奈米流體在水平流體層與多孔介質層之雙層系統中熱對流穩定性分析

Thermal instability of nanofluids in a horizontal fluid layer overlying a porous layer

林吉成(Ji-Cheng Lin)

指導教授 ： 陳發林

國立臺灣大學/工學院/應用力學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202001911

摘要

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。

關鍵字

流體穩定學 ； 奈米流體 ； 多孔介質 ； 熱對流

並列摘要

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.

並列關鍵字

flow stability ； nanofluids ； porous media ； thermal convection

參考文獻

1.Klaus D. Sattler, Handbook of Nanophysics: Nanoparticles and Quantum, 2011. : p. 30-5.

2.Choi, S., Enhancing thermal conductivity of fluids with nanoparticles. ASME-Publications-Fed, 1995. 231: p. 99-106.

3.Hung, Y.-H., T.-P. Teng, and B.-G. Lin, Evaluation of the thermal performance of a heat pipe using alumina nanofluids. Experimental Thermal and Fluid Science, 2013. 44: p. 504-511.

4.Wang, X.-Q. and A.S. Mujumdar, A review on nanofluids-part I: theoretical and numerical investigations. Brazilian Journal of Chemical Engineering, 2008. 25(4): p. 613-630.

5.J.-H. Lee, K. S. Hwang, S. P. Jang, B. H. Lee, J. H. Kim, S. U.S. Choi, and C. J. Choi, “Effective viscosities and thermal conductivities of aqueous nanofluids containing low volume concentrations of Al2O3 nanoparticles,” Int. J. Heat Mass Transfer, 2008. p. 2651-2656.