本論文透過拉凡格式法(Levenberg-Marquardt Method)配合B-spline surface控制點方法與套裝軟體CFD-ACE+的結合，配合模型底面溫度值為參考，來探討複合材質界面形狀變化對散熱率的影響。
本論文有兩個主題。在第二章中，吾人以套裝軟體CFD-ACE+為基礎,利用拉凡格式法配合B-spline surface控制點來設計二區複合材料之界面幾何形狀 (即一組界面形狀，r(x,y,z)) 希望能在相同體積的條件下計算出希望的散熱率。在第三章中，吾人亦以套裝軟體CFD-ACE+為基礎,來探討三區複合材料之未知界面幾何形狀(即二組未知界面形狀r1(x,y,z)及r2(x,y,z) ) 對於散熱率的影響。
本研究比較著重於使用拉凡格氏法搭配B-Spline自由的控制連接面的變化，相較於其他研究對於連接面的改變是設定參數限制其自由度的方式，有較大的差異。在本研究中有分兩個部分，分別是固定連接面邊界與不固定連接面邊界兩種，藉此比較哪一種狀況可以得到較大的熱通量。此外，吾人亦假設兩區或三區複合材料之界面為良好接觸(perfect thermal contact)，故求解時需利用兩材料交界面上溫度相同且達到熱平衡之原理來求解。
在本文中，吾人對於兩區及三區的範例都依序針對不同熱通量增加對連接面形狀影響來做討論，並且成功計算出各種不同情況下可以II增加熱通量最大值的幾何連接面形狀。希望本論文之發表，能給予相關領域研究提供一個解決問題的方向。

A shape design problem or inverse geometry problem, in determining the optimal interfacial geometry for a three-dimensional multiple region domains is examined in this study based on the Levenberg-Marquardt method (LMM), B-Spline surface, the commercial code CFD-ACE+ and the desired system heat flux.
There are two themes in the present thesis. In chapter two, different desired system heat fluxes are considered in the numerical test cases to justify the validity of the present algorithm in solving the three-dimensional two-layer shape design problems, i.e. estimate one irregular interfacial surfaces r1(x,y,z). In chapter three, the objective is to estimate simultaneously two irregular interfacial surfaces r1(x,y,z) and r2(x,y,z) in a three-layer-structure.
Finally it is concluded that when the boundary control points of interfacial surface are free to move, maximum system heat flux can be obtained by the present algorithm. We also learned that different thermal conductivity will lead to different results. When the smaller thermal conductivities are placed in Ω1 and Ω3, maximum system heat flux can be obtained by the present algorithm. Besides, the boundary conditions along the interface are assumed perfect thermal contact conditions.
In this thesis, different desired system heat flux in a two-layer and three-layer structures are considered and the correspondent shapes of interfacial surfaces are determined. Hopefully, this technique can be of some contribution in the field of shape design problem in the future.

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