纳米颗粒聚集形态对纳米流体导热系数的影响
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摘要
纳米流体中悬浮的纳米颗粒可以增强其导热性能已经得到广泛认可,然而纳米流体颗粒增强传热的机理目前尚不清楚.研究表明,纳米颗粒的聚集是纳米流体导热系数增大的重要机制,而且纳米颗粒聚集的形态对纳米流体的导热系数有重要影响,但是目前的导热系数模型大多是建立在Maxwell有效介质理论的"静态"和"均匀分散"假设基础上.本文用平衡分子动力学模拟Cu-Ar纳米流体,采用Green-Kubo公式计算导热系数,采用Schmidt-Ott关系式计算不同聚集形态下的分形维数.对比导热系数与分形维数可以发现:在相同体积分数下,较低的分形维数会有更高的导热系数,分析了分形维数与导热系数的定量关系.此外,通过径向分布函数可以看出纳米颗粒紧密聚集与松散聚集的差异,基液分子在纳米颗粒附近的纳米薄层中处于动态平衡状态.研究结果有助于理解纳米颗粒聚集形态对导热系数的影响机理.
The great interest of many researchers has been aroused in recent two decades due to the great heat transfer enhancement of nanofluid as a heat transfer medium. The reason why the nanofluid can enhance heat transfer is that a number of nanoparticles are suspended in the carry fluid. Most of researchers believe that the microconvection induced by Brownian motion of nanoparticle, the nanolayer around the nanoparticle, the aggregation of nanoparticles and near-field radiation are the underlying mechanisms for heat transfer enhancement by nanofluid. However, contradictories and inconsistencies among experimental results, theoretical results and numerical results are existent commonly because the mechanism of heat transportation by nanoparticles remains unclear so far. Quite a few researches have proven that the aggregation of nanoparticles is one of the important mechanisms for elevating the effective thermal conductivity(ETC) of nanofluid. However,the aggregation morphology(AM) of nanoparticles evaluated by fractal dimension(FD) will greatly influence the thermal conductivity of nanofluid. Unfortunately, all of the existing ETC models are based on the effective medium theory under the assumption of "static state" and "homo-dispersion". In the present work, equilibrium molecular dynamics(EMD) simulations are carried out to calculate the thermal conductivity of Cu-Ar nanofluid via Green-Kubo formula. In existing researches, fractal dimensions of the aggregations with various morphologies are obtained by Schmidt-Ott equation. Comparisons between the ETC and FD of the nanofluid with same volume fraction show that lower FD can possess greater ETC. It is the first time that the quantitative relationship between ETC and FD has been analyzed. In addition, the difference between loose and compact aggregation can be read out of the pair correlation function near nanoparticles. And the solvent atoms in nanolayer are mobilized and dynamically balanced. The results obtained in the present research are conducible to understanding the influence of AM of nanoparticles on the ETC of nanofluid.
The great interest of many researchers has been aroused in recent two decades due to the great heat transfer enhancement of nanofluid as a heat transfer medium. The reason why the nanofluid can enhance heat transfer is that a number of nanoparticles are suspended in the carry fluid. Most of researchers believe that the microconvection induced by Brownian motion of nanoparticle, the nanolayer around the nanoparticle, the aggregation of nanoparticles and near-field radiation are the underlying mechanisms for heat transfer enhancement by nanofluid. However, contradictories and inconsistencies among experimental results, theoretical results and numerical results are existent commonly because the mechanism of heat transportation by nanoparticles remains unclear so far. Quite a few researches have proven that the aggregation of nanoparticles is one of the important mechanisms for elevating the effective thermal conductivity(ETC) of nanofluid. However,the aggregation morphology(AM) of nanoparticles evaluated by fractal dimension(FD) will greatly influence the thermal conductivity of nanofluid. Unfortunately, all of the existing ETC models are based on the effective medium theory under the assumption of "static state" and "homo-dispersion". In the present work, equilibrium molecular dynamics(EMD) simulations are carried out to calculate the thermal conductivity of Cu-Ar nanofluid via Green-Kubo formula. In existing researches, fractal dimensions of the aggregations with various morphologies are obtained by Schmidt-Ott equation. Comparisons between the ETC and FD of the nanofluid with same volume fraction show that lower FD can possess greater ETC. It is the first time that the quantitative relationship between ETC and FD has been analyzed. In addition, the difference between loose and compact aggregation can be read out of the pair correlation function near nanoparticles. And the solvent atoms in nanolayer are mobilized and dynamically balanced. The results obtained in the present research are conducible to understanding the influence of AM of nanoparticles on the ETC of nanofluid.
