方向性凝固之鑄件微結構是沿著某一方向固定成長，本研究則希望利用數值分法分析其凝固過程之溫度場的變化情形。於此分析中，鑄件與模具間的界面熱傳性質的不確定問題會影響到分析的結果，所以本文利用Beck逆運算法與實驗溫測數據來計算鑄件與模具間的界面熱傳係數，再使用此界面熱傳係數來進行溫度場的模擬。
在本研究之實驗中，使用錫鉛(Sn-90wt％ Pb)合金針對不同的模具、加熱器溫度、冷激銅盒溫度及載台下降速率來進行方向性凝固，並觀察其凝固的巨觀微觀金相組織、量取冷卻曲線、估算溫度梯度及分析鑄件離開加熱區時間。
根據實驗溫測數據，以有限差分法與Beck逆運算法求得在鑄件四周沿軸向與徑向之界面熱傳係數，再依此界面熱傳係數，去計算鑄件凝固時的溫度場變化，並與實驗值作比較。從計算與實驗結果作比較，發現到達液相線與共晶溫度的時間是差不多的，同時兩者之冷卻曲線也很接近，因此本研究所建立的方法用來預測界面熱傳係數並估算溫度場是可行的。

In the directional solidification, the solidified microstructure grows along a fixed direction. The study is to numerically analyze the temperature variation during the solidification process. In the analysis, the uncertainty of the heat transfer condition between the mold and casting will influence the analysis results. Accordingly, in this thesis, the Beck inverse method with the experimentally temperature-measured data is applied to calculate the interfacial heat transfer coefficients and then the coefficients are used to simulate the temperature fields.

In the research, the Sn-90wt%Pb alloy is used as the testing material. Different mold materials, heater and copper-chill temperatures and the descending speeds of the platform are utilized for the experiments of directional solidification. In the study, the macro- and micro-structures are observed, the cooling curves are measured, the axial temperature gradients are estimated and the departure time of the casting from the heating zone is analyzed.

Based on the experimentally measured temperatures, the finite difference method and the Beck inverse scheme are employed to predict the interfacial heat transfer coefficients of the casting along the axial and radial directions. With the coefficients, the temperature distributions of the casting are computed during the solidification processes, which are compared with the experimental ones. From the comparison results, it can be found that the computed arrival times of liquidus and eutectic temperatures are very similar to those taken from the experiments. The computed cooling curves are also very close to the ones measured in the experiments. Consequently, it is feasible to use the method set up in the study to predict the interfacial heat transfer coefficients and to calculate the temperature distributions of the casting during the directional solidification processes.

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