在凝固熱傳問題中，相變化的過程中會有潛熱釋放的效應，而潛熱釋放會影響溫度場分布。本文以有限差分法和不同的數值方法與時間步伐方法分析凝固熱傳問題。
本文主要探討的一維暫態性熱傳、一維史蒂芬問題和一維紐曼問題，處理潛熱釋放的數值方法有等效比熱法和等效比熱/熱焓法，時間步伐方法有固定時間步伐、GLS法(ε=1e-3)、修正GLS法(ε<1e-3)和修正截尾誤差(修正LTE)。透過不同的數值方法與時間步伐方法來比較溫度場分布的準確性、潛熱釋放量和CPU運算時間，其中溫度場的準確性以總誤差(Total error)當作比較依據。
從分析的結果發現，在求解一維暫態線性熱傳問題時，GLS法可以有效的節省CPU運算時間和維持一定的精準度；在求解一維史蒂芬問題時，等效比熱法搭配修正GLS法和修正截尾誤差確實能比GLS法求得更精準的數值解，而搭配等效比熱/熱焓法時，一階的Euler法卻比GLS法來的精準；在求解一維紐曼問題時，等效比熱法和等效比熱/熱焓法搭配修正GLS法和修正截尾誤差比GLS法精準。

In the solidification heat transfer problems, the latent heat is released during the phase change process, affecting the distribution of temperature field. In this study, the solidification heat transfer problems are analyzed by using the finite difference methods, different numerical methods and time discretization techniques. Furthermore, the one-dimensional transient heat transfer problem, Stefan problem and Neumann problem will be investigated. The numerical methods for calculating latent heat release are the effective specific heat method and effective specific heat/enthalpy method. As for the time discretization techniques, the uniform time step, GLS methods(ε=〖10〗^(-3)), modified GLS methods(ε<〖10〗^(-3)) and modified local time truncation error scheme are utilized. In order to compare the accuracy of various numerical methods, the temperature field distribution, latent heat release and CPU computation time are important basis. From the analysis results, it is found that the GLS method can effectively save the CPU computation time and maintain precision when solving the one-dimensional transient heat transfer problem. In solving the Stefan problem, the effective specific heat method combined with the modified GLS method and modified local time truncation error scheme can be more accurate than the GLS methods. For the effective specific heat/enthalpy method, the first-order Euler methods is more precise than the GLS methods. However, when solving the Neumann problem, the effective specific heat method and the effective specific heat/enthalpy method combined with the modified GLS method and the modified local time truncation error scheme are more accurate than the GLS methods.

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