跳到主要內容

臺灣博碩士論文加值系統

(107.21.85.250) 您好!臺灣時間:2022/01/18 08:54
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

: 
twitterline
研究生:邱青煌
研究生(外文):Ching-Huang Chiu
論文名稱:Adomian分解法應用在非線性散熱片之熱傳分析
論文名稱(外文):Application of Adomian’s Decomposition method on the Analysis of Nonlinear Heat Transfer in Fins
指導教授:陳朝光陳朝光引用關係
指導教授(外文):Cha'o-Kuang Chen
學位類別:博士
校院名稱:國立成功大學
系所名稱:機械工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:186
中文關鍵詞:Adomian 分解法非線性微分方程式散熱片
外文關鍵詞:Adomian decomposition methodNonlinear differential equationFins
相關次數:
  • 被引用被引用:3
  • 點閱點閱:709
  • 評分評分:
  • 下載下載:140
  • 收藏至我的研究室書目清單書目收藏:2
摘 要
本文是依據G. Adomian所提出的逆算符理論方法,又稱為分解法,來探討縱向及環狀散熱片之熱傳性能分析。當散熱片的熱傳導係數為溫度的函數或散熱片表面具有輻射熱傳時,則散熱片的能量平衡方程式為非線性微分方程。當邊界條件考慮為固定溫度或絕熱時,則為線性邊界。但若考慮邊界具有輻射熱傳時,則將變成非線性邊界條件,而使得問題更加困難。
依據上述散熱片相關之問題,本文主要探討分析的內容有:考慮散熱片材料的熱傳導係數隨溫度變化;對於散熱片表面熱傳方面分別探討純對流,純輻射以及同時具有對流-輻射熱傳;在邊界條件上:考慮散熱片根部分別為受到一固定溫度,對流熱傳和週期性溫度變化之情形;而尾端考慮為絕熱邊界和具有對流及輻射熱傳之邊界。
在探討工程問題時,當系統的統御方程式或邊界條件或是兩者均為非線性時,則將使問題變成非常複雜的非線性問題。本論文應用Adomian分解法成功地解出含有線性或非線性邊界條件之非線性微分方程式,並將結果與數值解作比較,以探討分解法的收斂性和精確性。由計算結果足以證明Adomian分解法在非線性問題應用上實為一種有效且值得發展的計算方法。

Abstract
The Adomian’s decomposition is extended to predict the efficiency and optimal length of a longitudinal fin with variable thermal conductivity. The solutions of the nonlinear equations have been made for the special cases where the heat exchange of the fins with the surrounding may be caused by the pure radiation or the simultaneous convection and radiation, and the thermal conductivity of the fins is variable. An analytical solution is derived and formed as an infinite power series. This considerably reduces the numerical complexity.
The Temperature distributions are obtained for an annular fin of temperature dependent conductivity under periodical heat transfer condition. The heat transfer process is governed by the convectional fin parameter N, the thermal conductivity parameter ε, the frequency parameter B, and the amplitude parameter s.
Many of the practical fin problems have been completely performed. (1)The surface heat dissipation include mechanisms of pure convection, pure radiation, and simultaneous convection and radiation. (2)several situations give rise to heat transfer, such as a constant base temperature, convective base boundary condition and periodic oscillating base temperature.(3)the insulated and the convective-radiative fin tip are individually considered for evaluating the effect of the fin tip conditions.
The accuracy of The Adomian’s decomposition method with a varying number of terms in the series investigated. The comparison with the finite-difference method, based on a Newton linearization scheme, shown that the Adomian’s decomposition method is one of the most powerful techniques to solve nonlinear problems.

