電子設備散熱在工業科技中相當重要，為了將熱快速帶離發熱元件，近年開始微小化機械，而其中微通道是構成微系統的重要結構，且高熱傳效率一直是該系統的重要需求。針對微通道內奈米流體之熱流場模擬，有別於過去多數文獻中所使用之單相模型，本文將進一步採用Buongiorno所提出之兩相混和模型來研究微通道內之對流熱傳。此兩相模型將考慮奈米粒子與基礎載液間之滑動機制，包括布朗運動及熱泳擴散，而此方法亦被證實比單相模型具有更高之精準度。透過考慮壁面滑移速度與溫度跳躍之效應，本文將此兩相模型之應用範圍將由連續流態延伸至滑移流態。本研究透過改變流場雷諾數、瑞利數、克努森數、奈米粒子濃度與布朗熱泳比值(NBT)等參數，探討其對二維平板微通道內奈米流體熱傳特性及流場結構之影響。
　　結果表明，雷諾數的增加對於熱傳是有益的，因為發展長度的增加使得紐塞數上升，但對壓力損失卻是增加的；而瑞利數的提升對於紐塞數同樣是有所幫助的，因為溫度差的增加使得溫度梯度上升；在克努森數的提升下，紐塞數下降，因為溫度梯度的下降使紐塞數減少，但對於壓力損失是減少的，因為有滑移的存在使得能量損耗減少；而在布朗與熱泳之比值的增加情況下，熱傳增加、壓力損失下降，這對於微通道應用在微小物件上是相當有利的。此外，主導速度發展長度之變數因濃度而異，濃度低時雷諾數是主要影響變數，而濃度高時則由克努森數主導；在溫度發展長度上則是雷諾數的影響較克努森數要大，並發現入口處具較高之紐塞數；影響壓力損失的主要變數則為克努森數。

The heat dissipation of the electronic equipment is very important in industrial technology. In recent years, microchannels are basic structure of the microsystems and ultrahigh heat transfer performance is one of the most important needs in these systems for quickly remove heat from the heating elements. For the simulation of the thermal flow field of nanofluids in microchannels, which is different from the single-phase model used in most past papers, this paper will further use the two-phase mixed model proposed by Buongiorno to research the convective heat transfer in a microchannel. Both Brownian and thermophoresis diffusions are considered as the nanoparticle/base-fluid slip mechanisms in this two-phase model, and this method has also been proven to have higher accuracy than the single-phase model. By considering the effects of wall slip velocity and temperature jump, the application range of this two-phase model will be from continuum flow regime to slip flow regime. In this study, the effects of Reynolds number, Rayleigh number, Knudsen number, and nanoparticle concentration on the heat transfer and flow field situation of nanofluids in a two-dimensional parallel plate microchannel will be studied through numerical simulation.
The results show that the increase of the Reynolds number is beneficial to heat transfer, because it increases in thermal development length, and increases the Nusselt number, but it increases in pressure drop. The increase of the Rayleigh number is also helpful to Nusselt number, because the temperature difference increases, the temperature gradient rises. The increase of the Knudsen number decreases Nusselt number, because the temperature gradient decreases, and the Nusselt number decreases, and it is beneficial to the pressure drop, because decreased energy loss due to slip flow. In the case for increasing of ratio of Brownian and thermophoretic diffusivities, the heat transfer increases and the pressure drop reduces, which is quite advantageous for the application of microchannels to small objects. Besides the variation of the dominant hydrodynamic development length varies with concentration, and the Reynolds number is the main influence variable at low concentrations, while the Knudsen number is dominant at high concentrations. In terms of thermal development length, the effect of Reynolds number is larger than that of Knudsen number, and found that the entrance has a high Nusselt number. The main variable that affects the pressure drop is the Knudsen number.

