臺灣博碩士論文加值系統

本文使用晶格波茲曼法模擬密閉空穴與兩平行平板間垂直通道之奈米流體自然對流與混合對流，屬於二維穩態不可壓縮之流場 ，考慮在不同奈米流體濃度(0%、2%、4%)、不同瑞里數及不同理查森數的情況下對平均紐賽數之影響，並在垂直通道內加入一孔穴，考慮孔穴不同高寬比對局部紐賽數及平均紐賽數和溫度場之影響。並適當的設定入口的均勻流速度，以確保流場的適用性及避免太大的壓縮效應。

數值模擬結果顯示奈米流體之平均紐賽數較純水高，且隨著濃度的上升，平均紐賽數的增加更加顯著，同時平均紐賽數也會隨著瑞里數的增加帶來的溫差變化及理查森數的減少造成的特徵速度變快隨之升高，而孔穴之高寬比對孔穴內之流場及渦旋形狀有著顯著影響，且隨著孔穴愈大則平均紐賽數愈低。

In the present study, mathematical modeling is performed to simulate two-dimensional incompressible natural and mix convection of nanofluids in a vertical square enclosure and channel using the lattice Boltzmann method(LBM).Consider the effects of different concentration of nanofluids (0%, 2%, 4%), Rayleight number and Richardson number to averaged Nusselt number, and Consider the effects of putting a rectangle hole in vertical channel with different ratio of height and length to Nusselt number, averaged Nusselt number, and temperature field. The inlet velocity is chosen appropriately, so as to ensure the reasonable adaptation of fluid field and to avoid un-physical compressible effect.

Numerical results show that the averaged Nusselt number of nanofluids can be higher than pure water. Increasing the nanoparticle volume fraction will enhance the averaged Nusselt number. The averaged Nusselt number also increases by the temperature change caused by the increase of the Rayleigh number, the characteristic velocity change caused by Richardson number reduction. In the presence of significantly effects of the ratio of height and length of the rectangle hole to velocity field and vortex shape, and the averaged Nusselt number will decrease when the rectangle hole increased.

摘要I
ABSTRACTII
誌謝III
目錄IV
表目錄VI
圖目錄VII
符號說明XIII
第一章 緒論1
1-1 研究背景與動機1
1-2 文獻回顧3
1-3 本文架構6
第二章 數值方法與理論分析7
2-1 晶格波茲曼法簡介7
2-2 連續波茲曼方程式到晶格波茲曼方程式7
2-3 描述速度場的晶格波茲曼方法10
2-4 描述溫度場的晶格波茲曼方法13
2-5 浮力效應項的處理方法14
2-6 奈米流體理論分析16
2-7 速度場邊界處理方法18
2-7-1 完全反彈邊界18
2-7-2 速度與壓力邊界18
2-8 溫度場邊界處理方法21
第三章 數值方法驗證24
3-1 晶格波茲曼法模擬問題的步驟與程式流程24
3-2 自然對流於方型空穴驗證25
3-3 混和對流於平行平板間垂直通道驗證28
第四章 結果與討論36
4-1 方型空穴內奈米流體自然對流數值分析36
4-2 側壁驅動方型空穴內奈米流體混合對流數值分析40
4-3 兩平行平板間垂直通道自然對流數值分析45
4-3-1 平行平板間垂直通道自然對流流經一矩形孔穴47
4-4 兩平行平板間垂直通道混合對流數值分析50
4-4-1 平行平板間垂直通道混合對流流經一矩形孔穴53
第五章 結論與未來展望98
5-1 結論98
5-2 未來研究方向與建議99
參考文獻100

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