目 錄
中文摘要‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ I
英文摘要‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ II
誌 謝‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧IV
目錄‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧V
表目錄‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧IX
圖目錄‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧X
符號說明‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧XIII
第一章 緒論‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 1
1-1前言‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 1
1-2文獻回顧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 3
1-2-1散熱片熱傳問題‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 3
1-2-2散熱片設計與最佳化‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 15
1-2-3分解法‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 31
1-3 本文研究架構‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 31
第二章Adomian分解法‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 36
2-1分解法理論‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 37
2-2 Adomian多項式‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 42
2-2-1 簡單型非線性函數之Adomian多項式計算‧‧‧‧ 42
2-2-2 微分非線性運算符的An多項式算法‧‧‧‧‧‧‧ 45
2-2-3 Rach規則‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 46
2-2-4複合型非線性函數之Adomian多項式計算‧‧‧‧‧ 47
2-2-5 多變數函數的Adomian多項式計算‧‧‧‧‧‧‧ 52
2-3 格林函數(Green function)‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 54
2-4 收斂性‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 57
2-4-1分解法的收斂性‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 57
2-4-2收斂半徑‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 59
2-4-3 Adomian多項式加速收斂法‧‧‧‧‧‧‧‧‧‧‧ 61
2-4-4 Adomian多項式的收斂性‧‧‧‧‧‧‧‧‧‧‧‧ 64
2-4-5 歐拉轉換(Euler Transform) ‧‧‧‧‧‧‧‧‧‧‧ 66
2-5雙重分解法‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 68
2-6 修正分解法‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 71
2-7偏微分方程式‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 74
2-8邊界條件‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 77
2-8-1線性邊界條件‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 77
2-8-2非線性邊界條件‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 78
第三章 可變熱傳導矩形縱向對流散熱片熱傳分析‧‧‧‧ 83
3-1 統御方程式與邊界條件‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 85
3-2 散熱片溫度分佈‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 86
3-3級數解的收斂性‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 89
3-4 近似解的精確度‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 90
3-5 散熱片效率與最佳化‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 91
3-6 結果於討論‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 92
第四章 矩形縱向散熱片最佳化分析‧‧‧‧‧‧‧‧‧‧‧ 109
4-1統御方程式及邊界條件‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 109
4-2非線性邊界值之雙重分解法‧‧‧‧‧‧‧‧‧‧‧‧‧ 111
4-2-1雙重分解法‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 111
4-2-2非線性邊界條件‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 113
4-3散熱片的熱傳率與最佳化‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 122
4-4結果與討論‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 123
第五章 矩形環狀散熱片熱傳分析‧‧‧‧‧‧‧‧‧‧‧ 137
5-1 統御方程式與邊界條件‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 137
5-2 散熱片之溫度分佈‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 139
5-3結果與討論‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 142
第六章 環狀散熱片受制週期性溫度變化時之暫態熱傳分析‧‧‧‧ ‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧149
6-1統御方程式及邊界條件‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 150
6-2散熱片溫度分佈‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 151
