相變化在凝固過程中為一個很重要的物理現象，當中所涉及的潛熱效應是需要被重視的。本文主要目的為利用有限元素法搭配不同處理潛熱的數值方法，來分析相變化熱傳問題中的溫度場分布。
主要探討的凝固問題為一維史帝芬問題及二維Rathjen問題，並利用兩種處理潛熱的數值方法，等效比熱法與等效比熱/熱焓法來分析並比較其準確性與計算時間。分析結果發現，等效比熱/熱焓法不僅在計算時間上比等效比熱法還要快速，在處理潛熱效應也能提供更佳的準確性。
對於不同形狀的元素、不同積分方式以及不同點數的積分點加以討論，更進一步比較其總誤差(total-error)，可發現利用閉合式積分求解凝固問題效果並非理想，而利用四邊形元素求解凝固問題更能有效地得到比三角形元素還要好得精準度及誤差值。

Phase-change in a solidification process is a very important physical phenomenon, in which the latent-heat effect cannot be ignored. In the thesis, the finite element method with different numerical schemes of handling the latent-heat effect is used to analyze the temperature distributions of phase-change heat transfer problems.

In the work, the one-dimensional Stefan and the two-dimensional Rathjen problems are numerically studied. The effective specific heat and the specific heat/enthalpy methods are employed to deal with the latent-heat effect and the accuracy and CPU time of these schemes are compared and analyzed. From the results, it can be found that the latter method could solve the problems more accurately and faster than the former one.

With different integration methods and numbers of integration points, the rectangle and triangle elements are utilized to study the phase-change problems. The total error is used to compare the solution accuracies of these schemes. The closed-form integration formula is not a good way applied to solve the solidification problems. The rectangle element could have the more accurate result than the triangle one.

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