本論文的主旨為使用共軛梯度法(Conjugate Gradient Method)搭配套裝軟體 CFD-ACE+，探討穩態熱傳導與熱對流共軛之反算問題於封裝晶片未知體積熱源之研究（IHCCCP）。
許多工程問題使用傳統正算方法來求解其物理量，也就是探討將已知條件輸入系統模式來分析其輸出為何，這就是正算問題(Direct Problem)。然而在許多實際工程問題中，存在很多物理量因為客觀條件限制或量測技術不足而無法直接計算或量測其值。因此，為了取得所需之物理量，必須利用反算法藉由其它已知的參數或物理量反求之，這就是所謂的逆向或反算問題(Inverse Problem)。由於電子元件的散熱問題在現今科技產業，具有相當高的重要性，目前的趨勢走向高科技、微電子產業，故在晶片的發熱量增加且體積縮小的情形下，元件的壽命與其溫度分佈情形有極大之關連，對於電子產品而言，過高的溫度會損害到晶片的壽命，甚至造成整個系統的不穩定。
本論文第二章及第三章，均為討論穩態熱傳導與熱對流共軛之反算問題於封裝晶片未知體積熱源之研究，在第二章將反算法之共軛梯度法運用在預測晶片內部之熱傳及對流問題上，加入不同量測誤差並且使用不同風速進行預測，其結果顯示即使加入量測誤差並且提高風速預測結果仍然相當準確。第三章為了更貼近實際應用則是預測印刷電路板 (PCB)上多個發熱源強度預測之熱傳及熱對流反算問題，並且加入不同量測誤差並且使用不同風速進行預測，對於增加的入口速度和測量誤差，通過 CGM 所預測的多個晶片的預測熱源仍然相當準確。第二章與第三章皆使用商業軟體CFD-ACE+來建立複雜物理模型的幾何形狀與網格，以數值分析的方式利用CFD-ACE+所解得上表面溫度分佈情形作為反算的依據，即可預測出內部未知熱源強度。

A three-dimensional steady-state inverse heat conduction-convection conjugated problem (IHCCCP) is investigated in this work. The goal is to estimate the unknown spatially dependent volumetric heat generation of an encapsulated chip mounted on a printed circuit board. The functional form of the volumetric heat generation is considered to be unknown prior to the estimation. Therefore, it is known as the category of function estimation in inverse problems. Optimization is performed using the conjugate gradient method (CGM) because this method does not require a priori information regarding the functional form of the unknown functions. Using this method, a large number of unknowns can be corrected and estimated in each iteration, and good estimations can always be obtained. This efficient algorithm has never been applied to the IHCCCP. The results of the inverse estimations are verified using numerical simulations with various inlet air velocities and measurement errors. They reveal that using exact measurements always produces accurate volumetric heat generation and that the regular air velocity does not affect the estimates. The measurement errors and their influence on the estimated heat generation are analyzed. Finally, it is concluded that because the inverse problem is ill-posed, the estimated heat generation becomes less accurate as the measurement error increases.

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