6-3結果與討論‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 155
第七章 結論與建議‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 164
7-1 綜合結論‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 164
7-2 未來研究方向之建議‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 167
參考文獻‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 169
附錄
A. Adomian’s Polynomial ‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 180
A-1 非線性函數uu″的Adomian’s 多項式‧‧‧‧‧‧‧‧‧ 180
A-2 非線性函數(u′ )2的Adomian’s 多項式‧‧‧‧‧‧‧‧‧ 181
A-3 非線性函數u4的Adomian’s 多項式‧‧‧‧‧‧‧‧‧ 181
B. 無窮級數的Cauchy Products‧‧‧‧‧‧‧‧‧‧‧ 186
自述‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 187
表目錄
表4-1 在Tf = 600 K時,同時具有對流及輻射熱傳之情形下,近
似解分別由1個到11個分量解組合時在不同節點位置上
的溫度‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 127
表5-1固定熱傳導係數下,具有對流及輻射熱傳‧‧‧‧‧‧‧‧144
表5-2固定熱傳導係數下,純對流熱傳‧‧‧‧‧‧‧‧‧‧‧‧ 144
表5-3固定熱傳導係數下,純輻射熱傳‧‧‧‧‧‧‧‧‧‧‧‧ 144
表6-1 N = 0.2,ε = 0 暫態溫度‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 158
表6-2 N = 0.5,ε = 0 暫態溫度‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 158
表6-3 N = 1.0,ε = 0 暫態溫度‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 159
圖目錄
圖1-1 常見的散熱片‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 37
圖3-1矩形縱向散熱片幾何形狀‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 95
圖3-2(a)散熱片參數N = 1.0時分解法的收斂性,由不同項數
分量解組合的比值試驗‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 96
圖3-2(b)散熱片參數N = 1.5時分解法的收斂性,由不同項數
分量解組合的比值試驗‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 97
圖3-2(c)散熱片參數N = 2.0時分解法的收斂性,由不同項數
分量解組合的比值試驗‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 98
圖3-3(a)散熱片參數N = 1.0時分解法的精確度,由不同項數
分量解組合結果與數值方法結果在散熱片尾端處的
溫度差‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 99
圖3-3(b)散熱片參數N = 1.5時分解法的精確度,由不同項數
分量解組合結果與數值方法結果在散熱片尾端處的
溫度差‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 100
圖3-3(c)散熱片參數N = 2.0時分解法的精確度,由不同項數
分量解組合結果與數值方法結果在散熱片尾端處的
溫度差‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 101
圖3-4 係數C值‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 102
圖3-5(a)散熱片參數N = 1.0時,在不同的熱傳導參數ε下散
熱片之溫度分佈‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 103
圖3-5(b)散熱片參數N = 1.5時,在不同的熱傳導參數ε下散
熱片之溫度分佈‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 104
圖3-5(c)散熱片參數N = 2.0時,在不同的熱傳導參數ε下散
熱片之溫度分佈‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 105
圖3-6 對流散熱片之效率‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 106
圖3-7 無因次熱傳量Qn/B與散熱片參數N之關係‧‧‧‧‧‧‧ 107
圖3-8 最佳化N值與熱傳導參數ε之關係‧‧‧‧‧‧‧‧‧‧‧ 108
圖4-1矩形縱向散熱片示意圖‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 128
圖4-2分解法的邊界值精確度‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 129
圖4-3近似解的精確度,不同項數分量解組合結果‧‧‧‧‧‧‧ 130
圖4-4 流體溫度Tf = 450 K時,散熱片之溫度分佈‧‧‧‧‧‧‧ 131
圖4-5 流體溫度Tf = 600 K時,散熱片之溫度分佈‧‧‧‧‧‧‧ 132
圖4-6 流體溫度Tf = 900 K時,散熱片之溫度分佈‧‧‧‧‧‧‧ 133
圖4-7 流體溫度Tf = 450 K時,考慮純對流,純輻射和具有對流
及輻射熱傳之下,散熱片之最佳化尺寸‧‧‧‧‧‧‧‧ 134
圖4-8 流體溫度Tf = 600 K時,考慮純對流,純輻射和具有對流
及輻射熱傳之下,散熱片之最佳化尺寸‧‧‧‧‧‧‧‧‧ 135
圖4-9 流體溫度Tf = 900 K時,考慮純對流,純輻射和具有對流
及輻射熱傳之下,散熱片之最佳化尺寸‧‧‧‧‧‧‧‧‧ 136
圖5-1 矩形環狀散熱片幾何形狀‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 145
圖5-2 同時具有對流及輻射熱傳時,散熱片之無因次溫度分佈‧ 146
圖5-3 純對流熱傳時,散熱片之無因次溫度分佈‧‧‧‧‧‧‧ 147
圖5-4 純輻射熱傳時散熱片之無因次溫度分佈‧‧‧‧‧‧‧‧ 148
圖6-1 環狀散熱片示意圖和根部溫度變化情形‧‧‧‧‧‧‧‧‧ 160
圖6-2 散熱片參數N = 0.2,0.5,1.0時,不同的熱傳導參數ε之
下,在暫態時間ωt = 0,π時,散熱片的徑向溫度分佈‧‧ 161
圖6-3 散熱片參數N = 0.2,0.5,1.0時,不同的熱傳導參數ε之
下,在散熱片中間位置處(R = 1.5),暫態溫度變化情形‧ 162
圖6-4 散熱片參數N = 0.2,0.5,1.0時,不同的熱傳導參數ε之
下,在散熱片尾端處(R = 2.0),暫態溫度變化情形‧‧‧ 163

參考文獻
1.Q.D. Kern and D.A. Kraus,〝Extended surface heat transfer,〞McGraw-Hill, New York, 1972.
