臺灣博碩士論文加值系統

本文以座標轉換系統探討磁場及化學反應作用下微極流體通過垂直波形表面之混合對流的暫態行為。統制方程式之推導由完整的Navier-Stokes方程式著手，配合Eringen所推導之微極流體理論將牛頓流體擴展至非牛頓流體的應用。經轉換後之統制方程式可將不規則邊界展開成一規則的計算平面，並配合三次樣線交換方向定置法（SADI；Spline Alternating-Direction Implicit Method） 求解。
研究結果顯示，因微粒懸浮流體具有渦漩黏度、旋轉梯度黏度及微慣量密度等特性，因此造成流動阻力增加及熱傳率、質傳率下降。在加入磁場後，產生的Lorentz力為逆著浮力的方向，抵消了部分浮力效應，促使流體運動趨緩，熱傳、質傳效果因而變差。由於化學反應導致流體中濃度產生變化，流場中濃度梯度不再侷限在單一方向，在質傳率上的影響亦遠比熱傳率強烈。綜合本文實例發現，波形表面所增加的熱傳面積足以抵消因由表面幾何形狀所造成的流動不便所產生之熱阻抗。因此在波形表面的熱傳率皆高於相對應的平板。此外，值得注意的是，通常熱傳、質傳效率的增加亦隱含著板面摩擦係數的增加。

In this study, the coordinate transformation method is used to analyze the transient behavior of the mixed convection in micropolar fluids flow through a vertical wavy surface under magnetic field and chemical raction effect. The governing equations of system are derived from complete Navier-Stokes equations with theories of micropolar fluids, and we can expand the applications from in Newtonian fluids to in non-Newtonian fluids. The transformed governing equations can expand the irregular boundary into a calculable regular plane, and then solve it by using the spline alternating-direction implicit method (SADI).
Numerical results show that, in micropolar fluids, with the velocity of fluid and heat transfer rate and mass transfer rate would decrease since effets of vortex viscosity, spin-gradient viscosity and micro-inertia density. After entering the magnetic field, the produced Lorentz force opposed the
buoyancy effects, and urges the fluid motion into slowing, then the effects
on heat transfer and mass transfer are going to decrease. The chemical reaction induces the concentration change of the fluid, and the concentration gradient in the fluid is not only in one direction. It leads that the effects on mass transfer rate is much stronger than the effects on heat transfer rate.
The synthetic result show that the add quantity of heat transfer area in wavy surfaces is enough to offset the thermal resistance which is due to the geometry surfaces. Therefore, the heat transfer rate of wavy surface is higher than that of the corresponding flat plate in all fluids. Furthermore, it should be noted that the increase in heat transfer rate usually implies the increase in skin-friction coefficient.

中文摘要……………………………………………………………Ⅰ
ABSTRACT……………………………………………………………Ⅱ
誌謝…………………………………………………………………Ⅲ
目錄…………………………………………………………………Ⅳ
表目錄………………………………………………………………Ⅴ
圖目錄………………………………………………………………Ⅵ
符號說明……………………………………………………………Ⅶ
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 研究方法………………………………………………………5
1-4 論文結構………………………………………………………5
第二章、理論分析………………………………………………………7
2-1 基本擴散質傳遞理論…………………………………………7
2-2 理論模型的建構與假設………………………………………8
2-2.1 Prandtl 轉換理論……………………………………12
2-3 數值分析………………………………………………………19
2-3.1 解題程序 ………………………………………………20
第三章、結果與討論……………………………………………………22
3-1 混合對流Mixed Convection（Gr/Re2 ≠0、Gc/Re2 ≠ 0）……23
3-1.1 浮力參數Ri與Rd對混合對流的影響………………23
3-1.2 微極流體參數R對混合對流的影響………………26
3-1.3 化學反應參數 對混合對流的影響…………………27
3-1.4 廣義Prandtl數與Schmidt數對混合流體的影響……29
3-1.5 磁場強度Mn對混合流體的影響……………………31
3-1.6 波板振幅 對混合流體的影響………………………32
第四章、總結……………………………………………………………77
4-1 結論……………………………………………………………77
4-2 建議及展望……………………………………………………80
附錄一、三次樣線數值方法……………………………………………81
A-1 三次樣線背景…………………………………………………81
A-2 三次樣線法原理………………………………………………83
A-3 三次樣線法求解微分方程……………………………………86
A-3.1 求解一微二階偏微分方程式…………………………86
A-3.2 求解二微二階偏微分方程式…………………………88
A-4 三次樣線法邊界條件的處理…………………………………90
附錄二、基本磁性流體力學理論………………………………………93
參考文獻…………………………………………………………………96
自述……………………………………………………………………102

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