We show that a large set of nanofluid thermal conductivity data falls within the upper and lower Maxwell bounds for homogeneous systems. This indicates that the thermal conductivity of nanofluids is largely dependent on whether the nanoparticles stay dispersed in the base fluid, form large aggregates, or assume a percolating fractal configuration. The experimental data, which are strikingly analogous to those in most solid composites and liquid mixtures, provide strong evidence for the classical nature of thermal conduction in nanofluids.
Issue Section:
Micro/Nanoscale Heat Transfer
Keywords:
aggregation,
colloids,
fractals,
heat conduction,
nanoparticles,
percolation,
thermal conductivity
1.
Weitz
, D. A.
, Huang
, J. S.
, Lin
, M. Y.
, and Sung
, J.
, 1984, “Dynamics of Diffusion-Limited Kinetic Aggregation
,” Phys. Rev. Lett.
0031-9007, 53
, pp. 1657
–1660
.2.
Weitz
, D. A.
, Huang
, J. S.
, Lin
, M. Y.
, and Sung
, J.
, 1985, “Limits of the Fractal Dimension for Irreversible Kinetic Aggregation of Gold Colloids
,” Phys. Rev. Lett.
0031-9007, 54
, pp. 1416
–1419
.3.
Weitz
, D. A.
, and Oliveria
, M.
, 1984, “Fractal Structures Formed by Kinetic Aggregation of Aqueous Gold Colloids
,” Phys. Rev. Lett.
0031-9007, 52
, pp. 1433
–1436
.4.
5.
Fertman
, V. E.
, 1987, “Thermal and Physical Properties of Magnetic Fluids
,” J. Eng. Phys. Thermophys.
1062-0125, 53
, pp. 1097
–1105
.6.
Fertman
, V. E.
, Golovicher
, L. E.
, and Matusevich
, N. P.
, 1987, “Thermal Conductivity of Magnetite Magnetic Fluids
,” J. Magn. Magn. Mater.
0304-8853, 65
, pp. 211
–214
.7.
Popplewell
, J.
, Al-Qenaie
, A.
, Charles
, S. W.
, Moskowitz
, R.
, and Raj
, K.
, 1982, “Thermal Conductivity Measurements on Ferrofluids
,” Colloid Polym. Sci.
0303-402X, 260
, pp. 333
–338
.8.
Masuda
, H.
, Ebata
, A.
, Teramae
, K.
, and Hishinuma
, N.
, 1993, “Alteration of Thermal Conductivity and Viscosity of Liquid by Dispersing Ultra-Fine Particles (Dispersion of γ-Al2O3, SiO2, and TiO2 Ultra-Fine Particles)
,” Netsu Bussei
0913-946X, 7
, pp. 227
–233
.9.
Eastman
, J. A.
, Choi
, S. U. S.
, Li
, S.
, Thompson
, L. J.
, and Lee
, S.
, 1997, “Enhanced Thermal Conductivity Through the Development of Nanofluids
,” Mater. Res. Soc. Symp. Proc.
0272-9172, 457
, pp. 3
–11
.10.
Eastman
, J. A.
, Choi
, S. U. S.
, Li
, S.
, Yu
, W.
, and Thompson
, L. J.
, 2001, “Anomalously Increased Effective Thermal Conductivities of Ethylene Glycol-Based Nanofluids Containing Copper Nanoparticles
,” Appl. Phys. Lett.
0003-6951, 78
, pp. 718
–720
.11.
Patel
, H. E.
, Das
, S. K.
, Sundararajan
, T.
, Nair
, A. S.
, George
, B.
, and Pradeep
, T.
, 2003, “Thermal Conductivities of Naked and Monolayer Protected Metal Nanoparticle Based Nanofluids: Manifestation of Anomalous Enhancement and Chemical Effects
,” Appl. Phys. Lett.
0003-6951, 83
, pp. 2931
–2933
.12.
Wang
, X.
, Xu
, X.
, and Choi
, S. U. S.
, 1999, “Thermal Conductivity of Nanoparticle-Fluid Mixture
,” J. Thermophys. Heat Transfer
0887-8722, 13
, pp. 474
–480
.13.
Lee
, S.
, Choi
, S. U. S.
, Li
, S.
, and Eastman
, J. A.
, 1999, “Measuring Thermal Conductivity of Fluids Containing Oxide Nanoparticles
,” ASME J. Heat Transfer
0022-1481, 121
, pp. 280
–289
.14.
