在2006年，在國際知名期刊Science 之兩篇開創性文章 Pendry et al. (2006)及 Leonhardt (2006)，在電磁波理論中提出利用座標轉換的概念實現屏蔽效應，在短短幾年的時間裡引起各界學者熱烈的討論，從電磁波到光學、聲學、應力波、熱傳學，只要能夠維持控制方程式的不變性，能量傳播的控制在各個領域都有廣大的發展空間。熱是與我們生活息息相關的議題，對熱流的操控是工程應用上重要且實際的課題，文章中將以座標轉換的方法探討如何控制熱的流動達到我們想要的效果。本文之特色為在座標轉換之計算過程當中，利用特別的方法可以先決定材料係數之間的關係，再來反推座標轉換方程式，此法將為日後屏蔽裝置之發展建立新的基礎，其次本文將針對三維及二維的屏蔽裝置、旋轉器、集中器做詳細的模擬與探討，並詳細計算三者在各個情況下材料係數之解析解且驗證在三維下三者的材料係數以及在三維空間中的傳遞效果。本文亦對屏蔽裝置、旋轉器、集中器分別做了穩態及暫態數值模擬，並利用符合實際的尺寸與材料參數，詳細分析及探討三者在暫態及穩態中的詳細情況及變化，以利未來在工程上之應用，並期許能將其應用落實於生活當中。

we explore the possibility to control the flow of heat flux with the method of coordinate transformation. Three results are presented in this study. First, we derive the transformed heat conductivity tensor together with the transformed heat capacity in terms of transformation fuction. Second, we derive the analytical form for the material parameters of thermal cloak, concentrator, and rotator for transient and steady state in two and three dimensions. We also verify their correctness using the finite element method. Third, we simulate the performance of each device by using COMSOL and discuss their results in detail. By examining the distribution of streamline and isothermal line, we find good simulation performance.

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