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論文中文名稱:雙曲線熱傳導問題之數值方法探討 [以論文名稱查詢館藏系統]
論文英文名稱:Numerical Methods for the Hyperbolic Heat Conduction Problems [以論文名稱查詢館藏系統]
院校名稱:臺北科技大學
學院名稱:機電學院
系所名稱:機電科技研究所
畢業學年度:100
出版年度:101
中文姓名:陳金治
英文姓名:Chin-Chih Chen
研究生學號:94669017
學位類別:博士
語文別:中文
口試日期:2012-07-25
論文頁數:185
指導教授中文名:陳澤明
指導教授英文名:Tzer-Ming Chen
口試委員中文名:周煥銘;吳浴沂;朱紹舒;楊琳鏗
口試委員英文名:Huann-Ming Chou      ;Yuh-Yih Wu;Shao-Shu Chu
中文關鍵詞:Collection method混合格林函數法積分轉換法雙曲線熱傳導
英文關鍵詞:Collection methodHybrid Green function methodIntegral transforms methodhyperbolic heat conduction
論文中文摘要:為解決雙曲線熱傳導方程式數值結果振蘯的問題,本研究提出Collection method、混合格林函數法與混合積分轉換法用以解決雙曲線熱傳導問題中銳緣波前的現象。以Collection method求解一具曲率因素之實心體的一維雙曲線熱傳導問題,在研究中以拉氏轉換移除統御方程式中的時間項並結合雙曲線形狀函數用以求解雙曲線熱傳導問題,最後提出四個不同例子加以分析。
以混合格林函數法求解一維至三維的直角、圓柱與球狀座標之雙曲線熱傳導問題,在研究中使用拉氏轉換移除統御方程式的時間項,以格林函數求解空間域之溫度函數。在研究中分別提出四到六個例子加以分析。
以混合積分轉換法求解一維至三維的直角、圓柱與球狀座標之雙曲線熱傳導問題,在研究中使用拉氏轉換移除統御方程式的時間項,以積分轉換法求解空間域之溫度函數。在研究中分別提出五到六個例子加以分析。
經研究發現,三種方法之數值結果與Kao所求得的解析解比較均可獲致良好的一致性,且可有效的解決雙曲線熱傳導問題的數值振蘯的狀況。
論文英文摘要:The difficulty encountered in the numerical solutions of hyperbolic heat conduction problems (HHC) is the numerical oscillation in vicinity of sharp discontinuities. In the present study, we have proposed collection method, hybrid Green function and hybrid integral transform method to overcome the numerical oscillation on HHC.
Using the collection method investigates the effect of the surface curvature of a solid body on HHC. The present method combined the Laplace transform and the hyperbolic shape function to solve time dependent HHC equation; four different examples have been analyzed by the current method.
The hybrid Green function is developed to solve HHC problems in Cartesian, cylindrical and spherical coordinates system. The present method combines with the Laplace transform for the time domain, Green function for the space domain. For one- two-, and three- dimensional problems, four to six different examples have been analyzed.
A hybrid Integral transform method is applied in Cartesian, cylindrical and spherical coordinates of HHC problems. The present method combines with the Laplace transform for the time domain, integral transform scheme for the space domain. For one- two-, and three- dimensional problems, five to six different examples have been analyzed.
It is found from these examples that the three methods are in good agreement with the analytical solutions [19] and do not exhibit numerical oscillations at the wave front.
論文目次:摘 要 i
ABSTRACT ii
誌謝 iv
表目錄 vii
圖目錄 viii
第一章 緒論 1
1.1 研究背景 2
1.2 研究目的 5
1.3 研究方法 6
1.4 研究架構 7
第二章 文獻探討 9
2.1 熱波歷史 10
2.2 固態脈衝雷射於雙曲線熱傳導方程式的應用 16
2.3 雙曲線熱傳導方程式於薄膜之應用 18
2.4 雙曲線熱傳導方程式於雙相遲滯流之應用 20
2.5 雙曲線熱傳導方程式於生物熱傳之應用 22
2.6 雙曲線熱傳導方程式的反算問題 24
2.7雙曲線熱傳導方程式數值求解方法 25
第三章 Collection method 31
3.1 使用控制容積法推導一維雙曲線形狀函數 31
3.2 問題分析 42
3.3 問題示例 44
3.4 結論 55
第四章 混合格林函數 56
4.1 混合格林函數法應用於直角座標系統 56
4.1.1 問題分析 56
4.1.2 數值方法 57
4.1.3 問題示例 58
4.2 混合格林函數法應用於圓柱座標系統 77
4.2.1 問題分析 77
4.2.2 數值方法 78
4.2.3 問題示例 79
4.3 混合格林函數法應用於球狀座標系統 103
4.3.1 問題分析 103
4.3.2 數值方法 104
4.3.3 問題示例 105
4.4 結論 115
第五章 混合積分轉換法 116
5.1 混合積分轉換法應用於直角座標系統 116
5.1.1 問題分析 116
5.1.2 數值方法 117
5.1.3 問題示例 118
5.2 混合積分轉換法應用於圓柱座標系統 134
5.2.1 問題分析 134
5.2.2 數值方法 135
5.2.3 問題示例 136
5.3 混合積分轉換法應用於球狀座標系統 155
5.3.1 問題分析 155
5.3.2 數值方法 156
5.3.3 問題示例 158
5.4 結論 168
第六章 總結與未來展望 169
6.1 總結 169
6.2 未來展望 171
參考文獻 172
符號說明 183
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