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研究生:洪銘全
研究生(外文):Ming-Chuan Hung
論文名稱:局部熱傳數值分析在多孔介質容器中之自然對流研究
論文名稱(外文):Partial heat transfer numerical analysis in a porous medium container of Natural convection
指導教授:許燦輝
指導教授(外文):Tsan-Hui Hsu
學位類別:碩士
校院名稱:國立高雄應用科技大學
系所名稱:機械與精密工程研究所
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:2007
畢業學年度:95
語文別:中文
論文頁數:80
中文關鍵詞:微極流體多孔介質達西數三次樣線交換方向定置法
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本文係以數值計算方法來模擬求解多孔介質下微極流體在方體容器中之自然對流熱傳分析問題,在二維的方體容器中,充滿相同的密集氣孔和滲透性流動飽和的多孔介質。上下壁面及左側部份為絕熱,右側壁面保持低溫(Tl)狀態,左側壁面裝置W長溫度為Th之熱源且Th>Tl,重力方向為垂直朝下。統御方程式之推導由完整的 Navier-Stokes 方程式著手,配合微極流體之定律將牛頓流體擴展至非牛頓流體的應用。數值計算上是以三次樣線交換方向定置法(SADI;Spline Alternating Direction Implicit Method)在個人電腦上求解。無因次化轉換後的統御方程式以流線、渦旋函數、角動量及溫度函數等表示,並得到穩態的熱傳效應。而影響熱場的數值參數主要有 Pr、Gr、達西數和微極流體特有的參數。由數值模擬顯示得知,一般牛頓流體比微極流體的熱傳效果較佳,多孔性介質具有提昇熱傳效率的功能,本文將密閉容器所模擬結果的流場以及溫度場繪製並討論之。
Natural convection of micropolar fluids in a square enclosure filled with fluid-saturated porous medium is numerically investigated in this study. The model is a two-dimensional enclosure filled with porous media. Both the top and the bottom walls are adiabatic. The left wall is also adiabatic except a heat source with finite length w is installed on the lower part. The wall on the right side is kept at a lower temperature Ti and Th>Tl.
The governing equations for micropolar fluid were first presented by A.C.Eringen, wherein we furthermore expand the applications to non-Newtonian fluids. The numerical computations were obtained using the cubic spline collocation method in a personal computer. The governing equations, including stream function, vorticity, microrotation, and energy, were first put in dimensionless form. The governing parameters appearing in present study are Pr, Gr, Da, and several characteristic parametersof the micropolar fluids. The numerical results of the flow fields are discussed with plots of isotherms, streamlines, and velocity vectors. Computational results show that the Newtonian fluid has more significant convection heat transfer effect than that of micropolar fluid and the porous medium can effectively enhance the heat transfer rate.
中文摘要(橫式)……………………………………………………………. i
英文摘要(橫式)……………………………………………………………. ii
致謝…………………………………………………………………………… iii
目錄…………………………………………………………………………… iv
表目錄………………………………………………………………………… vi
圖目錄…………………………………………………………….......... vii
符號說明………………………………………………………….......... x
第一章 緒論………………………………………………………………….. 1
1-1 研究目的與動機及其背景……………………………………... 1
1-2 相關文獻回顧…………………………………………………... 2
1-3 研究方法……………………………………………………….. 4
1-4 本文架構……………………………………………………….. 4
第二章 理論分析與數值方法……………………………………………….. 5
2-1 物理模型……………………………………………………….. 5
2-2 基本假設……………………………………………………….. 6
2-3 統御方程式…………………………………………………… 6
2-4 系統的邊界狀況……………………………………………… 7
2-5 無因次化分析…………………………………………………. 8
2-6 邊界條件………………………………………………………. 10
第三章 數值方法…………...……………………………………...………12
3-1 數值解析…………….…….................................................. 12
3-2 數值方法……………………………………………....... 14
3-2.1 線函數表示法及其性質……………………..................15
3-2.2 利用三次樣線函數求解…………...……………..……. 18
3-3.3 邊界條件之處理…………………………...…..………. 22
3-4 解題方法與程序……………………………….……………….. 23
第四章 結果與討論………………………………………………………….. 24
4-1 數值方法正確性之測試……………...………………………… 24
4-2 格點測試…………………………..………………………………….24
4-3 流場之暫態過程……………………………………............. 24
4-4 Grashof數值與微極流體參數R之影響……………............25
4-5 達西數Da與微極流體參數R之影響…………………………… 26
4-6 微極流體λ參數的影響………………………………………... 27
4-7 不同微極流體參數的暫態影響………………………………… 28
4-8 不同達西數的暫態影響……………………………………… 28
4-9 不同Grashof數的暫態影響…………………………………… 28
4-10 Nusselt數在不同Grashof數的穩態分佈……………………… 28
4-11 Nusselt數在不同達西數的穩態分佈………………………… 29
第五章 結論與建議………………………………………………………….. 76
5-1 結論……………………………………...……………………… 77
5-2 對未來研究之建議…………………………………………… 77
參考文獻……………………………………………………………………… 78
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