Das
, S. K.
, Putra
, N.
, Thiesen
, P.
, and Roetzel
, W.
, 2003, “Temperature Dependence of Thermal Conductivity Enhancement for Nanofluids
,” ASME J. Heat Transfer
0022-1481, 125
, pp. 567
–574
.15.
Rusconi
, R.
, Rodari
, E.
, and Piazza
, R.
, 2006, “Optical Measurements of the Thermal Properties of Nanofluids
,” Appl. Phys. Lett.
0003-6951, 89
, p. 261916
.16.
Venerus
, D. C.
, Kabadi
, M. S.
, Lee
, S.
, and Perez-Luna
, V.
, 2006, “Study of Thermal Transport in Nanoparticle Suspensions Using Forced Rayleigh Scattering
,” J. Appl. Phys.
0021-8979, 100
, p. 094310
.17.
Zhang
, X.
, Gu
, H.
, and Fujii
, M.
, 2006, “Effective Thermal Conductivity and Thermal Diffusivity of Nanofluids Containing Spherical and Cylindrical Nanoparticles
,” J. Appl. Phys.
0021-8979, 100
, p. 044325
.18.
Zhang
, X.
, Gu
, H.
, and Fujii
, M.
, 2006, “Experimental Study on the Effective Thermal Conductivity and Thermal Diffusivity of Nanofluids
,” Int. J. Thermophys.
0195-928X, 27
, pp. 569
–580
.19.
Xie
, H.
, Wang
, J.
, Xi
, T.
, and Liu
, Y.
, 2002, “Thermal Conductivity of Suspensions Containing Nanosized SiC Particles
,” Int. J. Thermophys.
0195-928X, 23
, pp. 571
–580
.20.
Putnam
, S. A.
, Cahill
, D. G.
, Braun
, P. V.
, Ge
, Z.
, and Shimmin
, R. G.
, 2006, “Thermal Conductivity of Nanoparticle Suspensions
,” J. Appl. Phys.
0021-8979, 99
, p. 084308
.21.
Keblinski
, P.
, Eastman
, J. A.
, and Cahill
, D. G.
, 2005, “Nanofluids for Thermal Transport
,” Mater. Today
1369-7021, 8
, pp. 36
–44
.22.
Singh
, D.
, Timofeeva
, E.
, Yu
, W.
, Routbort
, J.
, France
, D.
, Smith
, D.
, and Lopez-Cepero
, J. M.
, 2009, “An Investigation of Silicon Carbide-Water Nanofluid for Heat Transfer Applications
,” J. Appl. Phys.
0021-8979, 105
, p. 064306
.23.
Ju
, Y. S.
, Kim
, J.
, and Hung
, M. -T.
, 2008, “Experimental Study of Heat Conduction in Aqueous Suspensions of Aluminum Oxide Nanoparticles
,” ASME J. Heat Transfer
0022-1481, 130
, p. 092403
.24.
Timofeeva
, E. V.
, Gavrilov
, A. N.
, McCloskey
, J. M.
, Tolmachev
, Y. V.
, Sprunt
, S.
, Lopatina
, L. M.
, and Selinger
, J. V.
, 2007, “Thermal Conductivity and Particle Agglomeration in Alumina Nanofluids: Experiment and Theory
,” Phys. Rev. E
1063-651X, 76
, p. 061203
.25.
Chon
, C. H.
, Kihm
, K. D.
, Lee
, S. P.
, and Choi
, S. U. S.
, 2005, “Empirical Correlation Finding the Role of Temperature and Particle Size for Nanofluid (Al2O3) Thermal Conductivity Enhancement
,” Appl. Phys. Lett.
0003-6951, 87
, p. 153107
.26.
Hong
, T. K.
, Yang
, H. S.
, and Choi
, C. J.
, 2005, “Study of the Enhanced Thermal Conductivity of Fe Nanofluids
,” J. Appl. Phys.
0021-8979, 97
, p. 064311
.27.
Kang
, H. U.
, Kim
, S. H.
, and Oh
, J. M.
, 2006, “Estimation of Thermal Conductivity of Nanofluid Using Experimental Effective Particle Volume
,” Exp. Heat Transfer
0891-6152, 19
, pp. 181
–191
.28.
Murshed
, S. M. S.
, Leong
, K. C.
, and Yang
, C.
, 2005, “Enhanced Thermal Conductivity of TiO2-Water Based Nanofluids
,” Int. J. Therm. Sci.
