臺灣博碩士論文加值系統

本文提出了一種解決長時間熱傳導問題的逆向分析方法，包含了雷射表面加熱問題及噴灑散熱問題。藉由最小均方誤差法將在物體內得到的實驗量測數據與經由時變性邊界的熱傳導問題之解析解得到的估算數據之誤差最小化，可以得到其未知邊界的溫度。我們可以求得所有位置與時間的溫度分佈和熱通量。此方法無需使用積分轉換及繁雜的數值運算，亦無需使用將時間區域分成數個微小時間區域的技巧。在數學和實驗上的範例更是說明了此方法為一個簡單、有效率及準確的方法。

This paper proposes a solution method for inverse analysis of long time heat conduction problems, include of laser surface heating problem and spray cooling problem. By minimizing the mean square error between the experimental data obtained from inside the body and estimated data from the derived analytical solution of a heat conduction problem with time-dependent boundary conductions, the temperature at the unknown boundary can be determined. Consequently, the temperature distribution and the heat flux over the entire time and space domains can also be obtained. The integral transform and tedious numerical operations are not required in the proposed solution method. In addition, the technique of dividing time into serval sub-time intervals is not required in long time heating treatment analysis. Mathematical and experimental examples are given to illustrate the simplicity, efficiency, and accuracy of the proposed method.

摘要 I
Abstract II
誌謝 III
Nomenclature XII
Contents V
Chapter 1 Introduction 1
1.1 Preface 1
1.2 Literature Review 1
1.3 Research Motive and Method 4
1.4 Scope 5
Chapter 2 Inverse Analysis of Heat Treatment Problem 7
2.1 Mathematical Modeling 7
2.2 Analytic solution form 9
2.2.1 Change of variable 9
2.2.2 Shifting functions 10
2.2.3 Solution of transformed variable 12
2.3 Fourier transform the measured temperature function 13
2.4 Least square error 16
Chapter 3 Example and Verification 29
3.1 Mathematical example 29
3.2 Experimental example 39
3.2.1 Inverse Analysis of Laser Surface Heating Problem 39
3.2.2 Inverse Analysis of Spray Cooling on a Hot Surface Problem 42
Chapter 4 Conclusion 69
References 71
Appendix A: Analytical solution of general system over entire domain of laser surface heating problem. 74
Appendix B: Analytical solution of general system over entire domain of spray cooling on a hot surface problem by using sine series method. 77
Appendix C: Analytical solution of general system over entire domain of spray cooling on a hot surface problem by using cosine series method. 81

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