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 隨著科技的進步，在微尺度下之熱傳行為已逐漸受到重視，而探討微觀尺度下之非傅立葉相變化熱傳問題之相關研究並不多，因此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做數值分析，相變化的潛熱計算則使用溫度回復法，並探討混合數值方法處理雷射非傅立葉熱傳問題的應用及數值疊代的不穩定問題。 ∂θ(δ,0)/∂β及(∂^2 θ(δ,0))/(∂^2 δ)為造成數值結果不穩定之原因，因此，本文在處理溫度線性疊代運算時，利用拉氏轉換法搭配控制體積法及有限差分法之數值解反推求得∂θ(δ,0)/∂β及(∂^2 θ(δ,0))/(∂^2 δ)作為修正值，再帶數值回疊代運算，有效解決在時間疊代造成的震盪問題，並進一步計算較複雜的雷射熱源問題。由本文的計算結果可知，以本文所提出之方法計算非傅立葉熱傳問題，皆有良好的準確性，並可應用於求解較複雜的非傅立葉相變化問題。使用混合拉氏轉換法搭配溫度回復法可準確的計算史蒂芬問題，在求解非傅立葉雙相差雷射熱源問題時，相變化需考慮融化及凝固兩個過程，融化時，雷射的一部份能量被潛熱吸收，造成其高點溫度相對於沒有考慮相變化之非傅立葉雷射熱源熱傳問題低，凝固時，需等待潛熱效應完成後，才繼續熱擴散，使得溫度擴散減緩，因此相對溫度較不考慮相變化之非傅立葉雷射熱源熱傳問題高。
 As technology advances, the heat transfer behavior on a micro scale has graduallybeen taken seriously. There is not muchresearch about the micro-scale non-Fourier phase change heat transfer problems.The main focus of this paper is to use the hybrid Laplace transform method to investigate Fourier and non-Fourier phase change heat transfer problems.Hybrid Laplace transform method is used in the research, with one using Riemann sum approximation based on inverse Laplace transform method and the other using the same Riemann sum approximation and control volume method.The temperature recovery method is applied to solve numerical problem of latent heat in phase-change.To solve non-Fourier heat transfer laser problems, study focuses on the application of hybrid numerical method and the instability ensued from iteration. ∂θ(δ,0)/∂β and (∂^2 θ(δ,0))/(∂^2 δ)can lead to unstable numerical results.As a result, Laplace transform methodis applied alone with control volume method and the finite difference method to acquire modified differential term. Then comes the iteration that effectively resolves the oscillated problem. Without the oscillation, the more complicated laser heat source issue can be addressed.Using the proposed method of this thesis to calculate the non –Fourier heat transfer problems can obtain anaccurate result and solve more complicated non-Fourier phase change problem.Applying the hybrid Laplace transform method together with temperature recovery method can solve the Steven problemaccurately.The non-Fourier dual phase laser heat source phase change problem involves two processes: the melting and solidification.In melting, part of the laser energy is absorbed by latent heat, making a relatively higher point in temperature than the point that does not consider phase change.On the other hand, in solidification, the release of latent heat mitigates the thermal diffusion. That makes a relatively higher point in temperature than the point that does not consider phase change.
 圖目錄.....................................................IV表目錄...................................................VIII致謝......................................................IX摘要.......................................................XAbstract.................................................XI符號說明..................................................XII希臘字母.................................................XIII第一章緒論..................................................11-1前言....................................................11-2文獻回顧.................................................21-3研究方法與目的............................................6第二章逆拉氏轉換之理論分析.....................................82-1黎曼和近似之逆拉氏轉換理論分析...............................82-2逆拉氏轉換法求解雙曲線熱傳問題..............................10第三章熱傳問題之數學模式與數值方法..............................163-1 混合逆拉氏轉換之數值方法..................................163-1-1 有限差分法...........................................163-1-2控制體積法............................................183-2 雙相差模式有雷射熱源.....................................213-2-1有限差分法雙相差模式有雷射熱源............................243-2-2控制體積法雙相差模式有雷射熱源............................24第四章時間疊代之方法.........................................364-1 非傅立葉熱傳(熱波模式)時間疊代.............................364-2 非傅立葉熱傳(雙相差模式)時間疊代...........................374-3 非傅立葉熱傳(雙相差模式有雷射熱源)時間疊代...................37第五章非傅立葉熱傳相變化問題...................................415-1 溫度回復法(凝固問題).....................................425-2 運用溫度回復法求解史蒂芬問題...............................435-3　溫度回復法（融化問題）...................................455-4 史蒂芬問題熱波模式.......................................475-5 史蒂芬問題雙相差模式.....................................485-6 雙相差模式雷射熱源潛熱效應................................49第六章結論.................................................64參考文獻...................................................66
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 1 混合拉氏轉換法求解相變化熱傳問題 2 解析暫態熱傳問題之新數值方法 3 混合拉氏轉換與數值分析法在傅立葉與非傅立葉熱傳問題之研究 4 熱遲滯現象之數值分析 5 混合數值分析法在暫態熱傳上之應用 6 混合拉氏轉換法求解非傅立葉相變化熱傳問題之研究 7 混合拉氏轉換法求解傅立葉和非傅立葉熱傳導問題 8 混合拉氏轉換法搭配曲線擬合法探討非線性熱遲滯現象及其潛熱效應 9 轉速對可擦拭相變化型碟片微結構、寫擦性質影響 10 非傅立葉型態熱傳導方程式之反算問題研究

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