2.W. Lau and C. W. Tan,〝Errors in one-dimensional heat transfer analysis in straight and annular fins,〞Trans. ASME, J. of Heat Transfer, November, pp.549-551, 1973.
3.R.K. Irey,〝Errors in the one-dimensional fin solution,〞Trans. ASME, J. of Heat Transfer, February, pp.175-176, 1968.
4.B. Aparecido, and R.M. Cotta,〝Improved one-dimensional fin solutions,〞Heat Transfer Engineering, Vol.11, pp.49-59, 1990.
5.H.S. Chu, C.K. Chen, and C.I. Weng,〝Transient response of circular pins,〞Trans. ASME, J. of Heat Transfer, Vol.105, pp.205-208, 1983.
6.R.J. Su and J.J. Hwang, 〝The reduced form of the transient heat transfer equation of two-dimensional rectangular plate fin,〞The Chinese J. Mechanics, Vol.13, pp.101-105, 1997.
7.A. Aziz and V.J. Lunardini,〝Multidimensional steady conduction in convecting, radiating, and convecting-radiating fins and fin assemblies,〞Heat Transfer Engineering, Vo.16, pp.32-64, 1995.
8.N.V. Suryanarayana,〝Transient response of straight fins,〞Trans. ASME, of Heat Transfer, August, pp.417-423, 1975.
9.N.V. Suryanarayana,〝Transient response of straight fins, part II,〞Trans. ASME, J. of Heat Transfer, May, pp.324-326, 1976.
10.A. Aziz and S. M. E. Hug,〝Perturbation solution for convecting fin with variable thermal conductivity,〞Trans. ASME, J. of Heat Transfer, May, pp.300-301, 1975.
11.A. Muzzio,〝Approximate solution for convective fins with variable thermal conductivity,〞Trans. ASME, J. of Heat Transfer, November, pp.680-682, 1976.
12.R.J. Krane,〝Discussion on a previously published paper by A. Aziz and S.M.E. Hug ,〞Trans. ASME, J. of Heat Transfer, Vol.98, pp.685-686, 1976.
13.A. Aziz and T.Y. Na,〝Transient response of fins by coordinate perturbation expansion,〞Int. J. Heat Mass Transfer, Vol.23, pp.1695-1698, 1980.
14.Y. M. Chang, C. K. Chen and J. W. Cleaver,〝Transient response of fins by optimal linearization and variational embeding methods,〞Trans. ASME, J. of Heat Transfer, Vol.104, pp.813-815, 1982.
15.H.C. Unal,〝Determination of the temperature distribution in an extended surface with a non-uniform heat transfer coefficient,〞Int. J. Heat Mass Transfer, Vol.28, pp 2279-2284, 1985.
16.P.J. Heggs, D.B. Ingham and M. Manzoor,〝The effects of nonuniform heat transfer from an annular fin of triangular profile,〞Trans. ASME, J. of Heat Transfer, Vol.103, pp.184-185, 1981.
17.C.Y. Chen and C.K. Chen,〝Transient response of annular fins of various shapes subjected to constant base heat flux,〞J. Phys. D:Appl. Phys. Vol.27, pp.2302-2306, 1994.
18.E. Assis and H. Kalman,〝Transient Temperature Response of different Fins to Step Internal Conditions,〞Int. J. Heat Mass Transfer, Vol.336 , pp.4107-4114, 1993.
19.A. Aziz,〝Radiating fin analysis with extended perturbation series,〞Letters in Heat and Mass Transfer, Vol.6, pp.199-203, 1979.
