本研究利用中性內含物的等效材料性質概念，將不同熱傳導係數的材料組合為內含物，使其成為與周圍的背景材料具有相同熱傳導係數的複合材料，達成熱中性，同時產生自然界中的材料不具有的熱傳導特性，如熱隱形和熱集中。而熱傳導的成因除了材料性質以外，也會受到幾何形狀及接觸界面情況等影響。本論文將模擬同向性及異向性材料做為內含物之核心或斗篷時的情況，而內含物的幾何形狀在二維圓柱或三維球模擬，接觸界面除了假設材料間的接觸面是完美結合，為了更加接近現實情況，加入兩種不完美界面：低傳導界面(lowly conducting interface)和高傳導界面(highly conducting interface)，兩者分別對溫度和熱通量在界面產生不連續導致對內含物的等效熱傳導係數產生影響，因為現實中存在著材料因性質及其微結構的差異而產生的不完美界面，又或是材料本身表面存在裂隙、材料間結合不緊密等等原因產生不完美界面，因此模擬這兩種不完美界面相比模擬完美界面更接近於現實，將以上情況全部考慮後設計出熱超材料，在此之上再次延伸為多層斗篷，使得研究或實作中能夠使用各自所需性質的材料，在熱傳導方面還能保持熱中性並維持所需的熱隱形或熱集中。並在此基礎上，求得內含物中的核心與背景材料的溫度比值之極值。

This study utilizes the concept of neutral inclusions in effective material properties, combining materials with different thermal conductivities into inclusions that have the same thermal conductivity as the surrounding background material, achieving thermal neutrality. This also generates thermal conduction characteristics not found in natural materials, such as thermal cloaking and thermal concentration. In addition to material properties, thermal conduction is influenced by geometric shapes and contact interfaces. This paper simulates the conditions when isotropic and anisotropic materials are used as cores or cloaks of inclusions. The geometries of the inclusions are modeled as two-dimensional cylinders or three-dimensional spheres. For contact interfaces, besides assuming perfect bonding between materials, two types of imperfect interfaces are introduced: lowly conducting interface and highly conducting interface. These interfaces cause temperature and heat flux discontinuities, affecting the effective thermal conductivity of the inclusions. In reality, imperfect interfaces arise due to differences in material properties and microstructures, surface cracks, and loose bonding between materials. Simulating these imperfect interfaces provides a more realistic representation compared to perfect interfaces. Considering all these factors, this study designs thermal metamaterials, further extending to multi-layer cloaks. This allows the use of materials with specific desired properties in practical applications, maintaining thermal neutrality while achieving the desired thermal cloaking or thermal concentration. Additionally, the study seeks to determine the extreme values of the temperature ratio between the core of the inclusions and the background material.

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