘静安,尹晓辉.我国铝轧制工业的发展现状及与国际先进水平的差距(续)[J].有色金属加工,2008,37(2)：1-3
[3]张文竹,王祝堂.中国铝加工工业现状及发展趋势[J].中国金属通报,2006,6(24)：6-9
[4]程磊,谢水生,黄国杰.中国铝板带箔轧制工业的发展[J].轻合金加工技术,2007,35(11)：12-17
[5]苏鸿英,世界铝板带箔的生产工艺技术和装备现状[J].世界有色金属,2001,36(10)：12-18
[6]王祝堂,易敏.中国铝加工生产与市场一览[J].轻合金加工技术,2004,32(10)：1-5
[7]李宗耀.我国铝加工的生产技术与工艺装备现状及发展趋势[J].中国铝业,1999,18(9)：3-6
[8]钟掘.我国铝业发展的重大技术创新[J].2007铝型材技术(国际论坛文集),2007,中国·广州
[9]卢焕瑞.铝加工业节能问题[J].有色金属加工,2004,33(2)：12-15
[10]刘蒙,柴西林.中国铝工业炉节能减排分析及展望[J].冶金设备,2010,181(3)：67-72
[11]崔凤岐,王祝堂.中国、美国铝加工材产能地区分布结构[J].轻合金加工技术,2006,34(2)：1-4
[12]赵世庆.对我国铝加工产业发展战略的浅见与建议[J].铝加工,2006,168(3)：1-6
[13]翁利民.新形势下宏观政策对我国铝加工的影响[J].有色金属加工,2009,38(3)：6-9
[14]王祝堂,陈冬一,王仕越.最新变形铝及铝合金国际四位数字体系牌号及化学成分[J].轻合金加工技术,2008,36(10)：34-41
[15]肖亚庆主编.铝加工技术实用手册[M].北京：冶金工业出版社,2005
[16]中国航空材料编委会主编.中国航空材料手册[M].北京：冶金工业出版社,2005
[17]Hufnggel W. key to aluminum alloys, Designations Compositions Trade Names of Aluminum Materials 1st additional. Published by the Aluminum-Zentrale,1982
[18]Hatch J E. Aluminum Properties and Physical Metallurgy. ASM Metals Park,1984138
[19]Mondolfo L T. Aluminum Alloy Structure and Properties, Butterworths, London-Boston
[20]L. Zhuang, R. de Haan, J. Bottema, C. T. W. Lahaye and P. De Smet. Improvement in Bake Hardening Response of A1-Si-Mg Alloys[J], MaterialS Science Forum,2000 Vol.331-337:1309-1314
[21]马邦娟.铝电解与铝加工一体化发展实现共赢[J].有色金属加工,2004,33(2)：13-16
[22]肖翠萍.铝加工厂的节能新途径[J].铝加工,2005,37(6)：18-21
[23]陈策,王京海.铝合金热轧技术的发展[J].轻合金加工技术,2002,27(4)：25-28
[24]秋海滨,张明.铝铝合金双辊铸轧-热连轧方法.2008年全国铝合金熔炼技术交流会集,2008
[25]林敦熹.双辊快速连续铸轧超薄带坯技术进展[J].轻合金加工技术,2001,29(10)：14-17
[26]王祝堂.世纪回首铝带坯连铸连轧技术[J].轻合金加工技术,2001,29(5)：21-25
[27]马道章.哈兹列特工艺在铝板带连铸连轧应用中若干问题的探讨[J].铝加工,2005,162：18-24
[28]刘小玲,马道章.浅谈哈兹列特连铸技术在我国铝板带生产上的应用[J].上海有色属,2004,25(2)：77-82
[29]马道章.美国哈兹列特有色连铸技术的最新进展[J].上海有色金属,1999,20(1)：64-75
[30]Hazelett Strip-casting Corporation. Method of and molten metal feeder for continuous casting [P]. World Intellectual Property Organization:Wo 2006/089419A1,2006-08-31
[31]Hazelett Strip-casting Corporation. Method and apparatus for continuous casting of metal under controlled load conditions [P]. UK patent application:GB 2 086 281 A
[32]Hazelett Strip-casting Corporation. Steam preheating and endless flexible casting belt in a continuous casting machine [P]. UK patent application:GB 2 085 779 A
[33]Hazelett Strip-casting Corporation. Non-rotating, levitating, cylindrical air-pillow apparatus and method for supporting and guiding an endless flexible casiting belt into the entrance of a continuous metal-casting machine [P]. World Intellectual Property Organization:Wo 01/08835A1,2001-08-02
[34]Hazelett Strip-casting Corporation. Magnetized finned backup rollers for guiding and stabilizing an endless casting belt [P]. Canadian intellectual property office:CA 2 259 604 2005.7.6
[35]Hazelett Strip-casting Corporation. Improvements in or relating to coated metal casting-surfaces [P]. Patent specification:1 450 778
[36]Hazelett Strip-casting Corporation. Surface texturing of casting belts of continuous casting machines [P]. World Intellectual Property Organization:Wo 2005/032743,2005-04-14
[37]胡汉起主编.金属凝固原理[M].北京：机械工业出版社,1987
[38]胡宾宾,潘复生.铝合金铸锭凝固及热变形微观组织的预测与模拟现状[J].材料导报,2007,21(5)：349-353
[39]怀刚,李梅娥.基于有限差分网格的凝固模拟后处理研究[J].铸造,2005,52(5)：350-352
[40]王迎春,朱立光.连铸凝固传热全过程数值模拟与控制[J].特种铸造及有色合金,2005,25(9)：532-534
[41]严波,李欣.连铸结晶器内钢液凝固热传导有限元方法[J].重庆大学学报,2004,27(4)：114-117
[42]赵鑫,温泽峰.铸件凝固过程中温度场的数值模拟[J].西南交通大学学报,2006,41(1)：16-20
[43]B. Farouk, D. Apelian, A Numerical and Experimental Study of the Solidification Rate in a Twin-belt Caster[J]. Metallurgical and Materials Transactions, vol 23B,1992
[44]A. G.Gerber, A. C. M.Sousa. A Parametric Study of the Hazelett thin-slab Casting Process [J]. Materials Processing Technology,49(1995),41-56.
