雙重溫度與濃度梯度下多孔性介質中磁流體之雙擴散對流現象

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曾家麟(Chia-Lin Tzeng) 查詢紙本館藏

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機械工程學系

論文名稱

雙重溫度與濃度梯度下多孔性介質中磁流體之雙擴散對流現象
(Hydromagnetic Double-diffusiveConvection In A Porous Medium With Opposing Temperature And Concentration Gradients)

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摘要(中)

本文利用數值模擬研究多孔性矩形封閉空間中，雙重溫度與濃度梯度下磁流體之雙擴散對流現象。多孔性介質內部考慮黏滯效應、慣性力與浮力效應之影響。定義上、下壁面為絕熱，左、右壁面為固定溫度與固定濃度，並在橫向上施加一均勻不隨時間變化之磁場作用於流場。這個受磁場影響的流場，我們指定研究浮力比（buoyancy ratio）範圍N=0~2.0，普朗特數（Prandtl number
Pr=1.0~5.0，路易士數（Lewis number）Le=0.1~2.0，瑞里數（Rayleigh number），以及設定此封閉區域的長寬比例為2：1、達西數（Darcy number）Da=10-5~10-1與孔隙率（porosity）ε=0.2~0.8。受磁場影響之流場熱質傳變化會因磁場大小不同而增大或降低。本文研究之結果，熱質傳的變化受到不同普朗特數、路易士數、浮力比、內部熱源、滲透率（permeability）、孔隙率，瑞里數與哈曼數（Hartmann number）之大小不同，高溫壁面平均之紐塞爾數（Nusselt number）與希吾爾德數（Sherwood number）的變化亦不同。
在暫態研究方面，流體依其熱慣性（thermal inertia）的不同，配合高瑞里數之條件下，流場流動會呈現不同程度之震盪變化，在磁場強度增強下會抑制這種現象，使流動震盪減緩並較快達到穩態。
本研究在瑞里數RaT=105下，將高溫壁面之平均紐塞爾數與平均希吾爾德數對磁場及孔隙率之關係統計成一半經驗式（correlation），期望提供工業界從事類似研究之先進一參考性的指標。

摘要(英)

The problem of hydromagnetic double-diffusive convective flow of a binary mixture in a porous rectangular enclosure is solved numerically in this work. The effects of viscosity and inertial force of the porous medium are considered. The upper and lower walls are insulated. Constant temperatures and concentrations are imposed along the left and right walls of the porous enclosure and a uniform magnetic field is applied in the x-direction. The buoyancy ratio is in the range of 0.0~2.0, Prandtl number in 1.0~5.0, Lewis number in 0.1~2.0, Rayleigh number in 105~107, Darcy number in 10-5~10-1, porosity in 0.2~0.8 and the enclosure aspect ratio is fixed at 2.0.
Results for various conditions were presented and discussed. It is found that the flow structure and heat transfer characteristics inside the enclosure depend strongly on the porosity, permeability, the magnetic field, the effect of buoyancy and the thermal inertia. The effect of the magnetic field is found to reduce the movement of the convection within the enclosure.
For the unsteady case, the flow oscillates periodically at high Rayleigh number and high heat capacity ratio. The application of magnetic field reduces the oscillation.
Finally, this work provides correlations of the Nusselt number vs. porosity and the Hartmann number.

關鍵字(中)

★ 磁流體
★ 多孔性介質
★ 雙擴散對流

關鍵字(英)

★ double-diffusive convection
★ hydormagnetic
★ porous medium

論文目次

中文摘要………………………………………………………………Ⅰ
英文摘要………………………………………………………………Ⅲ
誌謝……………………………………………………………………Ⅳ
目錄……………………………………………………………………Ⅴ
表目錄…………………………………………………………………Ⅷ
圖目錄…………………………………………………………………Ⅸ
符號說明………………………………………………………………XV
一、緒論……………………………………………………1
1.1 研究背景與動機……………………………………………1
1.2 磁流體構造與簡介…………………………………………4
1.3 文獻回顧……………………………………………………6
1.4 研究主題……………………………………………………10
二、磁流場理論與分析…………………………………12
2.1 幾何模型……………………………………………………12
2.2 統御方程式…………………………………………………13
2.3 初始條件與邊界條件………………………………………17
2.4 磁場與勞倫茲力……………………………………………19
2.5 Heat capacity ratio分析………………………………21
三、數值方法與驗證……………………………………23
3.1 數值方法……………………………………………………23
3.1.1 能量方程式…………………………………………23
3.1.2 連續與動量方程式…………………………………26
3.1.3 壓力修正方程式……………………………………30
3.2 格點與驗證………………………………………………32
3.2.1 格點驗證……………………………………………32
3.2.2 驗證………………………………………………33
3.3 程式驗證………………………………………………36
3.3.1 穩態解之驗證………………………………………36
3.3.2 暫態解之驗證………………………………………37
四、結果與討論……………………………………41
4.1 內部熱源之影響………………………………………41
4.2 磁場與滲透率之影響…………………………………43
4.3 孔隙率之影響…………………………………………44
4.4 不同浮力比之影響……………………………………44
4.5 不同普朗特數與路易士數之影響……………………45
4.6 暫態過程磁場效應之影響……………………………50
4.7 暫態過程浮力效應之影響……………………………51
4.8 暫態過程熱慣性之影響………………………………51
4.9 週期性震盪之現象……………………………………54
4.10 多孔介質中受磁場影響之經驗式…………………54
五、結論與建議……………………………………87
5.1 結論…………………………………………………87
5.2 未來研究方向與建議………………………………88
參考文獻…………………………………………………90

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指導教授

曾重仁(Chung-Jen Tseng)

審核日期

2004-7-16

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