根據Pendry et al. (2006)及Leonhardt (2006)兩篇開創性的文章，在電磁波中透過座標轉換設計新型的超材料，便可以引導電磁波行進的方向，進而達到隱形的現象，這套理論稱為轉換光學理論(transformation optics)。後續許多學者以此方法投入其他領域例如光學、應力波、聲學及熱學等，都有豐碩的成果。類似的概念在熱學中，主要影響其熱傳導機制，以被用於設計不同的熱轉換裝置，例如隱形斗篷、集中器及旋轉裝置等。本論文根據相同的概念，以二維正交曲線座標下轉換材料之通式，透過幾何關係以及轉換裝置欲達成的效果來設計轉換材料，除了上述隱形斗篷、集中器及旋轉裝置外，亦設計了一種平面平移假像裝置，該裝置除了可以使一穩態熱流通過裝置時，改變內部溫度曲線分佈以及流線，若將熱源置於該裝置內，從外部來看熱源的位置會像是在另外一側，為了確認此想法的可行性，我們以二維有限元素模擬，用模擬結果以熱流線及等溫線來驗證上述裝置的可行性。

In this thesis, we control heat flux with the method of coordinate transformation. Two geometric shapes and four illusion situations are considered in this study. Firstly, the transformed heat conductivity tensor can be derived from the transformation function. We derive the transformed heat conductivity tensor in two-dimensional curvilinear orthogonal coordinate in terms of chain-rule operations in the Jacobian matrix. Secondly, we propose several material parameters of thermal cloak, concentrator, rotator and translator for steady-state conduction for two different geometric shapes. Thirdly, we demonstrate their effectiveness by COMSOL Multiphysics finite element simulations. To investigate the effect of the transformation media, we demonstrate the distributions of streamlines and isothermal lines. In summary, the transformation media will not disturb the exterior fields in exterior heat boundary condition, but can make thermal illusions for an interior heat source.

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