臺灣博碩士論文加值系統

　　科技發展日新月異，為了解決工程應用上所遭遇的微尺度熱傳問題，必須仰賴巨觀的傅立葉熱傳現象之基礎，進而解析微觀的非傅立葉熱傳行為，最終才能夠探討實際的工程問題。
　　本文主要目的為使用混合拉氏轉換法，並適時搭配曲線擬合法分析非傅立葉熱傳問題，若熱傳過程中涉及相變化行為，則運用溫度回復法處理潛熱效應。
　　由於∂θ(δ,0)/∂β 為以混合拉氏轉換法進行時間迭代模擬非傅立葉熱傳問題-熱波模式結果震盪的主因，因此本文藉由研究修正式時間迭代法所得之∂θ(δ,0)/∂β數值，並且應用曲線擬合法尋找其數學關係，最終歸納而得另一種時間迭代方法，稱為擬合式時間迭代法，能夠有效模擬非傅立葉熱傳問題-熱波模式，進而分析其潛熱效應之影響；∂^2 θ(δ,0)/∂δ^2為混合拉氏轉換法進行時間迭代模擬非傅立葉熱傳問題-雙相差模式結果不穩定的主因，故本文同樣藉由研究修正式時間迭代法所求得之∂^2 θ(δ,0)/∂δ^2數值，並應用曲線擬合法歸納而得其數學關係，最終同樣運用擬合式時間迭代法有效模擬非傅立葉熱傳問題-雙相差模式，且探討其相變化行為。

Technology development advances rapidly day by day. To solve micro-scale heat transfer problems encountered in engineering applications is necessarily based on the macroscopic Fourier heat transfer phenomena. With the basis, the microscopic non-Fourier heat transfer problems would be analyzed effectively and therefore the actual heat transfer problems in engineering could be studied. The main purpose of this paper is using the hybrid Laplace transform method with curve fitting techniques to analyze the non-Fourier heat transfer problems. If the heat transfer process involves phase-change, the temperature recovery method is applied to handle the effect of latent-heat release.
∂θ(δ,0)/∂β is the main reason causing the numerical oscillating results in solving CV wave models by using the hybrid Laplace transform method and the time marching scheme. In the study, the oscillating problem is solved by developing a curve-fitting formula to calculate ∂θ(δ,0)/∂β, which is derived from the modified time-marching method of the previous works. The developed method is called the curve-fitting time marching scheme. Afterwards, the CV model with the release of latent heat could be analyzed numerically.
∂^2 θ(δ,0)/∂δ^2 is the primary cause leading to the unstable numerical results in solving dual-phase models. Similarly, a curve-fitting formula is obtained to calculate ∂^2 θ(δ,0)/∂δ^2, which could help to solve the dual-phase model effectively. Subsequently, the dual-phase model with phase change could be investigated numerically.

摘要 I
Abstract II
誌謝 III
目錄 IV
表目錄 VII
圖目錄 VIII
符號說明 XVII
第一章　緒論 1
1-1 文獻回顧 3
1-2 研究方法與目的 9
第二章　理論分析 12
2-1 熱傳問題之數學模式 14
2-2 史蒂芬問題 19
2-3 拉氏轉換法 21
第三章　數值分析方法 30
3-1 混合拉氏轉換法 32
3-1.1混合拉氏轉換-有限差分法 33
3-1.2 混合拉氏轉換-控制體積法 35
3-2 修正式時間迭代法 38
3-3 溫度回復法 42
第四章　熱波模式 55
4-1 剖析修正式時間迭代法 57
4-1.1 溫度對時間一次微分項 57
4-1.2 脈波數值擬合 59
4-2脈波數值擬合之修正 62
4-2.1 直接差分法 62
4-2.2 能量均分法 63
4-3 擬合式時間迭代法 64
4-4 非傅立葉相變化熱傳問題-熱波模式 69
第五章　雙相差模式 88
5-1 剖析修正式時間迭代法 90
5-2 二次微分項的計算方法 93
5-2.1 有限差分近似 94
5-2.2 特殊形式之有限差分近似 96
5-3 擬合式時間迭代法 98
5-4 非傅立葉相變化熱傳問題-雙相差模式 100
第六章　結論 126
參考文獻 128

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