引文
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[2]Choi S U S,Zhang Z G,Yu W 2001 Appl.Phys.Lett.79 52
[3]Maxwell J C 1873 A Treatise on Electricity and Magnetism(Oxford:Clarendon Press)p68
[4]Hamilton R L,Crosser O K 1962 Ind.Eng.Chem.Fundam.1187
[5]Xuan Y M,Li Q,Zhang X,Fujii M 2006 J.Appl.Phys.100043507
[6]Wang B X,Yan W S 2007 Prog.Nat.Sci.17 984(in Chinese)[王补宣,颜文盛2007自然科学进展17 984]
[7]Prasher R,Phelan P E,Bhattacharya P 2006 Nano Lett.61529
[8]Lin J Z,Xia Y,Ku X K 2016 Int.J.Heat Mass Transf.93 57
[9]Li Y T,Shen L P,Wang H,Wang H B 2013 Acta Phys.Sin.62 124401(in Chinese)[李屹同,沈谅平,王浩,汪汉斌2013物理学报62 124401]
[10]Xue L,Keblinski P,Phillpot S R,Choi S U S,Eastman J A2004 Int.J.Heat Mass Transf.47 4277
[11]Keblinski P,Prasher R,Eapen J 2008 J.Nanopart.Res.101089
[12]Hu Y Q,Zhao Y P,Yu T X 2008 Int.J.Nonlin.Sci.Num.Sim.9 315
[13]Hu Y Q,Zhao Y P,Yu T X 2008 Mater.Sci.Eng.A483-484 611
[14]Sedighi M,Mohebbi A 2014 J.Mol.Liq.197 14
[15]Hong J,Kim D 2012 Thermochim.Acta 542 28
[16]Philip J,Shima P D,Raj B 2007 Appl.Phys.Lett.91 203103
[17]Wu C,Cho T J,Xu J,Lee D G,Yang B,Zachariah M R2010 Phys.Rev.E 81 011406
[18]Thaseem T,Christopher J H 2011 J.Nanopart.Res.13 7099
[19]Xuan Y M,Li Q,Hu W 2003 AIChE J.49 1038
[20]Feng Y,Yu B,Xu P,Zou M 2007 J.Phys.D 40 3164
[21]Wang B X,Zhou L P,Peng X F 2003 Int.J.Heat Mass Transf.46 2665
[22]Evans W,Prasher R,Fish J,Meakin P,Phelan P,Keblinski P 2008 Int.J.Heat Mass Transf.51 1431
[23]Prasher R,Evans W,Meakin P,Fish J,Phelan P,Keblinski P 2006 Appl.Phys.Lett.89 143119
[24]Xiao B Q,Yang Y,Chen L X 2013 Powder Technol.239 409
[25]Cai J C,Hua X Y,Xiao B Q,Zhou Y F,Wei W 2017 Int.J.Heat Mass Transf.105 623
[26]Atmuri A K,Henson M A,Bhatia S R 2013 Colloids and Surfaces A 436 325
[27]Gaganpreet S S 2012 Appl.Nanosci.2 325
[28]Kang H,Zhang Y,Yang M,Li L 2012 J.Nanotechnol.Eng.Med.3 021001
[29]Duan F,Kwek D,Crivol A 2011 Nanoscale Res.Lett.6 248
[30]Lin J Z,Xia Y,Ku X K 2014 J.Heat Transf.T.ASME 136111701
[31]Kang H,Zhang Y,Yang M 2011 Appl.Phys.A 103 1001
[32]Lee S L,Saidur R,Sabri M F M,Min T K 2015 Num.Heat Transf.A 8 432
[33]Li L,Guo L,Yang M,Lu M,Yu M 2010 J.Eng.Thermophys.31 1933(in Chinese)[李凌,郭丽,杨茉,卢玫,余敏2010工程热物理学报31 1933]
[34]Gross D,Hauger W,Schr?der J,Wall W A 2014 Engineering Mechanics(Berlin:Springer)p104
[35]Daw M S,Baskes M I 1984 Phys.Rev.B 29 6443
[36]Jones R E,Mandadapu K K 2012 J.Chem.Phys.136 154102
[37]McQuarrie D A 2000 Statistical Mechanics(Sausalito:University Science Books)p55
[38]Jullien R,Botet R 1987 Aggregation and Fractal Aggregates(Singapore:World Scientific Publishing Co.)p138
[39]Schmidt-Ott A,Wüstenberg J 1995 J.Aerosol.Sci.26 S923
[40]Agresti F,Barison S,Battiston S 2013 Nanotechnology 24365601
[41]Rapaport D C 2004 The Art of Molecular Dynamics Simulations(New York:Cambridge University Press)p35
[42]Allen M P,Tildesley D J 1987 Computer Simulation of Liquids(New York:Oxford Press)p236
[43]Sarkar S,Selvam R P 2007 J.Appl.Phys.102 074302
[44]Fang X P,Xuan Y M,Li Q 2009 Appl.Phys.Lett.95 203108
[45]Gharagozloo P E,Goodson K E 2010 J.Appl.Phys.108074309
[46]Sadeghi R,Haghshenasfard M,Etemad S,Keshavarzi E 2016Int.Com.Heat Mass Transf.72 57
[47]Xie H,Wang J,Xi T,Liu Y,Ai F 2002 J.Appl.Phys.914568