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研究生:童凱煬
研究生(外文):Kai-Yang Tung
論文名稱:磁場作用下冪次定律流體通過傾斜波形板之暫態對流熱傳分析
論文名稱(外文):Transient Convection of Power-Law Fluids over an Inclined Wavy Plate with a Magnetic Field
指導教授:陳朝光陳朝光引用關係
指導教授(外文):Chao-Kuang Chen
學位類別:碩士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
學門:工程學門
學類:機械工程學類
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:100
中文關鍵詞:三次樣線法座標轉換傾斜波形表面冪次定律流體
外文關鍵詞:SADIcoordinate transformationpower-law fluidsinclined wavy surface
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本文以座標轉換系統探討磁場作用下冪次定律流體通過傾斜波形表面之層流強迫及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,配合冪次定律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。當問題簡化至牛頓流體或平板之特例時,所得之結果與相關文獻比較十分吻合,驗證本文所使用之座標轉換技巧及數值方法不僅有利於解析複雜的幾何邊界,且所得的結果亦相當合理。
研究結果顯示,冪次定律形式之非牛頓流體由於剪應力會隨著應變率而改變,因此其熱傳率與板面剪應力隨冪次指數的變化在強迫對流與在自然對流為主的熱傳模式有完全相反的結果。而當熱傳表面凸起或凹陷時,此種邊界上的位移將強迫導致流場發生變化,並進一步地影響到熱傳效率。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 laminar force and mixed convection in power-law fluids flow over an inclined wavy surface including the magnetic field effect. The governing equations of system are derived from complete Navier-Stokes equations with theories of power-law fluids, 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). When the mathematical model is simplified to a special case of in Newtonian fluids or on flat plates, the results have good agreement with previous works. This indicates that, the coordinate transformation and numerical methods used in this study are favorable to solve the complex geometry boundary and give reasonable results.
Numerical results show that, since the stress would change with rate shearing strain in power-law fluids of non-Newtonian fluid, the heat transfer rate and the skin-friction coefficient depend on power index would have opposite results as the heat transfer modes are nature convection and forced convection. When the heat transfer surface is lumpy, this displacement of boundary will disturb the flow and alter the 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………………………………………………………..……….. Ⅶ
圖目錄……………………………………………..…………….…………. Ⅷ
符號說明………………………………………………………..………ⅩⅥ

第一章、 緒論…………………………………………….……..……………1
1-1 研究動機及其背景…………………………………..………...…1
1-2 文獻回顧……………………………………………..…..……….3
1-3 研究方法……………………………………………..…………...6
1-4 本文架構…………………………………………..…..…………6

第二章、理論分析…………………………………………………..……….8
2-1 基本的磁性流體力學理論…………………………..…..……..8
2-2 基本假設及統制方程式………………………………..……….10
2-2.1 Prandtl 轉換理論…………………………………..…..…..13
2-3 數值分析………………………………………………..……….19
2-3.1 解題程序…………………………………………..……....20

第三章、數值方法………………………………………………..…………22
3-1 三次樣線函數的由來…………………………….……………22
3-2 三次樣線的數學理論……………………………….…………24
3-3 利用三次樣線函數求解偏微分方程式……………………27
3-4 邊界條件之處理………………………………………..……….31

第四章、結果與討論………………………………………………..……….34
4-1 強迫對流 Forced Convection( )………..……….36
4-1.1 冪次定律指數n對強迫對流的影響………….…………36
4-1.2 磁場強度Mn對強迫對流的影響……………….………38
4-1.3 廣義Prandtl數對強迫對流的影響…………….….….…39
4-1.4 波振幅 對強迫對流的影響……………...……….……40
4-2 混合對流 Mixed Convection( )…………….…..41
4-2.1 冪次定律指數n對混合對流的影響……...………….….41
4-2.2 磁場強度Mn對混合對流的影響……………………….44
4-2.3 廣義Prandtl數對混合對流的影響…………..….………45
4-2.4 波振幅 對混合對流的影響…………………….………46
4-2.5 傾斜角度 對混合對流的影響…………………………...48
4-2.6 浮力參數Ri對混合對流的影響…………………….……49

第五章、總結與展望………………………………………………….……..90
5-1 結論……………………………………………………….….….90
5-2 建議及展望…………………………………………….………93

參考文獻…………………………………………………………….……..94
自述………………………………………………………………….…….100
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