在精細金屬線條的連鑄過程中，影響鑄件品質的因素很多，所以有必要對不同的操作條件作影響評估。針對此目標，本研究建立一穩態的數學模式來模擬精細金屬之連鑄過程的熱傳行為，物理模型包含石墨模與模內以固定鑄造速度移動之金屬材料。數值方法是使用有限差分法，以等效比熱-熱焓法來處理凝固時潛熱釋放的問題，於電腦程式之建立中，使用史蒂芬問題來驗證凝固模式之數值計算的正確性。本文依此建立的模式，針對不同之鑄造條件（鑄造速度、冷卻效應、金屬材料等），來作分析比較，並將溫度計算結果代入套裝軟體ANSYS，來做熱應力分析。由計算結果發現鑄造速度越快，沿軸向之溫度下降會越減緩，而且液體轉變成固體的深度會越深。冷卻速率越大，最後拉出石墨模的金屬線條的溫度會越低，但金屬線條上端的溫度梯度還是一樣的，到了金屬線條中後端溫度才有改變。至於金屬部份，以純銀的出口溫度最低，而純銅的液體轉變成固體的深度會最淺。

　In the continuous casting process of metal wire rod, many factors influence the casting quality, so it is necessary to evaluate the effects of different operation conditions. To achieve this object, a mathematical model of steady state was built in this paper to simulate the heat transfer of the continuous casting of metal wire rod. The physical model includes graphite mold and the metal in the mold with a constant casting speed. The numerical method is the finite difference method and the effective specific heat/enthalpy method is used to handle the release of latent heat during solidification. The accuracy of the computer program was verified by testing the Stefan problem. With the proposed model, different working conditions (different casting speeds, cooling effects and materials) were analyzed. The computing results of the temperature field were put into the commercial package ANSYS to do the analysis of thermal stress. From the computing results, it can be found that the increase of casting speed makes the decrease of temperature along the axial direction slower and the depth of liquid/solid interface larger. The bigger cooling rate makes the outlet temperature of metal from the graphite mold lower. For copper, silver and gold metals, silver has the lowest outlet temperature and copper has the smallest depth of solid/liquid interface.

參考文獻
1. J. S. Hsiao, "An Efficient Algorithm for Finite Difference Analysis of Heat Transfer with Melting and Solidification," Numerical Heat Transfer, Vol. 8, pp. 653-666, 1985.
2. J. A. Dantzig, “Modeling Liquid-Solid Phase Changes with Melt Convection”, International Journal of Numerical Methods in Engineering V28, n8, pp. 1769-1785, August 1989.
3. 張建宏，”多晶矽薄膜製程之研究” 國立成功大學工程科學研究所碩士論文，2002。
4. J. P. Holman, “ Heat transfer,” 9th edition, Mcgraw-Hill company, New York, USA, 2002.
5. M. Uoti, M. Immonen, and K. Harkki, “Theoretical and Experimental Study of Vertical Continuous Casting of Copper.”
6. R. Wilson, “A Practical Approach to Continuous Casting of Copper-Based Alloys and Precious Metals,” IOM Communication Ltd., London, UK, 2000.
7. 何永和，”連鑄模中操作條件影響鋼液清淨度的數值模擬及驗證” 國立成功大學材料科學及工程學系博士論文，1998。
8. D.A. Anderson, J. C. Tannehill, and R.H. Pletcher, Computational Fluid Mechanics and Heat Trandfer, Hemisphere, Washington D.C.,U.S.A.,1984
9. S. Louhenkilpi, E. Laitinen, and R. Nieminen, “Real-Time simulation of heat Transfer in Continuous Casting”, Metallurgical Transactins B, Vol. 24B, 1993, PP. 685-693.
10. C. H Kuo, M. J. Lu, and Y. H. Chung, “Optimization of Air-Water Mist Cooling of Slab During Continuous Casting Process”, China steel Technical Report. No. 5, 1991, pp. 74-83.
11. H. C. Huang, Y. H. Chung, K. J. Lin, and Y. P. Chen, “A Continuous Casting Model of Air-Mist Cooling for Slab”, Symposium Proceedings on Transport Phenomena and Applications, Taipei, 1990, pp. 197-202.
12. S. K. Choudhary, D. Mazumdar, and A. Ghosh, “Mathematical Modeling of Heat Transfer Phenomena in Continuous Casting of Steel”, ISIJ International, Vol. 33, No. 7, 1993, pp. 764-774.
13. S. Lougenkilpi, “Modelling of Heat Transfer in Continuous Casting”, Materials Science Forum, Vol. 414-415, 2003, pp. 445-454.
14. B. Q. Li, P. N. Anualebechi, “A Micro/Macro Model for Fluid Flow Evolution and Microstructure Formation in Solidification Process”, Int. J. Heat. Mass. Transfer. Vol. 38, No. 13, 1995, pp.2367-2381.
15. J. M. Rodriguez, A. Esteva, S. Meza, “A Note on the Control of the Solidification Front in the Continusous Casting of Copper tubes”, Journal of Materials Processing Technology 96, 1996, pp. 42-47.