臺灣博碩士論文加值系統

　　本文應用Laplace Adomian 分解法解決變化輪廓環形鰭片之熱傳遞與熱應力問題。熱傳遞問題之參數包括變化傳導係數、變化對流係數與輻射常數，並給予環形鰭片底部有週期性溫度邊界，求解環形鰭片之溫度分布曲線，以該溫度分布曲線對照該溫度下之飽和水蒸氣壓，求解出環形鰭片之熱應力分布曲線（包含徑向應力與切向應力）。文中探討各熱傳遞參數與鰭片輪廓之變化對溫度分布與熱應力分布之影響，以及各熱傳遞參數與鰭片熱傳效率之關係曲線。
　　研究結果得知，溫度分布隨著傳導係數的降低，對流係數、輻射係數與鰭片厚度遞減率的提高而下降，然而改變各熱傳遞參數與鰭片輪廓對於熱應力分布幾乎沒有影響。
　　相對於傳導係數與對流係數，鰭片熱傳效率分布受輻射係數影響對曲線分布之影響劇烈，當三種熱傳遞參數非座落於微小區間時，鰭片熱傳效率會隨著熱傳遞參數增加而降低。相同熱傳遞參數下，凹形鰭片之鰭片熱傳效率略高於梯形鰭片與凸形鰭片。

In this article, the Laplace Adomian decomposition method (LADM) is used to solve the heat transfer and thermal stress analyses in variable profile annular fin. The heat transfer problem including the parameters of temperature-dependent conduction and convection, and the constant radiation coefficient, with the periodic temperature as boundary condition as well. Solving the temperature distribution in annular fin, and find out the saturated vapor pressure which is under the temperature meantime, to solve the thermal stress distribution, including the radial stress and the tangential stress. Investigating the effect of temperature distribution and thermal stress distribution by both heat transfer parameters and the diversification of fin profile and fin efficiency distribution with every heat transfer parameter.

The results show that temperature distribution lower by the lower conductivity, the higher convection coefficient, radiation coefficient and decline rate of fin thickness. But change any heat transfer coefficient and the fin profile would not change the thermal stress distribution. In the high temperature heat transfer process, there have obviously impact on having the radiation coefficient. Improve the radiation coefficient can dissipate heat quickly, make the fin cooling down.

摘要 I
Laplace Adomian Decomposition Method for Analyses of Heat Transfer and Thermal Stress with the Periodic Base Temperature in Variable Profile Annular Fin II
誌謝 IX
目錄 X
表目錄 XV
圖目錄 XVI
符號說明 XX
第一章 緒論 1
1-1 前言 1
1-2 非線性系統 3
1-3 本文架構 5
1-4 文獻回顧 6
1-4-1 Adomian分解法 7
1-4-2 環狀鰭片之熱傳遞與熱應力 9
第二章 Laplace Adomian 分解法 (LADM) 12
2-1 Adomian 分解法 12
2-2 Adomian 多項式 17
2-2-1 非線性(nonlinear)多項式 17
2-2-2 非線性微分(derivative)多項式 19
2-3 修正Adomian分解法 22
2-3-1 修正ADM（一） 22
2-3-2 修正ADM（二） 28
2-4 Laplace Adomian分解法 34
2-4-1 運算法則 34
2-4-2 文獻驗證 36
第三章 模型建構與理論分析 46
3-1 模型建構 46
3-1-1 熱傳遞理論之建構 49
3-1-2 彈性材料應力場理論之建構 53
3-2 Laplace Adomian 分解法分析 59
3-2-1 無因次化與位置平移 59
3-2-2 LADM解題程序 61
第四章 熱傳遞與熱應力分析結果與討論 66
4-1 溫度分布影響 66
4-1-1 傳導參數影響 66
4-1-2 對流參數影響 71
4-1-3 輻射參數影響 75
4-1-4 鰭片厚度遞減率影響 79
4-1-5 輪廓差異影響 83
4-2 徑向熱應力影響 85
4-2-1 傳導參數影響 86
4-2-2 對流參數影響 89
4-2-3 輻射參數影響 92
4-2-4 鰭片厚度遞減率影響 95
4-2-5 輪廓差異影響 98
4-3 切向熱應力影響 99
4-3-1 傳導參數影響 100
4-3-2 對流參數影響 103
4-3-3 輻射參數影響 106
4-3-4 鰭片厚度遞減率影響 109
4-3-5 輪廓差異影響 112
4-4 鰭片熱傳效率分布影響 113
4-4-1 傳導參數影響 113
4-4-2 對流參數影響 115
4-4-3 輻射參數影響 117
4-4-4 輪廓差異影響 119
第五章 總結與建議 122
5-1 參數對溫度分布影響之總結 122
5-2 參數對應力分布影響之總結 123
5-3 參數對鰭片熱傳效率分布影響之總結 124
5-4 建議 125
參考文獻 126

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