20.J. Mao and S. Rooke,〝Transient analysis of extended surfaces with convective tip,〞Int. Comm. Heat Mass Transfer, Vol.21, pp.85-94, 1994.
21.A. Aziz and T.Y. Na,〝Periodic heat transfer in fins with variable thermal parameters,〞Int. J. Heat Mass Transfer, Vol.24, pp.1397-1404, 1981.
22.J.W. Yang,〝Periodic heat transfer in straight fins,〞Trans. ASME, J. of Heat Transfer, August, pp.310-314, 1972.
23.A. Aziz, 〝Periodic Heat Transfer In Annular Fins,〞Trans. ASME, J. of Heat Transfer, pp.302-303, 1975.
24.R.G. Eslinger and B.T.F. Chung,〝Periodic heat transfer in radiating and convecting fins or fin arrays,〞AIAA Journal, Vol.17, pp.1134-1140, 1979.
25.A. Aziz and V.L. Lunardini,〝Analytical and numerical modeling of steady periodic heat transfer in extended surfaces,〞Computational Mechanics, Vol.14, pp387-410, 1994.
26.K.D. Papadopoulos, A.G. Guzman-Garcia and R.V. Bailey,〝The response of straight and circular fins to fluid temperature changes,〞 Int. Comm. Heat Mass Transfer, Vol.17, pp.587-595, 1990.
27.V.K. Garg and K. Velusamy,〝Heat transfer characteristics for a plate fin,〞Trans. ASME, J. of Heat Transfer, Vol.108, pp.224-226, 1986.
28.V.K. Garg and K. Velusamy,〝On the heat transfer from a cylindrical fin,〞Int. J. Heat Mass Transfer, Vol.32, pp.187-192, 1989.
29.W.W.S. Charters and S. Theerakulpisut,〝Efficiency equations for constant thickness annular fins,〞Int. Comm. Heat Mass Transfer, Vol.16, pp.547-558, 1989.
30.R.W. Knight, J.S. Goodling and B.E. Gross,〝Optimal thermal design of air cooled forced convection fins heat sinks-experimental verification,〞IEEE Transcations on Components Hybrids and Manufacturing Technology ,Vol.15, pp.754-760, 1992.
31.P. Razelos and E. Georgiou,〝Two-dimensional effects and design criteria for convective extended surfaces,〞Heat Transfer Engineering, Vol.13, pp.38-48,1992.
32.M.H. Cobble,〝Optimum fin shape,〞J. of The Franklin Institute, Vol.291, pp.283-292, 1971.
33.C.J. Maday, 〝The minimum weight one-dimensional straight cooling fin,〞Trans. ASME, of Engineering for Industry, pp.161-165, 1974.
34.L.T. Yu and C.K. Chen,〝Application of Taylor Transformation to Optimize rectangular fins with variable thermal parameters,〞Appl. Math. Modelling, Vol.22, pp.11-21, 1998.
35.A. Aziz,〝Optimization of rectangular and triangular fins with convective boundary condition,〞Int. Comm. Heat Mass Transfer, Vol.12, pp.479-482, 1985.
36.S. Biyikli,〝Optimum use of longitudinal fins of rectangular profiles in boiling liquids,〞Trans. ASME, J. of Heat Transfer, Vol.107, pp.968-970, 1985.
37.A.D. Snider and A.D. Kraus,〝The quest for the optimum longitudinal fin profile,〞Heat Transfer Engineering, Vol.8, pp.19-25, 1987.
38.B.T.F. Chung, M.H. Abdalla and F. Liu,〝Optimization of convective longitudinal fins of trapezoidal profile,〞Chem. Eng. Comm., Vol.80, pp.211-223, 1989.
39.B.T.F. Chung and B.X. Zhang, 〝Minimum mass longitudinal fins with radiation interaction at the base,〞J. of The Franklin Institute, Vol.328, pp.143-161,1991.
40.P. Razelos and B.R. Satyaprakash,〝Analysis and optimization of convective trapezoidal profile longitudinal fins,〞Trans. ASME, J. of Heat Transfer, Vol.115, pp.461-463, 1993.
