本研究選擇自行澆鑄之錫、鋁等金屬圓柱做為材料，並將外層包覆低熱導率玻璃纖維，使徑向熱散失最小化，達成軸向一維熱傳。為確保各逆運算(Beck逆算法及Yang逆運算法)模型正確，透過一維暫態熱傳問題之解析解與數值解進行反算，觀察結果是否合理。
將材料各別以不同功率進行加熱，並配合熱電偶紀錄金屬件中心溫度，隨後先將記錄溫度代入Beck逆算法及Yang逆運算法反算出邊界熱通量及比熱，再將其值以固定邊界條件形式代入Beck逆算法及Yang逆運算法模型中反算出熱傳導係數並和理論值做比對。本研究亦藉由觀察結果找出實驗誤差的原因及探討。
由結果可知，利用Beck逆算法及Yang逆運算法估算熱傳導係數各有其優缺點，其中Beck逆運算法的收斂速度較為優秀，Yang逆運算法則較能承受複雜的實驗環境。本研究為一維熱傳模式，故對於徑向熱傳之估算會有所缺失。

In this study, self-cast tin, aluminum, are selected as materials, and the outer layer is covered with low thermal conductivity glass fiber to minimize radial heat loss and achieve axial one-dimensional Heat transfer. In order to ensure the correctness of the inverse calculations (Beck Inverse Method and Yang Inverse Method) models, inverse calculations are carried out through the analytical and numerical solutions of the one-dimensional transient heat transfer problem to observe whether the results are reasonable.
Heat the materials with different powers(5,7.5,10W), and use thermocouples to record the center temperature of the metal parts. Then first substitute the recorded temperature into the Beck Inverse Method and the Yang Inverse Method to inversely calculate the boundary heat flux or specific heat, and then use the value to fix the thermal properties. The form is substituted into the Beck Inverse Method and the Yang Inverse Method to inversely calculate the heat transfer coefficient and compare with the theoretical value.
It can be seen from the results that the Beck Inverse Method and the Yang Inverse Method have good accuracy in estimating the thermal conductivity, Beck Inverse Method is more prominent in stability, Yang Inverse Method is more prominent in accuracy. However, this study is a one-dimensional heat transfer model, so the estimation of radial heat transfer will be lacking.

[1] J. V. Beck, Inverse heat conduction: Ill-posed problems, 1st ed., Wiley, Oct 1985.
[2] M. Necati Ozisik, Inverse Heat Transfer:Fundamentals and Applications, 1st ed., CRC, Apr 2000.
[3] K. Kurpisz and A.J. Nowak, Inverse thermal problems, WIT, Aug 1995
[4] Y. A. Cengel. Heat and mass transfer: a practical approach, McGraw-Hill, 2007.
[5] N. Shumakov,”A method for the experimental study of the process of heating a solid body,”Soviet Physics-Technical Physics, vol.2,pp.771-781,1957.
[6] G. Stolz,”Numerical solutions to an inverse problem of heat conduction for simple shapes,”Journal of heat transfer,vol.82,pp.20-25,1960.
[7] J. V. Beck,’’Calculation of suface Heat Flux from an Integral Temperature History,’’ASME Paper 62-HT-46 1962.
[8] E. Sparrow,A.Haji-Sheikh,and T.Lundgren,”The inverse problem in transient heat conduction,”Journal of Applied Mechanics,vol.31,pp.369-375,1964.
[9] J. V. Beck,”Surface heat flux determination using an integral method,”Nuclear Engineering and Design,vol.7,pp.170-178,1968.
[10] J. V. Beck,”Nonlinear estimation applied to the nonlinear inverse heat conduction problem,”International Journal of Heat and Mass Transfer,vol.13,pp.703-716,1969.
[11] Y. Jarny,M. Ozisik,and J. Bardon,”A general optimization method using adjoint equation for solving multidimensional inverse heat conduction,” International Journal of Heat and Mass Transfer,vol.34,pp.2911-2919,1991.
[12] A. Abbas Nejad,M. J. Maghrebi,H. Basirat Tabrizi,Y. Heng,A. Mhamdi,and W. Marquardt,”Optimal operation of alloy material on solidification process with inverse heat transfer,” International Communication in Heat and Mass Transfer,vol.37,pp.771-716,2010.
[13] M. Martorano and J. Capocchi,”Heat transfer coefficient at the metal-mould interface in the unidirectional solidification of Cu-8% Sn alloys,” International Journal of Heat and Mass Transfer,vol.43,pp.2541-2552,2000.
[14] 紀欽仁,”逆向熱傳方法之材料熱性質預測,” 國立成功大學工程科學所碩士論文, 1998.
[15] 郭孟遠,”材料凝固熱性質之估算,” 國立成功大學工程科學所碩士論文, 1999.
[16] 林立勝,”凝固熱性質之估算,” 國立成功大學工程科學所碩士論文, 2000.
[17] 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.
[18] 陳佩宜,”方向性凝固之界面熱傳與溫度場分析,” 國立成功大學工程科學所碩士論文, 2011.
[19] 施冠呈, "方向性凝固之金屬邊界等效熱傳係數的逆向分析," 國立成功大學工程科學所碩士論文, 2013.
[20] 徐意庭,”以逆運算法與總容量法估算錫鉛合金方向性凝固之界面熱傳係數,” 國立成功大學工程科學所碩士論文, 2014.
[21] 謝其丞,”以逆運算法估算錫棒與鋁棒之邊界熱通量,” 國立成功大學工程科學所碩士論文, 2019.
[22] 連振亦,”以逆運算法估算金屬熱性質,” 國立成功大學工程科學所碩士論文, 2020.