方向性凝固於鑄造中占有重要地位，然吾人通常難以知悉金屬與模壁間之熱傳率及其變化，故鑄件品質多半靠經驗掌握，研發過程往往耗費較高成本。
　　本文將金屬與模壁間的熱傳行為視作金屬邊界之等效熱傳係數的表現，使用逆運算法，探討其於凝固過程中的變化；透過設計控制方向性凝固為單一熱傳方向主導，使得計算上可以一維問題近似之。
　　由於逆運算法需以直接問題的解答作基礎，為確保結果可信，針對無相變化之暫態熱傳問題、史蒂芬問題，與理想澆鑄的情況做模擬分析，證明逆運算法與直接問題的求解正確。
　　如研究結果顯示，本研究成功估測鑄件上部邊界與下部邊界之等效熱傳係數，並推得相對應之金屬表面熱通量。此外，本文亦對逆運算過程所遭遇的現象提出解釋。
　　總體而言，本研究提供關於逆向估測等效熱傳係數之重要探悉，有助日後鑄造相關研究之發展。

　　The variation of the rate of heat-transfer between the metal and mold during directional solidification is still unclear. It forces one to manage the casting quality based on experiences and results in high cost.
　　In the thesis, the heat transfer behavior mentioned above is regarded as the action of the effective heat transfer coefficient on the boundary of the metal and the coefficient is analyzed by using an inverse method. Owing to the experimental design of axially directional solidification, the numerical simulation could employ one-dimensional approximation.
　　The solution of the direct problem is the foundation stone of solving the inverse problem. To ensure the reliability, the transient heat conduction problem without phase change, the Stefan problem and an ideal casting case are numerically studied first. Afterward, the inverse problems of predicting the heat transfer coefficients for the previous problems are investigated. Finally, the inverse method is used to analyze the heat transfer coeffients of directional solidification experiments.
　　The results demonstrate the estimated effective heat transfer coefficients on both upper and lower boundary of the pure metal, and show not only the corresponding surface heat fluxes but also the surface temperatures. Furthermore, some explanations of the phenomena encountered in the research process are proposed.
　　In brief, this thesis presents details of estimating effective heat transfer coefficients, which is expected to be helpful to the further relevant studies of casting problems.

[1] W. Kurz and D.J. Fisher, “Fundamental of Solidification”, Trans Tech Publications, Switzerland, 1998.
[2] 張晉昌，“鑄造學”，全華科技圖書股份有限公司，民78。
[3] OMEGA, “Operator’s Manual of OS-650 Series”.
[4] J. V. Beck, B. Blackwell, and C. R. St. Clair, Jr., “Inverse Heat Conduction: Ill-posed Problems”, Wiley, 1985.
[5] N. V. Shumakov, “A Method for the Experiment Study of the process of Heating a Solid Body”, Soviet Physics-Technical Physics, vol. 2, p. 771, 1957.
[6] G. Stolz, Jr., “Numerical Solutions to an Inverse Problem of Heat Conduction for Simple Shapes”, J Heat Transfer 82, 20-26, 1960.
[7] M. N. Özişik, “Heat Conduction”, Wiley, Second Edition 1993.
[8] J. Hadamard, “Sur les problèmes aux dérivées partielles et leur signification physique”, Princeton University Bulletin, pp. 49–52, 1902.
[9] M. N. Özişik, H. R. B. Orlande, “Inverse Heat Transfer: Fundamentals and Applications”, Taylor & Francis, 2000.
[10] H. C. Sun and L. S. Chao, “An Investigation into the Effective Heat Transfer Coefficient in the Casting of Aluminum in a Green-Sand Mold”, Materials Transactions, Vol. 50, No. 6, pp. 1396 to 1403, 2009.
[11] K. A. Hoffmann and S. T. Chiang, “Computational Fluid Dynamics for Engineers”, Engineering Education System, 1993.
