本研究是根據期望的最佳熱傳導係數比值及填料含量來探討反算問題於預測兩個導體填料在二維及三維多區區域的最佳幾何形狀。此反算設計利用拉凡格式法(Levenberg-Marquardt method)、雲形線B-Spline curve的生成技術及商用套裝軟體CFD-ACE+來完成形狀設計分析。
在第二章中考慮到二維不同填料含量及不同填料熱傳導係數的兩個數值實驗範例來證實此研究的正確性。本研究結果與Zhang et al. [1]現有的填充物形狀設計比較，其優點歸納如下：(i)當固定填料熱傳導係數值時及在不同的填料含量下，有效熱傳導係數值增加36.4%~50.5%，(ii)當固定填料含量及在不同的填料熱傳導係數值時本研究之有效熱傳導係數值增加35.5%~63.4%。此外也說明了最佳形狀非Zhang et al. [1]所指出的“I”形狀，而是“T-like”形狀。
在第三章中利用B-Spline surface產生三維的填充物形狀，並考慮到不同填料含量及不同填料熱傳導係數的兩個數值實驗範例來證實此研究的正確性，其優點歸納如下，(i)當固定填料熱傳導係數值時及在不同的填料體積下，有效熱傳導係數值增加3.29%~30.7%，(ii)當固定填料體積及在不同的填料熱傳導係數值時，有效熱傳導係數值增加5.89%~15.2%，結果顯示最佳形狀為“Tee”形狀。

The inverse problems in determining the optimal geometry of filler shape between two conductive bodies in a two-dimensional and three-dimensional multiple region domains, based on the desired thermal conductivity ratio and content of filler, are examined in the present study. The Levenberg-Marquardt method (LMM), B-Spline curve generation technique and commercial software CFD-ACE+ are utilized in this inverse design algorithm.
In chapter two, the validity of this two-dimensional shape design analysis is examined using the numerical experiments. Different filler content and conductivity are considered in the numerical test cases to justify the validity of this study. The estimated results in the present work are then compared with the existing filler shapes designed by Zhang et al. [1] and it is found that (i) by fixing the filler conductivity, the effective thermal conductivity can be increased from 36.4% to 50.5% depending on different content of filler and (ii) by fixing the filler content, the effective thermal conductivity can be increased from 35.3% to 63.4% depending on different filler conductivity. Moreover, it is also concluded that the optimal fillers are not of “I” shape, which was suggested by Zhang et al. [1], instead, they are in a family of “T-like” shape.
In chapter three, a three-dimensional filler shape is generated by a B-spline surface and different filler content and conductivity are also considered in the numerical experiments. It is found that (i) by fixing the filler conductivity, the effective thermal conductivity can be increased from 3.29% to 30.7% depending on different volume of filler and (ii) by fixing the filler volume, the effective thermal conductivity can be increased from 5.89% to 15.2% depending on different filler conductivity, it is also conclude that they are in the family of “Tee” shape.

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