本文重新整理熱學架構下的三種不完美介面關係式(低熱傳導型、高熱傳導型及廣義不完美型)，並利用平均值定理的概念整理出三種不完美介面各自的等效熱傳導係數，接著再以Dilute模式及GSCS模式(Generalized Self Consistent Scheme)求出內含物為三維球型及二維圓柱型的等效熱傳導係數。而本文的重點是藉由二維架構下Duality轉換後材料係數會變為倒數的特殊性質，證明此特殊性質在廣義不完美介面下應用時，會使溫度不連續介面係數及法向熱通量不連續介面係數經過Duality轉換後，出現「互換」的特殊現象。若廣義不完美介面的特例─低熱傳導型介面為例，Duality性質可以使原本低熱傳導型介面的複合材料轉換為高熱傳導型介面，反之亦然。

The present thesis studies the effect of three different types of imperfect interfaces (highly conducting, lowly conducting, general interface) in the context of thermal conduction. Based on average theorem, closed-form expressions for the size-dependent effective conductivity of the composites with spherical and cylindrical particle are derived using the dilute approximation and the generalized self-consistent scheme. In addition, we present duality relations for the effective conductivities of two-dimensional composites with general imperfect interface. A remarkable feature of the derived duality relation is that the interchange relation also applies for the interface parameter. Take a lowly conducting interface as an example, duality relation could transform a composite medium to a dual medium with highly conducting interface, and vice versa.

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