1290-0729, 44
, pp. 367
–373
.29.
Murshed
, S. M. S.
, Leong
, K. C.
, and Yang
, C.
, 2006, “Determination of the Effective Thermal Diffusivity of Nanofluids by the Double Hot-Wire Technique
,” J. Phys. D
0022-3727, 39
, pp. 5316
–5322
.30.
Chopkar
, M.
, Das
, P. K.
, and Manna
, I.
, 2006, “Synthesis and Characterization of Nanofluid for Advanced Heat Transfer Applications
,” Scr. Mater.
1359-6462, 55
, pp. 549
–552
.31.
Chopkar
, M.
, Kumar
, S.
, Bhandari
, D. R.
, Das
, P. K.
, and Manna
, I.
, 2007, “Development and Characterization of Al2Cu and Ag2Al Nanoparticle Dispersed Water and Ethylene Glycol Based Nanofluid
,” Mater. Sci. Eng., B
0921-5107, 139
, pp. 141
–148
.32.
Li
, C. H.
, and Peterson
, G. P.
, 2007, “The Effect of Particle Size on the Effective Thermal Conductivity of Al2O3-Water Nanofluids
,” J. Appl. Phys.
0021-8979, 101
, p. 044312
.33.
Zhu
, H. T.
, Zhang
, C. Y.
, Tang
, Y. M.
, and Wang
, J. X.
, 2007, “Novel Synthesis and Thermal Conductivity of CuO Nanofluid
,” J. Phys. Chem. C
1932-7447, 111
, pp. 1646
–1650
.34.
Zhu
, H.
, Zhang
, C.
, Liu
, S.
, Tang
, Y.
, and Yin
, Y.
, 2006, “Effects of Nanoparticle Clustering and Alignment on Thermal Conductivities of Fe3O4 Aqueous Nanofluids
,” Appl. Phys. Lett.
0003-6951, 89
, pp. 023123
.35.
Li
, Q.
, and Xuan
, Y.
, 2006, “Enhanced Heat Transfer Behaviors of New Heat Carrier for Spacecraft Thermal Management
,” J. Spacecr. Rockets
0022-4650, 43
, pp. 687
–689
.36.
Li
, C. H.
, and Peterson
, G. P.
, 2006, “Experimental Investigation of Temperature and Volume Fraction Variations on the Effective Thermal Conductivity of Nanoparticle Suspensions (Nanofluids)
,” J. Appl. Phys.
0021-8979, 99
, p. 084314
.37.
Yoo
, D. -H.
, Hong
, K. S.
, and Yang
, H. -S.
, 2007,“Study of Thermal Conductivity of Nanofluids for the Application of Heat Transfer Fluids
,” Thermochim. Acta
0040-6031, 455
, pp. 66
–69
.38.
Vázquez Peñas
, J. R.
, Ortiz de Zárate
, J. M.
, and Khayet
, M.
, 2008, “Measurement of the Thermal Conductivity of Nanofluids by the Multicurrent Hot-Wire Method
,” J. Appl. Phys.
0021-8979, 104
, p. 044314
.39.
Philip
, J.
, Shima
, P. D.
, and Raj
, B.
, 2008, “Nanofluid With Tunable Thermal Properties
,” Appl. Phys. Lett.
0003-6951, 92
, p. 043108
.40.
Schmidt
, A. J.
, Chiesa
, M.
, Torchinsky
, D. H.
, Johnson
, J. A.
, Nelson
, K. A.
, and Chen
, G.
, 2008, “Thermal Conductivity of Nanoparticle Suspensions in Insulating Media Measured With a Transient Optical Grating and a Hotwire
,” J. Appl. Phys.
0021-8979, 103
, p. 083529
.41.
Sinha
, K.
, Kavlicoglu
, B.
, Liu
, Y.
, Gordaninejad
, F.
, and Graeve
, O. A.
, 2009, “A Comparative Study of Thermal Behavior of Iron and Copper Nanofluids
,” J. Appl. Phys.
0021-8979, 106
, p. 064307
.42.
Shima
, P. D.
, Philip
, J.
, and Raj
, B.
, 2009, “Role of Microconvection Induced by Brownian Motion of Nanoparticles in the Enhanced Thermal Conductivity of Stable Nanofluids
,” Appl. Phys. Lett.
0003-6951, 94
, p. 223101
.43.
Gharagozloo
, P. E.
, Eaton
, J. K.
, and Goodson
, K. E.
