本研究的主要目標是透過梯度法進行最佳化控制，實現圓管出口流體的等溫溫度控制。我們將面對的挑戰是在長距離或大面積的熱傳導過程中，如何確保穩定的溫度控制。為解決這問題，我們採取了一種創新的策略：透過最佳化外管壁的熱通量來控制內管壁的溫度，並以此內管壁的溫度對流體進行加熱。這種策略能更精確地調控熱通量分佈，並克服因外管壁溫度變化帶來的不確定性，以提高溫度控制的精確度。
梯度法在許多領域，包括熱流管理，均有廣泛的應用。該方法利用數學的梯度概念來尋找函數的最小或最大值，提供了一種能夠進行有效的優化操作的策略。該方法的靈活性、高效率，並對物理過程的深入理解提供了可能性。
在模擬中，我們選擇使用CFD-ACE+套裝軟體，此軟體具有出色的計算性能和精確的模擬能力，能有效提升模擬效率，並可在多核心或多處理器上同步運行。該軟體採用如二階上風差分等高級計算方案，進行流體流動細節的模擬，並能準確地模擬出熱交換、壁面摩擦等影響。結合CFD-ACE+套裝軟體和我們以Fortran撰寫的程式，使用梯度法進行運算，進行不同溫度分佈下所需的最佳熱通量的計算，進而控制出口溫度。
結果顯示，透過給定內管壁溫度分佈，我們成功得到了期望的流體平均出口溫度，同時出口溫度的均勻度之誤差僅為0.3K。此外，在導入權重係數後，雖然均勻度變差，但只需較少的迭代次數且能有效緩解熱通量的劇烈變化。

綜合以上結果，本研究提供了一種創新且有效的等溫控制策略，這對於溫度敏感的科技研究和工業應用將具有顯著的影響。這個策略的成功運用，不僅提升了溫度控制的精準性，也為長距離或大面積的熱傳導提供了可行的解決方案。

The main goal of this thesis is to use the gradient-based method in an optimal heating problem to achieve uniform temperature control of the fluid at the pipe outlet. We adopted an innovative approach: by optimizing the heat flux on the external pipe wall to control the temperature of the internal pipe wall, and then using this internal wall's temperature to heat up the fluid. This strategy allows for more precise control of the heat flux distribution and overcomes uncertainties caused by changes in the external pipe wall temperature, leading to better temperature control. The gradient-based method is popular in many areas, including heat flow management. This method uses the mathematical concept of gradient to find the minimum or maximum of a function, providing a way for effective optimization. In our simulation, we combined the CFD-ACE+ software and our Fortran program, and used the gradient-based method for calculations to determine the optimal heat flux needed under different desired uniform outlet temperature distributions. The results indicated that by setting a specified temperature distribution on the internal pipe wall, we achieved the desired average fluid outlet temperature with a temperature uniformity error of only 0.3K. Moreover, after introducing a weighting factor, even though the uniformity decreased, fewer iterations were needed and the drastic changes in heat flux were effectively reduced. This research offers an innovative and effective temperature control method, which not only improves temperature control accuracy but also gives a practical solution for optimal heating problem over long distances or large areas.

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