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研究生:王春富
研究生(外文):Chun-Fu Wang
論文名稱:二維異向性材料溫度場理論解析
論文名稱(外文):Theoretical investigation for two-dimension temperaturefield in an anisotropic material
指導教授:薛明憲
指導教授(外文):Ming-Hsien Hsueh
學位類別:碩士
校院名稱:北台灣科學技術學院
系所名稱:機電整合研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:中文
論文頁數:84
中文關鍵詞:異向性材料二維異向性材料溫度場理論解析
外文關鍵詞:two-dimension temperature
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在處理與解決異向性材料熱傳問題上, 往往需要用到複雜的數學精密運算, 才可以解得合理之解析解, 否則就是運用數值分析之方法去解析與運算。本文將以一個多元廣義的角度去解析異向性材料而運用線性座標轉換的方法, 去證明複雜的材料係數在控制方程式中的問題, 並且可以得到一種優化的處理方式又不會將原本問題的邊界條件複雜化的方法。本文將以二維異向性溫度熱傳系統來模擬一個線性座標轉換之數學模式進行推演, 此線性座標轉換可對不同狀況做解析, 並不只適用於某些特定系統。之後根據二維系統進行分析線性座標轉換對控制方程式, 以及對邊界條件產生如何變化, 使得把困難問題更為簡化。
本文中將探討二維異向性材料中給予不同的溫度預設下, 異向性材料內部所產生的溫度分佈, 經由分析當中研討異向性材料的溫度分析及熱傳導造成的變化。之後將分析在無窮域、半無窮域、層板、多層板等在點熱源、點溫度的情況下, 對所預設的材料造成溫度分析及熱傳導結果。
This study focuses on investigating the two-dimensional heat conduction in anisotropic materials with corresponding boundary conditions. The heat conduction problem can be reduced to an equivalent isotropic one without complicating the geometry and boundary conditions by using a linear coordinate transformation method. By using the Fourier transform method, the exact closed-form temperature solutions of the specific problems are derived. The complete analytical solutions of heat condition problems for the half-plane or thin-film domain can consist only of the series solutions for an infinite homogeneous medium with concentrated heat source or temperature. The two-layers anisotropic medium heat conduction problems with corresponding boundary condition are discussed in this paper.
中文摘要.............................................................................................. i
英文摘要............................................................................................ iii
誌謝.................................................................................................... iv
目錄..................................................................................................... v
圖目錄............................................................................................... vii
表目錄................................................................................................ ix
第一章 緒論....................................................................................... 1
1-1 研究動機...................................................................................... 1
1-2 論文回顧...................................................................................... 2
1-3 研究方法與架構.......................................................................... 5
第二章 二維異向性材料基本理論與熱傳推導............................... 8
2-1 前言.............................................................................................. 8
2-2 異向性熱傳問題之基本理論...................................................... 8
2-3 二維異向性材料穩態熱傳方程式............................................ 11
2-4 異向性熱傳問題之線性座標轉換 .......................................... 12
2-5 異向性熱傳問題之解題步驟.................................................... 19
第三章 異向性暫態與穩態熱傳導問題之全場解析..................... 21
3-1 前言............................................................................................ 21
3-2 二維異向性材料之無窮域穩態熱傳問題解析....................... 21
3-3 二維異向性材料之半無窮域穩態熱傳問題解析................... 25
3-4 二維異向性材料之單層板穩態熱傳導問題之解析............... 28
3-5 數值結果與討論........................................................................ 37
3-6 結論............................................................................................ 39
第四章 二維穩態異向性熱彈性問題解析..................................... 41
4-1 前言............................................................................................ 41
4-2 二維異向性材料之穩態多層板問題基本理論........................ 41
4-3 二維異向性材料之薄層問題穩態熱傳問題解析.................... 42
4-4 二維異向性材料之雙層板穩態熱傳問題解析........................ 47
4-5 數值結果與討論........................................................................ 57
4-6 結論............................................................................................ 59
第五章 結論與探討......................................................................... 61
5-1 本文成果.................................................................................... 61
5-2 未來研究方向............................................................................ 62
參考文獻........................................................................................... 63
作者簡歷........................................................................................... 84
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