, 2008, “Diffusion, Aggregation, and the Thermal Conductivity of Nanofluids
,” Appl. Phys. Lett.
0003-6951, 93
, p. 103110
.44.
Garg
, J.
, Poudel
, B.
, Chiesa
, M.
, Gordon
, J. B.
, Ma
, J. J.
, Wang
, J. B.
, Ren
, Z. F.
, Kang
, Y. T.
, Ohtani
, H.
, Nanda
, J.
, McKinley
, G. H.
, and Chen
, G.
, 2008, “Enhanced Thermal Conductivity and Viscosity of Copper Nanoparticles in Ethylene Glycol Nanofluid
,” J. Appl. Phys.
0021-8979, 103
, p. 074301
.45.
Philip
, J.
, Shima
, P. D.
, and Raj
, B.
, 2007, “Enhancement of Thermal Conductivity in Magnetite Based Nanofluid due to Chainlike Structures
,” Appl. Phys. Lett.
0003-6951, 91
, p. 203108
.46.
Buongiorno
, J.
, Venerus
, D. C.
, Prabhat
, N.
, McKrell
, T.
, Townsend
, J.
, Christianson
, R.
, Tolmachev
, Y. V.
, Keblinski
, P.
, Hu
, L.-W.
, Alvarado
, J. L.
, Bang
, I. C.
, Bishnoi
, S. W.
, Bonetti
, M.
, Botz
, F.
, Cecere
, A.
, Chang
, Y.
, Chen
, G.
, Chung
, S. J.
, Chyu
, M. K.
, Das
, S. K.
, Di Paola
, R.
, Ding
, Y.
, Dubois
, F.
, Dzido
, G.
, Eapen
, J.
, Escher
, W.
, Funfschilling
, D.
, Galand
, Q.
, Gao
, J.
, Gharagozloo
, P. E.
, Goodson
, K. E.
, Gutierrez
, J. G.
, Hong
, H.
, Horton
, M.
, Hwang
, K. S.
, Iorio
, C. S.
, Jang
, S. P.
, Jarzebski
, A. B.
, Jiang
, Y.
, Jin
, L.
, Kabelac
, S.
, Kamath
, A.
, Kedzierski
, M. A.
, Kieng
, L. G.
, Kim
, C.
, Kim
, J.-H.
, Kim
, S.
, Lee
, S. H.
, Leong
, K. C.
, Manna
, I.
, Michel
, B.
, Ni
, R.
, Patel
, H. E.
, Philip
, J.
, Poulikakos
, D.
, Reynaud
, C.
, Savino
, R.
, Savino
, R.
, Singh
, P. K.
, Song
, P.
, Sundararajan
, T.
, Timofeeva
, E.
, Tritcak
, T.
, Turanov
, A. N.
, Van Vaerenbergh
, S.
, Wen
, D.
, Witharana
, S.
, Yang
, C.
, Yeh
, W.-H.
, Zhao
, X.-Z.
, and Zhou
, S.-Q.
, 2009, “A Benchmark Study on the Thermal Conductivity of Nanofluids
,” J. Appl. Phys.
0021-8979, 106
, p. 094312
.47.
Maxwell
, J. C.
, 1881, A Treatise on Electricity and Magnetism
, Vol. 1
, 2nd ed., Claredon
, Oxford
.48.
Hashin
, Z.
, and Shtrikman
, S.
, 1962, “A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials
,” J. Appl. Phys.
0021-8979, 33
, pp. 3125
–3131
.49.
Nan
, C. -W.
, Birringer
, R.
, Clarke
, D. R.
, and Gleiter
, H.
, 1997, “Effective Thermal Conductivity of Particulate Composites With Interfacial Thermal Resistance
,” J. Appl. Phys.
0021-8979, 81
, pp. 6692
–6699
.50.
Benveniste
, Y.
, 1987, “Effective Thermal Conductivity of Composites With a Thermal Contact Resistance Between the Constituents: Nondilute Case
,” J. Appl. Phys.
0021-8979, 61
, pp. 2840
.51.
Kim
, S. H.
, Choi
, S. R.
, and Kim
, D.
, 2007, “Thermal Conductivity of Metal-Oxide Nanofluids: Particle Size Dependence and Effect of Laser Irradiation
,” ASME J. Heat Transfer
0022-1481, 129
, pp. 298
–307
.52.
Hong
, K. S.
, Hong
, T. -K.
, and Yang
, H. -S.
