方向性凝固是工業界相當重要的製程技術，由於一般難以量測鑄件與模壁間之熱通量及其暫態變化，若要得到精確的物理量，則必須付出成本高的代價，故鑄件品質都半靠經驗掌握。
本研究針對純錫及錫鉛合金(Sn-10wt%.Pb)，透過逆運算法及多段式總容量法搭配實驗數據來估算其於方向性凝固過程中界面熱傳係數隨時間的變化。為確保其估算結果具有可行性，首先進行無相變化暫態熱傳問題的計算，其次在求解含有相變化的史蒂芬問題、紐曼問題，最後再將上述問題作延伸估算界面熱傳係數及求解溫度場。
金相試驗在材料評估的工作上扮演著重要的角色，為提高材料之使用壽命，本研究利用冷激銅盒提供一軸向溫度梯度，使晶粒成長為沿著熱通量方向生長的柱狀晶。此外透過實驗量測之溫度數據，繪製冷卻曲線圖、溫度梯度圖、各位置離開加熱區時間及凝固時間關係圖，並搭配巨觀顯微組織、微觀金相組織，探討上述參數對晶體形態、底部等軸晶產生區、優選方向競爭區、晶粒成長區、頂部空氣接觸區大小之影響。
由結果顯示，模擬值與實驗值差異極小，推論逆運算法及總容量法求解含有相變化的問題有良好的估算結果。

Directional solidification is a very important industrial manufacturing technology. Because it is difficult to measure the heat flux transferred from the casting to its mold, the heat-transfer estimation needs theoretical methods and numerical simulations. In the study, the Beck inverse and the lumped capacitance methods are applied to experimentally measured temperatures for predicting the interfacial heat transfer coefficient between the casting and its mold. To ensure the feasibility of the numerical analysis, some tested problems with known solutions are used, such as the Stefan and Neumann problems. In the numerical analysis, the effective specific heat method and the enthalpy/effective specific heat scheme are employed to deal with the latent-heat release of phase change. Besides, the effects of experimental parameters on the morphology of crystals are also investigated. From the results, it can be found that the resulting temperature distributions with the estimated the interfacial heat transfer coefficients are consistent with the temperature measurements.

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