臺灣博碩士論文加值系統

本文探討磁場作用下非牛頓流體通過楔型板之邊界層流、熱傳與熵產生率問題。非牛頓流體為導電的冪次律流體，以Falkner-Skan方程式描述流體的運動，磁場與楔型板表面溫度隨著位置變化。透過相似轉換 (Similarity Transformation) 將控制方程式由非線性偏微分方程式轉換為非線性常微分方程式，並引入與冪次律流體的流動特性、磁場、楔型板角度和溫度相關的物理參數。
使用Laplace Adomian混合解法(LADM-Padé)求解控制方程式，此方法結合Adomian分解法與Laplace轉換，用於求解非線性微分方程式，其結果為一截斷級數，以Padé近似達到收斂。
數值結果為速度與溫度的分布曲線，熵產生率由所得的溫度與速度帶入計算。本文探討影響流體速度、溫度與熵產生率的各項物理參數，並計算表面摩擦係數與局部紐賽數與現有文獻進行比較。

The problem of magnetohydrodynamic flow, heat transfer and entropy generation rate for a non-Newtonian power-law fluid past a stationary wedge in the presence of a transverse magnetic field is analyzed. The Falkner-Skan equation is applied for the wedge flow. The magnetic field density and surface temperature of the wedge are assumed to vary with the distance from the origin. The governing equations are transformed to nonlinear ordinary differential equations by similarity transformation and several physical parameters related to flow behavior of power-law fluid, magnetic field, angle and surface temperature are introduced.
The governing equations are solved numerically by Hybrid Laplace Adomian Decomposition Method. Laplace Adomian Decomposition Method (LADM) combines the Laplace transformation and Adomian Decomposition Method and is used to solve the nonlinear differential equations. In order to make the result of LADM converge, Padé approximant is employed and the method is named Hybrid Laplace Adomian Decomposition Method.
The results of this study concerns with the velocity and temperature profiles. The Second-law of characteristic of the system is considered and computed from the velocity and temperature. Parameters effecting velocity, temperature and entropy generation rate will be discussed in this study. The local skin-friction coefficient and the local Nusselt number are also tabulated and analyzed.

中文摘要 I
Extended Abstract II
誌謝 X
目錄 XI
表目錄 XIV
圖目錄 XV
符號說明 XVIII
第一章、 緒論 1
1-1 研究動機及背景 1
1-2 文獻回顧 3
1-3 本文架構 5
第二章、 數值方法 6
2-1 Adomian分解法 7
2-1.1 Adomian多項式 9
2-1.2 Modified Adomian 分解法 11
2-1.3 Laplace Adomian分解法 12
2-2 Padé近似 14
第三章、 理論分析 15
3-1 基本假設與數學方程式 15
3-1.1 冪次律流體 17
3-1.2 磁場與動量方程式 17
3-2 相似轉換 18
3-3 熵產生率 21
第四章、 數值方法結果 24
4-1 Laplace Adomian分解法 24
4-2 Padé 近似 29
4-3 討論 31
4-3.1 LADM項數設定 31
4-3.2 Padé近似設定 34
4-3.3 數值結果準確性比較 35
第五章、 結果與討論 38
5-1 流場分析 38
5-1.1 流動特性指數n對流場的影響 38
5-1.2 速度指數參數m對流場的影響 40
5-1.3 磁性參數Mn對流場的影響 42
5-2 熱傳分析 44
5-2.1 流動特性指數n對熱傳的影響 44
5-2.2 速度指數參數m對熱傳的影響 45
5-2.3 磁性參數Mn對熱傳的影響 47
5-2.4 修正普朗特數Npr對熱傳的影響 47
5-2.5 溫度指數參數r對熱傳的影響 50
5-3 表面摩擦係數與局部紐賽數 52
5-4 熱力學第二定律分析 55
5-4.1熵產生數(Entropy Generation Number) 56
5-4.2比贊數(Bejan number) 62
第六章、 結論與建議 69
6-1 結論 69
6-2 未來研究方向與建議 72
參考文獻 73

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