熱傳導會受到不同材料組成、幾何形狀、排列以及材料交界面連結等情況影響。如何利用材料性質的差異來導引或操控熱流，達到特定功能需求，近年來吸引許多相關領域學者投入心力研發。利用複合材料力學等效介質觀念，結合不同材料特性，以二種或多種材料組成，搭配適當之微結構設計，使其能夠在宏觀上展現特定的等效材料性質，此客製化與具可調性的人造材料，即為熱傳導超材料的主要概念。而在實際製作上，無論是超材料與內含物或與外界材料的交界面，或是超材料本身為利用複合材料疊層所製造而產生之材料交界面，皆有可能產生不完美界面。尤其當熱裝置尺度愈小時，其影響愈顯著。然而，過往大部份相關研究皆未考量界面非理想時所造成之影響，亦缺乏詳盡理論解析結果來探討其不完美界面性質。本文將探討高傳導與低傳導二類極端的不完美界面對於熱傳導超材料設計的影響。在熱穩態情況且考慮不完美界面效應下，本文證明當滿足「強隱形條件」時，二維圓形或三維球形超材料所包覆的物件皆可完美隱形；反之，在考慮暫態反應時，僅能在滿足「弱隱形條件」下可以使觀察者對物件的可見度最小化。本文在考慮不完美界面下，推導穩態強隱形條件與暫態弱隱形條件，並皆以明確與簡潔的形式呈現，以利於描繪其物理現象，及便於熱超材料的設計。此外，本文亦探討在滿足隱形條件下，操控熱集中與熱屏蔽效應之可能性。除了理論分析外，亦以COMSOL有限元素法軟體模擬並與理論解相互印證。本研究希望能夠在未來讓學者針對複合材料在熱傳導過程中可能遇到的不完美界面影響，參考本文之理論結果而設計更符合現實狀況之熱傳導超材料。

Thermal metamaterials, defined as artificial materials suitably designed to act as functional materials that can exhibit desired physical properties, have drawn massive research recently. Most of the previous studies tacitly considered that the interface between two dissimilar materials in contact is perfectly bonded. In principle, imperfectness across the interface always exists and the effect is particularly pronounced in small length-scales. In this dissertation the effect of two typical imperfect interfaces, which are referred to as low conductivity- and high conductivity-type interfaces, will be thoroughly investigated. Incorporating the effect of imperfect interfaces, we show that an object can be made completely invisible for the steady-state cases under a certain condition referred to as “invisibility condition”, or referred to as “strong invisibility condition”. This unprecedented condition is analytically derived in closed forms and numerically examplified. On the other hand, it is shown that an object can only be made partially concealed in a transient state. In the quasi-static limit, the “weak invisibility conditions” that can minimize the visibility to the observers with or without the effect of imperfect bonding interfaces are derived in an explicit and concise expression. Thermal shielding and concentrating effect are exemplified. Finite element simulations based on the software COMSOL are presented to validate our theoretical results as well. This work opens an avenue to design thermal metamaterials through a complete thermal transient conduction process counting into the effect of imperfect interfaces.

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