, 2006, “Thermal Conductivity of Fe Nanofluids Depending on the Cluster Size of Nanoparticles
,” Appl. Phys. Lett.
0003-6951, 88
, p. 031901
.53.
Li
, C. H.
, Williams
, W.
, Buongiorno
, J.
, Hu
, L. -W.
, and Peterson
, G. P.
, 2008, “Transient and Steady-State Experimental Comparison Study of Effective Thermal Conductivity of Al2O3/Water Nanofluids
,” ASME J. Heat Transfer
0022-1481, 130
, p. 042407
.54.
Jha
, N.
, and Ramaprabhu
, S.
, 2009, “Thermal Conductivity Studies of Metal Dispersed Multiwalled Carbon Nanotubes in Water and Ethylene Glycol Based Nanofluids
,” J. Appl. Phys.
0021-8979, 106
, p. 084317
.55.
Every
, A. G.
, Tzou
, Y.
, Hasselman
, D. P. H.
, and Raj
, R.
, 1992, “The Effect of Particle Size on the Thermal Conductivity of ZnS/Diamond Composites
,” Acta Metall. Mater.
0956-7151, 40
, pp. 123
–129
.56.
Sofian
, N. M.
, Rusu
, M.
, Neagu
, R.
, and Neagu
, E.
, 2001, “Metal Powder-Filled Polyethylene Composites. V. Thermal Properties
,” J. Thermoplastic Composite Materials
, 14
, pp. 20
–33
.57.
Hasselman
, D. P. H.
, and Donaldson
, K. Y.
, 2000, “Role of Size in the Effective Thermal Conductivity of Composites With an Interfacial Thermal Barrier
,” J. Wide Bandgap Mater.
1524-511X, 7
, pp. 306
–318
.58.
Geiger
, A. L.
, Hasselman
, D. P. H.
, and Donaldson
, K. Y.
, 1993, “Effect of Reinforcement Particle Size on the Thermal Conductivity of a Particulate Silicon-Carbide Reinforced Aluminum-Matrix Composite
,” J. Mater. Sci. Lett.
0261-8028, 12
, pp. 420
–423
.59.
Pal
, R.
, 2007, “New Models for Thermal Conductivity of Particulate Composites
,” J. Reinf. Plast. Compos.
0731-6844, 26
, pp. 643
–651
.60.
Zhang
, H.
, Ge
, X.
, and Ye
, H.
, 2005, “Effectiveness of the Heat Conduction Reinforcement of Particle Filled Composites
,” Modell. Simul. Mater. Sci. Eng.
0965-0393, 13
, pp. 401
–412
.61.
Kumar
, D. H.
, Patel
, H. E.
, Kumar
, V. R. R.
, Sundararajan
, T.
, Pradeep
, T.
, and Das
, S. K.
, 2004, “Model for Heat Conduction in Nanofluids
,” Phys. Rev. Lett.
0031-9007, 93
, p. 144301
.62.
Bhattacharya
, P.
, Saha
, S. K.
, Yadav
, A.
, Phelan
, P. E.
, and Prasher
, R. S.
, 2004, “Brownian Dynamics Simulation to Determine the Effective Thermal Conductivity of Nanofluids
,” J. Appl. Phys.
0021-8979, 95
, pp. 6492
–6494
.63.
Koo
, J.
, and Kleinstreuer
, C.
, 2004, “A New Thermal Conductivity Model for Nanofluids
,” J. Nanopart. Res.
1388-0764, 6
, pp. 577
–588
.64.
Jang
, S. P.
, and Choi
, S. U. S.
, 2004, “Role of Brownian Motion in the Enhanced Thermal Conductivity of Nanofluids
,” Appl. Phys. Lett.
0003-6951, 84
, pp. 4316
–4318
.65.
Jang
, S. P.
, and Choi
, S. U. S.
, 2007, “Effects of Various Parameters on Nanofluid Thermal Conductivity
,” ASME J. Heat Transfer
0022-1481, 129
, pp. 617
–623
.66.
Prasher
, R.
, Bhattacharya
, P.
, and Phelan
, P. E.
, 2005, “Thermal Conductivity of Nanoscale Colloidal Solutions (Nanofluids)
,” Phys. Rev. Lett.
0031-9007, 94
, p. 025901
.67.
Prasher
, R.
, Bhattacharya
, P.
, and Phelan
, P. E.