[12] 郭晉凱，“混合拉氏轉換法求解相變化熱傳問題”，成功大學工程科學系碩博士班學位論文，民98。
[13] J. A. Dantzig, “Modelling Liquid-Solid Phase Changes with Melt Convection”, International Journal for Numerical Methods in Engineering, Volume 28, Issue 8, pages 1769–1785, August 1989.
[14] Y. C. Liu and L. S. Chao, “Modified Effective Specific Heat Method of Solidification Problems”, Materials Transactions, Vol. 47, No. 11, pp. 2737 to 2744, 2006.
[15] J. V. Beck and K. J. Arnold, “Parameter estimation in Engineering and Science”, John Wiley & Sons, 1977.
[16] 孫憲琪，“濕砂模與金屬界面之熱傳模式研究暨鑄造充填的模擬分析”，成功大學工程科學系碩博士班學位論文，民98。
[17] W. Donald Rolph III, Klaus-JÜRgen Bathe, “An Efficient Algorithm for Analysis of Nonlinear Heat Transfer with Phase Changes”, International Journal for Numerical Methods in Engineering, Volume 18, Issue 1, pages 119–134, January 1982.
[18] J. Stefan, “Ueber die Theorie der Eisbildung, insbesondere über die Eisbildung im Polarmeere”, Annalen der Physik, Volume 278, Issue 2, pages 269–286, 1891.
[19] N. B. Vargaftik, Y. K. Vinogradov, V. S. Yargin, “Handbook of physical properties of liquids and gases : pure substances and mixtures”, New York, Begell House, 1996.
[20] D. R. Lide, H. V. Kehiaian, “CRC handbook of thermophysical and thermochemical data”, Boca Raton, CRC Press, 1994.
[21] Y. A. Çengel, “Heat and mass transfer: a practical approach”, McGraw-Hill, 2007.
[22] Z. X. Gong and A. S. Mujumdar, “Non-convergence versus non-conservation in effective heat capacity methods for phase change problems”, International Journal of Numerical, Methods for Heat & Fluid Flow, Vol. 7 No. 6, 1997, pp. 565-579.
[23] J. V. Beck , “Surface heat flux determination using an integral method”, Nuclear Engineering and Design, Volume 7, Issue 2, February 1968, Pages 170-178.
[24] A. M. Osman, K. J. Dowding and J. V. Beck, “Numerical Solution of the General Two-Dimensional Inverse Heat Conduction Problem”, J. Heat Transfer, Vol. 119, February 1997, pp. 38-45.
[25] 蕭美枝，“逆運算法在生物熱傳邊界估算之研究”，工程科技與教育學刊，第五卷，第四期，民97十二月，第617-628頁。
[26] 陳毓儒，“金屬之熱傳導係數預測”，中華民國第二十七屆力學會議，2003十二月。
[27] R. I. L. Guthrie, M. Isac, J. S. Kim, and R. P. Tavares, “Measurements, simulations, and analyses of instantaneous heat fluxes from solidifying steels to the surfaces of twin roll casters and of aluminum to plasma-coated metal substrates”, Metallurgical and Materials Transactions B, October 2000, Volume 31, Issue 5, pp. 1031-1047.
[28] D. O'Mahoney and D.J. Browne, “Use of experiment and an inverse method to study interface heat transfer during solidification in the investment casting process”, Experimental Thermal and Fluid Science, Volume 22, Issues 3-4, September 2000, Pages 111-122
[29] C.H. Huang, M.N. Özişik, and B. Sawaf, “Conjugate gradient method for determining unknown contact conductance during metal casting”, International Journal of Heat and Mass Transfer, Volume 35, Issue 7, July 1992, Pages 1779-1786.
[30] 紀欽仁，“逆向熱傳方法之材料熱性質預測”，成功大學工程科學系碩博士班學位論文，民87。
[31] 王惠森，曾樺玲，黃文星，與葉俊麟，“高溫合金鋼在砂模及陶模鑄造過程中界面熱傳係數之量測”，鑄造工程學刊，2003六月，第29卷，第2期(第177期)，第67-76頁。
[32] 林世銘，“應用循次算則於逆向熱傳問題之研究”，成功大學機械工程學系碩博士班學位論文，民93。