在工程上常見的熱傳問題中，常使用傳統正算法來求解其物理量，亦就是給定輸入，遵循一定物理規律，例如熱對流或熱傳導機制，我們就可以獲得相對確定的輸出結果，這就是正算問題(Direct Problem)。但是在實際的工程問題中，存在許多無法直接量測或是計算之物理量，必須透過其他相對容易取得之物理量，進而得到待求之物理量，因此，為了求得所需之物理量，必須利用反算法藉由其它已知的參數或量測資料反求之，這就是反算問題(Inverse Problem)。
本論文可以分為兩個章節，均在探討穩態熱傳導與熱對流共軛之反算問題於平板表面未知熱通量之預測。在第二章與第三章中吾人探討平板未知熱通量相關的反算問題時皆以商業軟體CFD-ACE+來建立物體幾何模型與網格，再使用共軛梯度法(Conjugate Gradient Method)藉由已知邊界條件，配合模擬或真實之溫度感測器測量物體表面溫度來預測未知熱通量。
第二章中，考慮平板底部有一未知熱通量，並研究本平板模型在不同風速與板厚下對本未知熱通量預測之影響。結果表明，當考慮薄板且不考慮量測誤差時均能準確的預測出熱通量，且入口速度不會影響預測。接著加入量測誤差觀察其對反算的影響。最後，得出的結論是，因為反算問題是不適定的，因此對於厚度較厚的情況下，底部熱通量對表面溫度影響力變小，因此即使表面溫度能準確預測，但是底部熱通量仍無法精確預測。

第三章為實驗部分，為驗證第二章數值模擬可信度，吾人設計出一系列的實驗來加以驗證。吾人在不同風速與板厚下，使用紅外線熱像儀測量平板上表面溫度，搭配熱像儀分析軟體TAS20，配合Surfer內差方法來擷取所需之溫度分佈，進而利用共軛梯度法(Conjugate Gradient Method)藉由平板上表面溫度與商業軟體CFD-ACE+，預測物體表面未知熱通量。Design A(均勻)與Design B(非均勻)加熱方式在不同板厚與風速下所預測之熱通q(S1)與溫度T(S2)的結果得知不管是實驗或是數值模擬都有著非常準確的預測結果，雖然沒有完全再現所設計之步階函數熱通量之形狀，但熱通量的預測是可靠的，數值模擬與實驗的結果也非常相符，這也證明了數值模擬的可信度。

A three-dimensional steady-state inverse heat conduction-convection conjugated problem (IHCCCP) in estimating the unknown spatial-dependent surface heat flux is investigated in this thesis. The functional form of the heat flux is considered unknown prior to the estimation, therefore it is known as the category of function estimation in the inverse problems. The Conjugate Gradient Method (CGM) is utilized for the optimization process since it does not require a priori information regarding the functional form of the unknown functions, huge 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 IHCCCP previously. Results of the inverse solutions are justified based on the numerical simulations with various inlet air velocity and plate thickness. It reveals that when considering exact measurements, accurate boundary heat fluxes can always be obtained for thin plate condition and air velocities do not affect the estimations. The measurement errors are included and the influence on the inverse solutions are discussed. Finally it is concluded that due to the ill-posed characteristic of the inverse problem, when the plate thickness becomes thicken, the estimation of heat flux becomes worse.

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