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系統識別號 U0026-0406202000321400
論文名稱(中文) 使用自然材料以最佳化方法解任意幾何形狀熱遮罩之研究
論文名稱(英文) An Optimization Method for Solving Arbitrary Geometry of Thermal Cloaking Problems Using Natural Materials
校院名稱 成功大學
系所名稱(中) 工程科學系
系所名稱(英) Department of Engineering Science
學年度 108
學期 2
出版年 109
研究生(中文) 楊富堯
研究生(英文) Fu-Yao Yang
學號 N96071407
學位類別 碩士
語文別 中文
論文頁數 164頁
口試委員 口試委員-楊鏡堂
口試委員-張建成
口試委員-張志彰
口試委員-楊煥成
指導教授-楊瑞珍
中文關鍵字 熱學超材料  雙層熱遮罩  任意幾何形狀  最佳化理論  逆向問題 
英文關鍵字 Thermal metamaterials  Bilayer theory  Arbitrary geometry  Optimization method  Inverse heat conduction 
學科別分類
中文摘要 熱遮罩的發展主要分為兩個主要方向,分別為轉換熱力學與雙層理論。轉換熱力學需要非均質且各向異性的熱學超材料,而雙層理論則採用均質且等向性的自然材料。根據雙層理論,目前已推導出圓形及橢圓形的解析解,然而,內層熱導率等於零是理論解析解的必要條件,實際上內層難以找到完美的絕熱材料。因此,本研究提出只使用雙層自然均質材料來實現隱身效果,同時擴展了雙層理論的幾何結構,提供更多元的應用方案。此外,我們將複雜的雙層熱遮罩問題簡化為單變數函數問題,本文運用最佳化過程和逆向熱傳導方法,求得最接近於理想熱遮罩效果的外層熱導率。透過此方法,即使內層使用低熱導率的實際自然材料,也能得到最佳的熱遮罩效能,並修正理論解析解因內層為非理想絕熱材料所產生的差異。對於非線性的背景溫度分布,我們也可以計算出最佳的外層熱導率,並經由數值模擬驗證其可行性。本文透過幾個例子說明該方法的性能。總括來說,提出的方法相當有用,可適用於任意幾何形狀,未來可能擴展到其他熱遮罩問題,例如熱對流和輻射。
英文摘要 The design of thermal cloaks follows two main directions: transformation thermodynamics and bilayer theory. Transformation thermodynamics requires heterogeneous and anisotropic thermal metamaterials, while the bilayer theory uses homogeneous and isotropic natural materials. According to the bilayer theory, analytical solutions for circles and ellipses have been derived. However, the thermal conductivity of the inner layer is restricted to be zero for the analytical solutions. It is difficult to find a such perfect insulating material for the inner layer. Therefore, this study proposes a method using two homogeneous natural materials to achieve the cloaking effect in analogy to the bilayer theory. Furthermore, we extend the bilayer approach to design arbitrary geometric thermal cloaking problems. In this study, an optimization method based upon inverse heat conduction approach is used to obtain the best thermal conductivity for the outer layer so as to achieve ideal thermal cloaking effects. Since we use natural materials with low thermal conductivity for the inner layer, the best thermal cloaking performance can still be obtained. In addition to conventional linear background temperature distribution for thermal cloaking problems, the proposed method is extended to design problems involving non-linear background temperature distribution. The proposed method is validated to be useful via numerical simulations and may be extended to other thermal cloaking problems, such as thermal convection and radiation.
論文目次 摘要 I
致謝 XI
目錄 XII
圖目錄 XV
表目錄 XXIX
符號說明 XXX
第一章 緒論 1
1.1 前言 1
1.2 隱形斗篷的起源 2
1.3 熱超材料的概述 4
1.4 研究動機與方針 8
第二章 文獻回顧 9
2.1 熱遮罩的誕生 9
2.2 轉換熱學 11
2.3 多層理論 14
2.4 雙層理論 17
2.4.1 圓形熱遮罩 17
2.4.2 橢圓形熱遮罩 20
2.5 最佳化理論 24
第三章 理論推導 27
3.1 轉換熱學 27
3.1.1 轉換熱學的重要關係式 27
3.1.2 圓形熱遮罩的異向性參數 29
3.1.3 任意形狀熱遮罩的異向性參數 33
3.2 雙層理論 36
3.2.1 圓形熱遮罩的解析解 36
3.2.2 橢圓形雙層熱遮罩的解析解 39
3.3 最佳化理論 44
3.3.1 逆向問題 44
3.3.2 最佳化理論的簡述 45
3.4 割線法(Secant Method) 47
3.5 割線法的收斂速率 49
第四章 模擬設置 52
4.1 有限元素法 52
4.2 COMSOL Multiphysics 53
4.3 MATLAB程式設計 54
4.4 模型架構 63
4.4.1 圓形熱遮罩 63
4.4.2 共焦點橢圓形熱遮罩 65
4.4.3 共形橢圓形熱遮罩 67
4.4.4 方形熱遮罩 70
4.4.5 不規則形狀熱遮罩 73
第五章 結果與討論 76
5.1 圓形熱遮罩 76
5.1.1 熱遮罩內層為理想絕熱條件 76
5.1.2 熱遮罩內層為非理想絕熱條件 81
5.2 共焦點橢圓形熱遮罩 86
5.2.1熱傳方向與橢圓形長軸平行 86
5.2.2熱傳方向與橢圓形長軸垂直 95
5.3 共形橢圓形熱遮罩 106
5.3.1 共形橢圓形熱遮罩之第一種情況 106
5.3.2 共形橢圓形熱遮罩之第二種情況 110
5.3.3 共形橢圓形熱遮罩之第三種情況 114
5.3.4 關於層厚比之綜合討論 118
5.4 方形熱遮罩 119
5.4.1 方形熱遮罩之第一種情況 119
5.4.2 方形熱遮罩之第二種情況 127
5.5 不規則形狀熱遮罩 136
5.6 非線性熱傳之情況 140
5.7 總結與討論 145
第六章 結論與展望 147
6.1 結論 147
6.2 展望 149
參考文獻 150
附錄 155
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