以往於熱遮罩設計的研究中通常採用熱超材做為遮罩材料，但礙於其製程相當繁瑣與困難，因此發展出多層理論與雙層理論，然而，多層理論中的各層均質材料在自然界中難以尋得，雙層理論又是假設內層為絕熱絕緣的理想物質，因此基於這些理論的後續遮罩研究皆僅能夠獲得符合需求的遮罩設計參數，而並未深入去探討遮罩製作的可行性。此外，過去的遮罩研究大多都專注於探討單一物理場下之表現，但在例如印刷電路板、通電裝置與設備等電子迴路之真實情況下，熱場與電場由於熱電效應之關係而經常同時存在並且相互影響，雖在近期陸續有學者也投入針對熱電耦合之雙物理場的遮罩研究，但由於求解出符合需求的遮罩設計參數後，除了不易找到同時符合熱、電場表現的自然材料外，也沒有考慮到遮罩構成材料與應用背景之間的合適性，所以目前仍難以將遮罩相關技術研究普及的實際應用於各項工程中。

而本文為改善與突破此現況，使遮罩相關之研究能夠更加貼近於實際情況，提高研究結果的可應用性，將利用真實存在於自然界當中的自然材料作為研究基礎，針對應用背景考慮材料合適性後選定遮罩建構之材料，再以其固定的材料參數來求解在熱電耦合雙物理場情況下的雙層雙功能遮罩之最佳化的尺寸設計，並利用目標函數分析、探討其隱形效能，因此本文與以往研究不同之處在於以固定的材料參數為基礎，同時優化雙功能遮罩的內、外層尺寸，達到利用真實存在的材料並考量實際應用面去建構遮罩之目的，於印刷電路板與植入式醫療器材之實際應用皆有不錯的成果。

The cloak design method proposed in the past is to use the optimization method to obtain the physical parameters that meet the performance of the cloak under the condition that the thickness dimensions of the inner and outer layers of the cloak are known, but it faces the problem that it is not easy to find the natural materials in the nature that correspond to the physical parameters. Although metamaterials can be adjusted by human control of the material's physical properties, the cumbersome and costly manufacturing process is still a major obstacle to the practical construction of cloaks, and therefore most of the research on thermo-electric cloaks remains at the theoretical stage, making it difficult to be applied in practice. In this study, based on the easier-to-construct bilayer structure, we take the real materials existing in nature as the research basis, consider the suitability of the cloak construction materials for the application background of the cloak, and then select the materials to be used in each layer of the cloak, and calculate the optimal dimensional design of the bilayer thermo-electric cloak under the thermo-electrical coupling of dual physical fields with the fixed material parameter, and utilize the cost function to analyze and explore the cloaking performance of the cloak. Therefore, the difference between this paper and previous studies lies in the optimization of the inner layer and outer layer dimensions of the bifunctional cloaks based on fixed material parameters, in order to achieve the purpose of constructing the cloaks by using real existing materials and considering the actual application surface. In this paper, the optimal design of cloak dimensions is calculated by using two different application backgrounds, namely, printed circuit boards (PCBs) and implantable medical devices (IMDs), and the cloaking and protection efficacies of the results of this optimization of the cloaks are explored.

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