41.A. Aziz,〝Optimum design of a rectangular fin with a step change in cross-sectional area,〞Int. Comm. Heat Mass Transfer, Vol.21, pp.389-401, 1994.
42.S. Guceri and C.J. Maday,〝A least weight circular cooling fin,〞Trans. ASME, J. of Engineering for Industry, pp.1190-1193, 1975.
43.A. Razani and G. Ahmadi,〝On optimization of circular fins with heat generation,〞J. of The Franklin Institute, Vol.303, pp.211-218, 1977.
44.P. Razelos and K. Imre,〝The optimum dimension of circular fins with variable thermal parameters,〞Trans. ASME, J. of Heat Transfer, Vol.102, pp.420-425, 1980.
45.M. N. Netrakanti and C. L. D. Huang,〝Optimization of annular fins with variable thermal parameters by invariant imbedding,〞Trans. ASME, J. of Heat Transfer, Vol.107, pp.966-968, 1985.
46.S.M. Zubair, A.Z. Al-Garni and J.S. Nizami,〝The optimal dimensions of circular fins with variable profile and temperature-dependent thermal conductivity,〞Int. J. Heat Mass Transfer, Vol.39, pp.3431-3439, 1996.
47.A. Bccini and H.M. Soliman,〝Optimum dimensions of annular fin assemblies,〞Trans. ASME J. of Heat Transfer, Vol.108 pp.459-462, 1986.
48.A. Sonn and A. Bar-Cohen,〝Optimum cylindrical pin fin,〞Trans. ASME, J. of Heat Transfer, Vol.103, pp.814-815, 1981.
49.P. Razelos,〝The optimum dimensions of convective pin fins,〞Trans. ASME, J. of Heat Transfer, Vol.105, pp.411-413, 1983.
50.P. Razelos,〝The optimum dimensions of convective pin fins with internal heat generation,〞J. of The Franklin Institute, Vol.321, pp.1-19, 1986.
51.U. Natarajan and U.V. Shenoy,〝Optimum shapes of convective pin fins with variable heat transfer coefficient,〞J. of The Franklin Institute, Vol.327, pp.965-982, 1990.
52.A. Razani and H. Zohoor,〝Optimum dimensions of convective radiative spines using a temperature correlated profile,〞J. of The Franklin Institute, Vol.328, pp.471-486, 1991.
53.J. Reardon and A. Razani,〝The optimization of variable cross-section spines with temperature dependent thermal parameters,〞Int. Comm. Heat Mass Transfer, Vol.19, pp.549-557, 1992.
54.P. Razelos and K. Imre,〝Minimum mass convective fins with variable heat transfer coefficients,〞J. of The Franklin Institute, Vol.315, pp.269-282, 1983.
55.K. Laor and H. Kalman,〝The effect of tip convection on the performance and optimum dimensions of cooling fins,〞Int. Comm. Heat Mass Transfer, Vol.19, pp.569-584, 1992.
56.A. Aziz and A.D. Kraus,〝Optimum design of radiating and convecting-radiating fins,〞Heat Transfer Engineering, Vol.17, pp.44-78, 1996.
57.A. Aziz,〝Optimum dimensions of extended surface operating in a convective environment,〞Trans. ASME, Appl. Mech. Rev.,Vol.45, pp.155-173, 1992.
58.G. Adomian,〝A review of the decomposition method in applied mathematics,〞J. Math. Anal. Appl., Vol.135, pp.501-544, 1988.
59.G. Adomian,〝A review of the decomposition method and some recent results for nonlinear equations,〞Computers Math. Applic., Vol.21, pp.101-127, 1991.
60.G. Adomian and R. Rach, 〝On the solution of algebraic equations by the decomposition method,〞J. Math. Anal. Appl., Vol.105, pp.141-166, 1985.
61.N. Bellomo, L. H. DE Socio and R.Monaco,〝Random heat equation: solution by the stochastic adaptive interpolation method,〞Computers Math. Applic., Vol.16, pp. 759-766, 1988.
