# 臺灣博碩士論文加值系統

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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………………………………………………………………….. 11-1 研究目的與動機及其背景……………………………………... 11-2 相關文獻回顧…………………………………………………... 21-3 研究方法……………………………………………………….. 41-4 本文架構……………………………………………………….. 4第二章 理論分析與數值方法……………………………………………….. 52-1 物理模型……………………………………………………….. 52-2 基本假設……………………………………………………….. 62-3 統御方程式…………………………………………………… 62-4 系統的邊界狀況……………………………………………… 72-5 無因次化分析…………………………………………………. 82-6 邊界條件………………………………………………………. 10第三章 數值方法…………...……………………………………...………123-1 數值解析…………….…….................................................. 12 3-2 數值方法……………………………………………....... 143-2.1 線函數表示法及其性質……………………..................153-2.2 利用三次樣線函數求解…………...……………..……. 183-3.3 邊界條件之處理…………………………...…..………. 223-4 解題方法與程序……………………………….……………….. 23第四章 結果與討論………………………………………………………….. 244-1 數值方法正確性之測試……………...………………………… 244-2 格點測試…………………………..………………………………….244-3 流場之暫態過程……………………………………............. 244-4 Grashof數值與微極流體參數R之影響……………............254-5 達西數Da與微極流體參數R之影響…………………………… 264-6 微極流體λ參數的影響………………………………………... 274-7 不同微極流體參數的暫態影響………………………………… 284-8 不同達西數的暫態影響……………………………………… 284-9 不同Grashof數的暫態影響…………………………………… 284-10 Nusselt數在不同Grashof數的穩態分佈……………………… 284-11 Nusselt數在不同達西數的穩態分佈………………………… 29第五章 結論與建議………………………………………………………….. 765-1 結論……………………………………...……………………… 775-2 對未來研究之建議…………………………………………… 77參考文獻……………………………………………………………………… 78
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 1 微極流體在充滿多孔介質之方形移動蓋口容器中混合對流熱傳研究 2 微極流體在開放內穴之自然對流熱傳研究 3 飽和多孔隙介質流體於垂直雙通渠道內之流動與熱傳 4 局部熱源對充滿多孔介質封閉容器內微極流體自然對流影響之研究 5 橫向磁化雙層平板多孔介質磁泊蘇葉-庫頁流之理論分析 6 徑向磁化多孔圓環介質中圓柱磁庫頁流之理論分析 7 方形開放容器中微極流體之自然對流熱傳研究

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