一般自然界的材料無法有效的控制熱傳導的方向，本研究將轉換光學之數學方法應用於控制熱傳導，並利用熱超常材料之模擬實現新穎的熱元件。
本文首先分析了文獻所提出之熱傳導隱形斗篷（簡稱熱斗篷），並指出其設計上之限制以及實現上的困難，因而提出了兩種新的方法，第一種為地毯式熱斗篷，地毯式熱斗篷可使用層狀的超常材料實現，本研究選取由矽層和矽聲子晶體層所構成之超常材料。由有限元素軟體Comsol Multiphysics模擬可知當熱絕緣體放置在地毯式熱隱形斗篷下時即有良好的熱隱形效果。此外，地毯式熱斗篷也可使不規則表面的溫度均勻化。而因為其簡單的材料參數，使得地毯式熱斗篷較易實現。第二個方法為利用熱電阻網絡概念設計網狀熱斗篷。與實心的多層熱斗蓬不同，網格狀熱斗篷由離散熱傳導組件所構成。而斗篷之熱隱形效能可透過有限元素軟體Comsol Multiphysics模擬，並與多層熱斗篷比較。此外，根據模擬，可找出不同離散組件的數目、尺寸和熱傳導率之最佳設計。本研究之模擬結果表明，所提出的網格狀熱斗篷不僅實現了比多層熱斗篷更好的熱隱形效果，同時也擁有較小的物理尺寸、較便宜的成本和更多設計通用性。
另一方面，本文也將其他的轉換熱元件－熱集中器，以有限元素軟體Comsol Multiphysics模擬，並以實際之材料設計。總括來說，本文對於熱傳導之操縱提供了可行方案，而可應用於微電子、國防和綠色能源等領域。

Using natural material cannot effectively manipulates the directional distribution of heat conduction. Accordingly, this study applies the mathematics method of transformation optics in controlling the heat transfer. In addition, a thermal metamaterial simulation is used to realize the novel thermal devices.
First, the present study analyzes the invisibility cloak of thermal conductivity (thermal cloak) proposed by former research. The former thermal cloak has a lot of limitations on design, and is not easily achieved. Therefore, two new methods for thermal conduction cloaking are proposed. In the first method, a thermal carpet cloak is proposed theoretically using a layered metamaterial, which is composed of homogeneous silicon layer and a phononic crystal silicon layer. The thermal cloaking effect is demonstrated using COMSOL Multiphysics Finite Element software. Great cloaking performance is achieved when a thermal insulator is well hidden under the thermal carpet cloak. In addition, the thermal carpet cloak can homogenize the temperature on irregular surface. Thermal carpet cloak can be easily realize because of its simple material composition. The second method design a mesh-like thermal conductivity cloak by means of thermal resistance network simulations. Compared to the solid multi-layered cloaks, the proposed cloak comprises a mesh-like array of discrete conductance components. The thermal shielding performance of the proposed cloak is compared with that of a layered cloak by means of COMSOL Multiphysics Finite Element software. In addition, simulations are performed to determine the optimal design of the mesh-like web in terms of the number, dimensions and conductivity of the discrete conductance components. In general, the results presented in this study show that the proposed mesh-like cloak not only achieves a better thermal shielding effect than a layered cloak, but also has a smaller physical size, a cheaper cost, and a greater design versatility.
On the other hand, other transformed thermal devise, thermal concentrator, is also designed and simulated using COMSOL Multiphysics Finite Element software. As a result, it provides a promising solution for various thermal manipulating applications in the microelectronics, national defense, green energy field etc..

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