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研究生：	蔡幀宇 Tsai, Cheng-Yu
論文名稱：	具廣義不完美界面之複合圓柱或圓球之熱傳導超材料 Thermal metamaterials composed of composite cylinders or spheres with general imperfect interface
指導教授：	陳東陽 Chen, Tung-Yang
學位類別：	碩士 Master
系所名稱：	工學院 - 土木工程學系 Department of Civil Engineering
論文出版年：	2025
畢業學年度：	113
語文別：	英文
論文頁數：	135
中文關鍵詞：	熱導超材料、熱功能裝置、中性內含物、廣義不完美界面、
外文關鍵詞：	thermal metamaterials, thermal functional devices, neutral inclusion, general imperfect interface
相關次數：	點閱：18 下載：1
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本論文針對可調式熱導超材料的模擬行為，進行了深入的分析與理論探討。研究中所採用的模型是一個等向性核心與各異向性的包覆層所構成的複合圓柱或圓球。在核心及包覆層之間，設置一個具有限厚度的各異向性薄層，該薄層與核心、包覆層之間皆為完美界面，由於薄層的解析在數學上較為繁複，因此本研究採用廣義不完美界面模型來進行等效簡化，該模型同時具有溫度場以及法向熱通量的不連續性，並且可透過漸進分析推導出相關的界面條件。為進一步探討熱中性條件與內部熱強度，我們運用中性內含物的等效介質理論證明，透過適當的參數調控，不僅可實現整體系統的熱中性。我們也進一步探討這些參數如何影響內部的溫度分布，讓熱量集中或屏蔽，達到設計所需的效果。在整個研究中，我們將強調利用廣義不完美界面所推導出的結果，不但可以在特定狀況下涵蓋既有的研究成果，同時也具備更高的參數彈性與應用廣度，可作為未來設計與模擬各類熱導超材料的基礎架構。

This thesis develops an exact analytical framework for tunable thermal metamaterials with thin interphase effects. The structure under investigation consists of a composite cylinder or sphere composed of an isotropic core coated with an anisotropic layer. Between the core and the outer layer lies a thin interphase of finite thickness, which is perfectly bonded to both adjacent regions and possesses anisotropic thermal conductivity. Based on this configuration, we employ a general imperfect interface model, wherein the thin interphase is asymptotically replaced by a general imperfect interface characterized by temperature and normal heat flux jumps derived through asymptotic analysis. This treatment enables a rigorous and unified description of a broad class of interfacial thermal transport phenomena. By applying the effective medium theory of neutral inclusion, we demonstrate that thermal transparency with respect to the background medium can be achieved through appropriate tuning of the material, geometric, and interface parameters. Furthermore, we illustrate how these parameters influence the thermal intensity within the targeted region, allowing for either pronounced concentration or shielding effects depending on the design. More importantly, an insightful result is revealed: a single general imperfect interface model is capable of reproducing previous analytical results corresponding to both low-conductivity and high-conductivity interface types, while offering a clearer interpretation of the compensating and substitutive relationship between the core conductivity and interface imperfection. Throughout this thesis, we emphasize that our formulation not only recovers existing results in the literature as limiting cases, but also provides a more versatile parametric framework for modeling and designing a broader class of thermal metamaterials.

中文摘要 i
Abstract ii
Acknowledgements iii
Table of contents iv
Lists of Tables	vi
Table of Figures vii
Chapter 1 Introduction 1
1 Theoretical background and Literature review 1
2 Motivation 4
3 Outlines 5
Chapter 2 Mathematical framework of general imperfect interface 7
1 Heat conduction theory 8
2 General imperfect interfaces 9
3 General imperfect interface jump condition: isotropic case 20
4 General imperfect interface: anisotropic case 22
4.1 Cylinder configuration 23
4.2 Sphere configuration 25
4.3 The other expression of jump condition in terms of ξ and η	27
5 Limiting cases of general imperfect interface 28
Chapter 3 Composite cylinders and spheres with general imperfect interface 33
1 Composite cylinders and spheres withgeneral imperfect interface 36
1.1 Interface conditions of general imperfect interface 39
2 Application to limiting cases 42
2.1 Application to LC-type interface with anisotropic interphase 42
2.2 Application to HC-type interface with anisotropic interphase 43
3 Asymptotic expansion and numerical illustrations 45
3.1 Cylindrical configuration 46
3.2 Spherical configuration 46
4 Thermal neutrality condition: k_1=k ̌_1 56
4.1 Asymptotic expansion and analysis	57
5 Conclusion 61
Chapter 4 Neutrality condition and thermal intensity of composite cylinder and sphere with general imperfect interface 63
1 Thermal invisibility cloak with a general imperfect interface 64
2 Thermal invisibility conditions with a general imperfect interface 69
2.1 Composite cylinder configuration 71
2.2 Composite sphere configuration 74
3 Numerical illustrations for thermal invisibility condition 78
3.1 Effects of anisotropy parameter λ^((2)) 80
3.2 Coupled effects of anisotropy parameters λ^((i)) and λ^((2)) 86
3.3 Effects of thickness parameter ε 89
4 Numerical illustrations for core intensity 91
4.1 Effects of anisotropy parameter λ^((2)) 91
4.2 Coupled effects of anisotropy parameters λ^((i)) and λ^((2)) 98
4.3 Effects of thickness parameter ?	 102
4.4 The effects of area or volume fraction c	 104
5 Summary 106
Chapter 5 Conclusions and Future works	 107
1 Conclusions	107
2 Future work 110
References 111
Appendix A Introduction to imperfect interface 114
Appendix B Full expansion of Chapter 3 118
Appendix C Detailed derivation supporting Chapter 4 119
                                    

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簡琨展，廣義不完美介面的數學架構及其等效熱傳導係數，國立成功大學土木所碩士論文 (2017)。

林俊宏，考慮不完美界面影響之熱傳導超材料設計，國立成功大學土木所博士論文(2022)。

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