62.G. Adomian,〝Nonlinear stochastic operator equation,〞Kluwer Academic Publisher, Dordrecht, 1986.
63.G. Adomian,〝Nonlinear stochastic system theory and application to physics,〞Kluwer Academic Publisher, Dordrecht, 1988.
64.G. Adomian and R. Rach, 〝Nonlinear stochastic differential-delay equations,〞J. Math. Anal. Appl., Vol.91, pp.94-101, 1983.
65.G. Adomian and R. Rach,〝On composite nonlinearities and the decomposition method,〞J. Math. Anal. Appl., Vol.113, pp.504-509, 1986.
66.G. Adomian,〝Solving frontier problems modelled by nonlinear partial differential equations,〞Computers Math. Applic., Vol.22, pp.91-94, 1991.
67.G. Adomian, R. Rach and M. Relrod,〝On the solution of partial differential equations with specified boundary condition,〞J. Math. Anal. Appl., Vol.140, pp. 569-581, 1989.
68.G. Adomian and R. Rach, 〝Equality of partial solutions in the decomposition method for linear or nonlinear partial differential equations,〞Computers Math. Applic. ,Vol.19, pp. 9-12, 1990.
69.G. Adomian,〝A new approach to the heat equation-an application of decomposition method,〞J. Math. Anal. Appl., Vol.113, pp.202-209, 1986.
70.G. Adomian, 〝Application of decomposition method to the navier-stokes equations,〞J. Math. Anal. Appl. , Vol.119, pp. 340-360, 1986.
71.B. K. Datta,〝A new approach to the wave equation: an application of the decomposition method,〞J. Math. Anal. Appl., Vol.142, pp.6-12 , 1989.
72.R. Baker and D.G. Zeitoun,〝Application of adomian’s decomposition procedure to the analysis of a beam on random winkler support,〞Int. J. Solids Structures ,Vol.26, pp.217-235, 1990.
73.G. Adomian and R.Rach,〝Analytic solution of nonlinear boundary-value problems in several dimensions by decomposition,〞J. Math. Anal. Appl., Vol.174, pp.118-137, 1993.
74.R. Rach, G. Adomian and R.E. Meyers,〝A modified decomposition,〞Computers Math. Applic., Vol.23, pp. 17-23, 1992.
75.R. Rach,〝A convenient computational form for the adomian polynomials,〞J. Math. Anal. Appl., Vol.102, pp.415-419, 1984.
76.G. Adomian,〝Stochastic system,〞Kluwer Academic Publisher, Dordrecht, 1983.
77.G. F. Roach,〝Green’s functions,〞Cambridge 1981.
78.I. Stakgold〝Green’s functions and boundary value problem,〞Wiley 1979.
79.P. Vadasz and S. Olek,〝Convergence and accuracy of adomian’s decomposition method for the solution of lorenz equations,〞Int. J. Heat Mass Transfer, Vol.43, pp. 1715-1734, 2000.
80.G. Adomian,〝Convergent series solution of nonlinear equation,〞J. of Computational and Applied Mathematics, Vol.11, pp.225-230, 1984.
81.A. Re’paci,〝Nonlinear dynamical system: on the accuracy of adomian’s decomposition method,〞Appl. Math. Lett., Vol.3, pp.35-39, 1990.
82.G.Adomian,〝Solving frontier problems in physics: the decomposition method,〞Kluwer Academic Publisher, Dordrecht, 1994.
83.T. M. Shih,〝Numerical heat transfer,〞Springer-Verlag, New-York, pp. 187-191, 1984.
84.D.A. Anderson, J.C. Tannehill and R.H. Pletcher,〝Computational fluid mechanics and heat transfer,〞McGraw-Hill, New York, pp. 336-341, 1984.
85.L.T. Yu and C.K. Chen, 〝Application of the hybrid method to the transient thermal stresses response in isotropic annular fins,〞Trans. ASME, J. of applied Mechanics, Vol.66, pp.340-346, 1999.

QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top