隨著科技的進步，在微尺度下之熱傳行為已逐漸受到重視，本文的主要目的是使用混合拉氏轉換法分析並探討傅立葉及非傅立葉相變化熱傳問題。混合拉氏轉換法為運用黎曼和近似之逆拉氏轉換法搭配有限差分法，並探討混合數值方法處理非傅立葉熱傳問題時所產生的震盪現象。
本文使用溫度回復法做相變化的數值分析，並運用混合拉氏轉換法搭配溫度回復法求解非傅立葉相變化熱傳問題。溫度回復法相較其它方法顯得更有效率因為其代次數最少，並且其準確度接近熱焓法。
初始溫度對時間的一階微分項為造成數值結果不穩定之原因，因此，本文在處理溫度線性時間推進疊代運算時，利用拉氏轉換法搭配控制體積法先求取估算每個時間所需之溫度場解，再推求得微分項，然後作疊代運算，如此可有效解決震盪問題。
使用本文之數值方法求解非傅立葉相變化問題，結果趨勢與文獻一致，因此運用溫度回復法分析傅立葉相變化熱傳問題具有不錯的可行性。

With the high-tech progress, the heat transfer behavior in micro scale has gradually taken seriously. The present study employs the hybrid Laplace transform method to investigate Fourier and non-Fourier phase-change heat transfer problems. The inverse Laplace transform of Riemann approximation method and finite difference method are applied to the hybrid Laplace transform method. Furthermore, the numerical oscillated problem of non-Fourier heat transfer problems are also discussed in this research.
The temperature recovery method is applied to deal with the phase-change problem and combined with the hybrid Laplace transform method to solve the non-Fourier phase-change heat transfer problem. The temperature recovery method is more efficient than any other phase-change numerical scheme since it has the smaller number iteration and its accuracy is close to that of the enthalpy method.
The simulate result is unstable that causes by the differential term. This study uses the inverse Laplace transform of Riemann approximation method with the control volume method to obtain the temperature solutions, which are needed for estimating the differential term, and then the differential term is calculated by using the solutions. Finally, the newly computed term is substituted in the time-marching iteration, which could make the oscillated problem eliminated.
From applying the present method in this study to solve the non-Fourier phase-change problem, the simulated results are agreed well with those from the numerical data reported in the literature. Accordingly, the proposed method is feasible for solving the non-Fourier phase-change problem.

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