臺灣博碩士論文加值系統

本研究主要探討不可壓縮飽和多孔隙介質之黏彈性流體在均勻磁場影響下受半無限拉伸邊界驅動的穩定態邊界層流動與溫度分析解，其熱邊界條件主要考慮了二次分布表面溫度即二次分布表面熱通量兩種，並引用Prandtl於1904年所建立之邊界層理論(boundary layer theory)，將邊界層內動量、能量方程式加以簡化並參考前人之解析方法與數學模式加以延伸，以求得流體之動量方程式之正合解(exact solution)；能量方程式則考慮了黏性耗散、內部熱生成或吸收、流體變形功、焦耳熱及輻射等效應影響，分析在不同參數下其給定表面溫度條件之表面溫度梯度及給定表面熱通量之表面溫度等熱特徵，並以圖表表示之。對於熱特徵本文也提出適當的物理解釋，同時也給出當修正普朗特數很大時，在兩種熱邊界條件下溫度函數的漸進解。

The study for flow and heat transfer in a steady laminar boundary layer flow is presented analytically for an incompressible viscoelastic fluid saturated in a porous medium subject to a transverse uniform magnetic field past a semi-infinite stretching sheet with a quadratic distribution of surface temperature and quadratic distribution of surface heat flux, respectively. Applying the boundary layer theory proposed by Prandtl in 1904, we simplify the momentum and energy equations to a set of ordinary differential equations using a similarity transform. The energy equation we considered includes the viscous dissipation, internal heat generation or absorption, work due to deformation, Joule heating and radiation. The exact solutions for temperature are given in tems of the Kummer`s functions as well as Gamma functions. The surface temperature gradient for the prescribed surface temperature (PST) and surface temperature for the prescribed heat flux (PHF) for various parameters are drawn and tabulated. The appropriate physical interpretations about thermal characteristic are proposed in this thesis, and the asymptotic solutions for temperature functions with two heating conditions when modified Prandtl number is very large are also given.

中文摘要 Ⅰ
英文摘要 Ⅱ
目錄 Ⅲ
圖目錄 Ⅵ
表目錄 Ⅷ
符號說明 Ⅸ

第一章 緒論
1-1 研究動機及目的 1
1-2 本文研究方向 2
1-3 文獻回顧 2
1-3-1 非牛頓流體流經拉伸邊界及熱傳之分析 3
1-3-2 非牛頓多孔隙流體流經拉伸邊界及熱傳之分析 3
1-3-3 磁性流體流經拉伸邊界之流動及熱傳分析 4
1-4 非牛頓流體基本特性 6
第二章 基本磁性流體及多孔隙介質之理論模式 12
2-1 基本磁性流體力學理論 12
2-2 多孔隙介質之基本理論模式 14
第三章 理論基礎 17
3-1 基本系統描述 17
3-2 基本假設 17
3-3 統御方程式 18
3-4 Walters’ liquid B之流動分析 19
3-5 Walters’ liquid B之熱量傳遞分析 22
3-5-1 在給定表面溫度(PST)條件下之理論解 23
3-5-2 在給定表面熱通量(PHF)條件下之理論解 26
3-6 對Walters’liquid B溫度場之漸進分析 28
3-6-1 在給定表面溫度(PST)條件下之漸進分 28
3-6-2 在給定表面熱通量(PHF)條件下之漸進分析 30
3-7 二階流體之流動分析 31
3-8 二階流體之熱量傳遞 33
3-8-1 在給定表面溫度(PST)條件下之理論解 33
3-8-2 在給定表面熱通量(PHF)條件下之理論解 34
3-9 對二階流體溫度場之漸進分析 35
3-9-1 在給定表面溫度(PST)條件下之漸進分析 36
3-9-2 在給定表面熱通量(PHF)條件下之漸進分析 37
第四章 結果與討論 38
4-1 流場之分布情形 38
4-2 溫度場之分布情形 39
4-2-1在給定PST及PHF情況下溫度分布情形 39
4-2-2在給定PST及PHF情況下之表面溫度梯度及表面溫度之分布情形 41
4-3 溫度函數的漸進解 43
第五章 結論與建議 44
5-1 結論 44
5-1-1 流場之分布情形 44
5-1-2 溫度場之分布情形 44
5-2 建議 45
參考文獻 46
附錄 50

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