[45]Pedro G, Q. Netto, A Technique For the Evaluation of Instantaneous Heat Flux For the Horizontal Strip Casting Aluminum Alloys [J]. ISIJ International, Vol.41(2001).
[46]秦永健,孙国雄.双带式薄板连铸数值模拟[J].东南大学学报,1995,25(2)：35-41
[47]W.D. Beanon, E.P. lncorpera. A Continuum Model for Momentum, Heat and Species Transport in Binary Solid-Liquid Phase Change Systems--Model Formulation [J], Int. J. Heat Mass Transfer, Vol 30, No6,2162—2170,1987
[48]W.D. Beanon, E.P. Incorpera, A Continuum Model for Momentum, Heat and Species Transport in Binary Solid-Liquid Phase Change Systems--Application to solidifieation in a rectangular cavity[J]. Int.J. Heat Mass Transfer, Vol 30,No.6,2171-2187,1987
[49]R.I.L. Guthrie, R.P. Tavares, Mathematical and physical modelling of steel flow and solidification in twin-roll/horizontal belt thin-strip casting machines [J]. Applied Mathematical Modelling 22(1998) 851-872
[50]Yu-Chuan Miao, Xiao-Ming Zhang, Numerical simulation of the fluid flow, heat transfer, and solidification of twin-roll strip casting [J]. Journal of Materials Processing Technology,174 (2006)7-13
[51]S.M. Wang, Y.H. Kang, Analysis of flow and heat transfer in twin-roll strip casting by finite element method [J]. Trans. ASME--J. Eng. Ind.117 (1995) 304-315
[52]Y. Kim, B. Farouk, A mathematical model for thermal analysis of thin strip casting of low carbon steel [J]. Trans. ASME--J. Eng. Ind.113 (1991) 53-58
[53]R.W. Hazelett, The present status of continuous casting between moving flexible belts, [J]. Iron Steel Eng, (1966) 105-110.
[54]徐宏,侯华,赵宇宏.铝铸件凝固模拟边界热交换系数的测定[J].中国有色金属学报2003,13(4)：881-886.
[55]杜风山,张沛,许志强.铝铸锭凝固边界热交换规律及温度场模拟[J].中国有色金属学报,2007,17(11)：1750-1754.
[56]车芳,程常桂,物性参数对连铸结晶器传热模型计算结果的影响[J].过程工程学报2010,10(1)：26-31
[57]刘旭东,朱苗勇,连铸凝固传热过程钢的热物性参数分析,第十四届全国炼钢学术议文集
[58]高思云.基于热传导反问题的材料热物性预测方法研究[D].硕士学位论文,重庆大学2005.
[59]姜华,张佳秋,铸造材料热物性参数数据库[J].第61届世界铸造会议论文集,1995
[60]张伟,周建新,凝固模拟热物性参数数据库系统的研究与开发[J].铸造技术,2004,26(11)：1072-1074
[61]王向群,刘瑞祥,铸造CAE热物性参数数据库的开发与设计[J].中国铸造装备与技术,1(2004)
[62]Jyrki M, Seppo L, Coupled Simulation of Heat of Transfer and Phase Transformation in Continuous Casting Steel [J]. ISIJ International,1996,36,183-186
[63]Lally B, Bieger L, Finite difference heat-transfer modeling for continuous casting [J]. Metal Trans B,1990,21 B(2).761-770
[64]F. Kavicka, J. Stetina, The optimization of a concasting technology by two numerical models [J]. Materials Processing Technology,185 (2007) 152-159
[65]Lei Zhang, Hou-Fa Shen, Numerical simulation on solidification and thermal stress of continuous casting billet in mold based on meshless methods [J]. Materials Science and Engineering A 466 (2007) 71-78
[66]X.Q. Kong, Application of FEM in Heat Transfer Process[J]. Science Press, Beijing,1998
[67]杨永昌,关绍康,陈斌斌,哈兹列特连铸连轧3003铝合金板带组织和性能研究[J].轻合金加技术,2010,38(10)：15-18
[68]A.G.Gerber, A.C.M.Sousa, Numerical Investigation of the Influence of Air Gaps Uponthe Solidification in a Rotary Caster [J]. Materials Processing Technology 48, (1995) 657-665
[69]Kaiho, Robert D. Pehlke. Metal-Mold Interracial Heat Transfer [J].Metallurgical Transaction B,1985, Vol 16B:585.594.
[70]竹励萍,金属型铸造凝固过程铸件/铸型界面换热系数的研究[D].硕士学位论文,天津理工大学,2009