臺灣博碩士論文加值系統

本論文將對流體層與多孔介質層組成的雙層系統添加奈米顆粒，並對該系統進行熱對流線性穩定性分析。主要討論的機制包括奈米流體的熱泳機制與布朗運動，以及雙層系統的厚度比例影響，其比例關係稱為厚度比，定義為流體層厚度與多孔介質層厚度的比值。
分析結果發現熱泳是一個影響系統不穩定性的重要機制，由於該參數與濃度有關，而濃度則又與溫度相關。由基態解的結果可知溫差愈大，奈米顆粒會越累積在冷端。鑒於此首先探討奈米顆粒濃度隨厚度比變化對系統的不穩定性影響。研究結果指出，當使用符合實際情況的奈米顆粒濃度時，系統是無條件不穩定的，亦溫差只要一點點就造成不穩定，但為了探討此問題的存在，因此不再探討中性穩定曲線的變化，取而代之的是觀察擾動波的成長。結果發現當系統的厚度比較小時，長波處的成長率大於短波處，代表長波對流比短波更加不穩定。對流主要發生區域在多孔介質層，稱之為多孔介質模態。而隨著厚度比增加，短波對流比長波對流不穩定，對流主要發生在流體層，稱之為流體層模態。此現象稱為系統的模態轉換。
而模態轉換的發生不僅存在於奈米顆粒濃度的改變，亦發生在如溫度差的變化與雙層系統有關之參數，其參數如孔隙率、Beavers-Joseph constant、與Darcy number，而其結果也都表明當厚度比到達一定值時，其模態皆會由多孔介質層轉變為流體層模態，其結果也符號物理的機制。

In this paper, nanoparticles will be added to a two-layer system which is consisting of a fluid layer and a porous medium layer, and the thermal convection linear stability of the system will be analyzed. The Brownian motion and thermophoretic mechanism of the nanofluids will be discussed, and also discuss the proportional effect of the two-layer system, the effect is called the depth ratio, which is defined as the ratio of the thickness of the fluid layer to the thickness of the porous medium layer.
The results found that thermophoresis is an important mechanism which affects the instability of the system. Because this parameter is related to the concentration, also the concentration is related to temperature difference. From the result of the basic state solution, it can be seen that the larger temperature difference, the more nanoparticles will accumulate at the cold side. In view of this, we first discuss the influence of nanoparticle concentration with depth ratio on the instability of the system. The results indicate that the system is unconditionally unstable when the concentration of nanoparticles in accordance with actual conditions is used, and the small temperature difference will cause instability easily. However, in order to discuss this problem, the neutral curves will not be discussed. Instead, we observe the growth rate of disturbance. It was found that when the depth ratio of the system is relatively small, the growth rate at the long wave is greater than at the short wave, which indicates that the long wave convection is more unstable than the short wave. So convection mainly occurs in the porous medium layer, which is called porous medium mode. As the depth ratio increases, short wave convection is more unstable than long wave convection, and convection mainly occurs in the fluid layer, which is called the fluid layer mode. This phenomenon is called mode conversion.
The mode conversion occurs not only in the change of nanoparticle concentration, but also in the change of temperature difference and the parameters related to the porous medium, such as porosity, Beavers-Joseph constant, and Darcy number. The results also show when the depth ratio reaches a certain value, its mode will change from the porous medium layer to the fluid layer mode.

致謝 i
摘要 ii
Abstract iii
目錄 iv
圖目錄 vi
表目錄 vii
符號說明 viii
第一章 緒論 1
1.1 研究背景 1
1.2 文獻回顧 4
1.3 研究動機 5
1.4 本文架構 6
第二章 理論模型 7
2.1 物理模型與基本假設 7
2.2 奈米流體模型的介紹 8
2.2.1 熱泳 (Thermophresis) 11
2.2.2 布朗運動(Brownian Motion) 12
2.3 統御方程式 13
2.3.1奈米顆粒在流體層的方程式 13
2.3.2奈米顆粒在多孔隙介質層的方程式 14
2.3.3邊界條件 16
第三章 線性穩定性分析 18
3.1 無因次化分析 18
3.1.1流體層無因次化 18
3.1.2多孔介質層無因次化 20
3.1.3邊界條件無因次化 22
3.2 穩定基態解 23
3.2.1流體層的溫度、濃度基態解 24
3.2.2多孔介質層的溫度、濃度基態解 25
3.3 線性微擾化 26
3.3.1流體層統御方程式之線性微擾化 26
3.3.2流體層統御方程式之線性微擾化 27
3.3.3邊界條件之線性微擾化 28
3.4 正規模態展開 29
3.4.1統御方程式之正規模態展開 29
3.4.2邊界條件之正規模態展開 31
3.5 數值方法 32
第四章 結果與討論 35
4.1 參數設定 35
4.2 厚度比與 對穩定基態解之影響 37
4.3 厚度比與濃度間的雙模態轉換關係 39
4.4 厚度比與溫度間的雙模態轉換關係 42
4.5 厚度比與孔隙率對成長率之影響 44
4.6 厚度比與Beavers-Joseph constant對成長率之影響 46
4.7 厚度比與達西數對成長率之影響 48
第五章 結論與未來展望 50
5.1 結論 50
5.2 未來展望 51
參考文獻 52

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