目錄
中文摘要 .................................................................................III
英文摘要 .................................................................................IV
致謝 ..........................................................................................V
目錄 .........................................................................................VI
表目錄 ....................................................................................IⅩ
圖目錄.......................................................................................Ⅹ
符號說明.................................................................................ⅩII
第一章 緒論...............................................................................1
1-1 前言.........................................................................1
1-2 文獻回顧..................................................................2
1-2-1 Falkner-skan方程式..........................................2
1-2-2 Adomian分解法................................................3
1-3 本文架構..................................................................4
第二章 數值方法.......................................................................6
2-1 Adomian分解法理論....................................................6
2-2 Adomian 多項式.........................................................11
2-2-1非線性(nonlinear)多項式..................................11
2-2-2非線性微分(derivative)多項式..........................13
2-3 修正Adomian分解法.................................................15
2-4 Laplace Adomian分解法..............................................21
2-4-1運算法則........................................................21
2-4-2討論...............................................................23
2-5 Padé近似法................................................................27
2-6 LADM- Padé近似混合法............................................29
第三章 邊界層流流經楔形板流場分析.................................37
3-1 Falkner-Skan方程式推導............................................37
3-2 LADM-Pade混合法求解邊界層流之流場....................40
3-3 求解項數問題............................................................43
3-4求解Padé與ƒ'(0)步驟...............................................48
3-5 求解未知數ƒ'(0)與Padé值.......................................49
3-6取Padé先後順序........................................................54
3-7 數值分析討論與比較.................................................57
第四章 邊界層流流經楔形板熱傳分析.................................65
4-1 能量方程式推導........................................................65
4-2 LADM-Pade混合法求解邊界層流之熱傳....................67
4-3求解未知數θ(0)........................................................69
4-4數值分析討論與比較..................................................70
第五章 結論與建議.................................................................77
5-1 綜合結論...................................................................77
5-2 未來研究方向與建議.................................................79
參考文獻...................................................................................80
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