目錄
摘要 I
Abstract II
誌謝 IV
目錄 V
表目錄 VII
圖目錄 VIII
符號說明 X
第一章 緒論 1
1.1文獻探討 1
1.2 研究動機 6
第二章 數值和研究方法 7
2.1 數值方法 7
2.1.1 統御方程式(Governing Equations) 7
2.1.2 本構方程式(Constitutive Equations) 8
2.1.3 本文所使用的參數與數值方法 9
2.2 研究方法 13
2.2.1 模擬模型 13
2.2.2 邊界條件 15
2.2.3 網格生成與驗證 16
第三章 結果與討論 18
3.1 對速度發展長度影響 18
3.1.1 雷諾數對速度發展長度之影響 18
3.1.2 瑞利數對速度發展長度之影響 22
3.1.3 克努森數對速度發展長度之影響 24
3.1.4 奈米粒子濃度對速度發展長度之影響 25
3.1.5 布朗熱泳比值對速度發展長度之影響 25
3.2 對溫度發展長度之影響 27
3.2.1 雷諾數對於溫度發展長度之影響 27
3.2.2 瑞利數對於溫度發展長度之影響 32
3.2.3 克努森數對於溫度發展長度之影響 34
3.2.4奈米粒子濃度對於溫度發展長度之影響 35
3.2.5 布朗熱泳比值對溫度發展長度之影響 35
3.3 對紐賽數之影響 36
3.3.1 雷諾數對於紐賽數之影響 37
3.3.2 瑞利數對於紐賽數之影響 42
3.3.3 克努森數對於紐賽數之影響 46
3.3.4 奈米粒子濃度對於紐賽數之影響 48
3.3.5 布朗熱泳比值對於紐賽數之影響 48
3.4 對壓力損失之影響 50
3.4.1 雷諾數對於壓力損失之影響 50
3.4.2 瑞利數對於壓力損失之影響 53
3.4.3 克努森數對於壓力損失之影響 55
3.4.4 奈米粒子濃度對於壓力損失之影響 57
3.4.5 布朗熱泳比值對於壓力損失之影響 57
第四章 總結 59
4.1 結論 59
4.2 未來展望 60
參考文獻 61

表目錄
表1 微通道內黏滯係數與熱傳導係數統計表 5
表2 滑移參數表 10
表3 實驗所使用的奈米流體及濃度 12
表4 基本性質表(1大氣壓40⁰C) 14

 
圖目錄
圖1 克努森數範圍 2
圖2 模型示意圖 13
圖3 網格測試及Niu et al. [39]比對 17
圖4 固定∆T之速度發展長度與濃度關係圖 19
圖5 速度contour圖,∆T=50K,Kn=0.01 20
圖6 固定克努森數之速度發展長度與濃度關係圖 22
圖7 固定雷諾數之速度發展長度與濃度關係圖 24
圖8 固定∆T，雷諾數與克努森數對速度發展長度的影響力 25
圖9 固定克努森數之速度發展長度與布朗熱泳比值關係圖 27
圖10 固定∆T之溫度發展長度與濃度關係圖 29
圖11 溫度contour圖,∆T=50K,Kn=0.01 30
圖12 固定克努森數之溫度發展長度與濃度關係圖 31
圖13 固定雷諾數之溫度發展長度與濃度關係圖 33
圖14 固定∆T，雷諾數與克努森數對溫度發展長度影響力 35
圖15 固定雷諾數之溫度發展長度與布朗熱泳比值關係圖 36
圖16 固定∆T之紐賽數與濃度關係圖 38
圖17 ∆T=30K，Kn=0.01，X=0.1下，不同雷諾數的θ分布曲線 39
圖18 固定克努森數之紐賽數與濃度關係圖 41
圖19 雷諾數的紐賽數隨X位置變化分布曲線 42
圖20 固定雷諾數之紐賽數與濃度關係圖 44
圖21 X=0.1，∆T的溫度分布曲線 45
圖22固定克努森數，∆T與雷諾數對紐賽數影響力 46
圖23 X=0.1，克努森數的θ分布曲線 47
圖24 固定雷諾數之紐賽數與布朗熱泳比值關係圖 50
圖25 固定∆T之壓力損失與濃度關係圖 51
圖26 固定克努森數之壓力損失與濃度關係圖 53
圖27 固定雷諾數之壓力損失與濃度關係圖 55
圖28 不同克努森數下U隨X位置變化分布曲線 56
圖29 固定克努森數之壓力損失與布朗熱泳比值關係圖 58

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