, 2006, “Brownian-Motion-Based Convective-Conductive Model for the Effective Thermal Conductivity of Nanofluids
,” ASME J. Heat Transfer
0022-1481, 128
, pp. 588
–595
.68.
Li
, C. H.
, and Peterson
, G. P.
, 2007, “Mixing Effect on the Enhancement of the Effective Thermal Conductivity of Nanoparticle Suspensions (Nanofluids)
,” Int. J. Heat Mass Transfer
0017-9310, 50
, pp. 4668
–4677
.69.
Patel
, H. E.
, Sundararajan
, T.
, Pradeep
, T.
, Dasgupta
, A.
, Dasgupta
, N.
, and Das
, S. K.
, 2005, “A Micro-Convection Model for Thermal Conductivity of Nanofluids
,” Pramana, J. Phys.
0304-4289, 65
, pp. 863
–869
.70.
Yu
, W.
, and Choi
, S. U. S.
, 2003, “The Role of Interfacial Layers in the Enhanced Thermal Conductivity of Nanofluids: A Renovated Maxwell Model
,” J. Nanopart. Res.
1388-0764, 5
, pp. 167
–171
.71.
Xue
, Q. -Z.
, 2003, “Model for Effective Thermal Conductivity of Nanofluids
,” Phys. Lett. A
0375-9601, 307
, pp. 313
–317
.72.
Xie
, H.
, Fujii
, M.
, and Zhang
, X.
, 2005, “Effect of Interfacial Nanolayer on the Effective Thermal Conductivity of Nanoparticle-Fluid Mixture
,” Int. J. Heat Mass Transfer
0017-9310, 48
, pp. 2926
–2932
.73.
Xue
, Q.
, and Xu
, W. -M.
, 2005, “A Model of Thermal Conductivity of Nanofluids With Interfacial Shells
,” Mater. Chem. Phys.
0254-0584, 90
, pp. 298
–301
.74.
Tillman
, P.
, and Hill
, J. M.
, 2007, “Determination of Nanolayer Thickness for a Nanofluid
,” Int. Commun. Heat Mass Transfer
0735-1933, 34
, pp. 399
–407
.75.
Avsec
, J.
, and Oblak
, M.
, 2007, “The Calculation of Thermal Conductivity, Viscosity and Thermodynamic Properties for Nanofluids on the Basis of Statistical Nanomechanics
,” Int. J. Heat Mass Transfer
0017-9310, 50
, pp. 4331
–4341
.76.
Gao
, L.
, and Zhou
, X. F.
, 2006, “Differential Effective Medium Theory for Thermal Conductivity in Nanofluids
,” Phys. Lett. A
0375-9601, 348
, pp. 355
–360
.77.
Zhou
, X. F.
, and Gao
, L.
, 2006, “Effective Thermal Conductivity in Nanofluids of Nonsperical Particles With Interfacial Thermal Resistance: Differential Effective Medium Theory
,” J. Appl. Phys.
0021-8979, 100
, p. 024913
.78.
Prasher
, R.
, Evans
, W.
, Meakin
, P.
, Fish
, J.
, Phelan
, P.
, and Keblinski
, P.
, 2006, “Effect of Aggregation on Thermal Conduction in Colloidal Nanofluids
,” Appl. Phys. Lett.
0003-6951, 89
, p. 143119
.79.
Jie
, X.
, Yu
, B. -M.
, and Yun
, M. -J.
, 2006, “Effect of Clusters on Thermal Conductivity in Nanofluids
,” Chin. Phys. Lett.
0256-307X, 23
, pp. 2819
–2822
.80.
Feng
, Y.
, Yu
, B.
, Xu
, P.
, and Zou
, M.
, 2007, “The Effective Thermal Conductivity of Nanofluids Based on the Nanolayer and the Aggregation of Nanopartciles
,” J. Phys. D: Appl. Phys.
0022-3727, 40
, pp. 3164
–3171
.81.
Xu
, J.
, Yu
, B.
, Zou
, M.
, and Xu
, P.
, 2006, “A New Model for Heat Conduction of Nanofluids Based on Fractal Distributions of Nanoparticles
,” J. Phys. D
0022-3727, 39
, pp. 4486
–4490
.82.
Ren
, Y.
, Xie
, H.
, and Cai
, A.
, 2005, “Effective Thermal Conductivity of Nanofluids Containing Spherical Nanoparticles
,” J. Phys. D
0022-3727, 38
, pp. 3958
–3961
.83.
Wang
, B. -X.
, Zhou
, L. -P.
, and Peng
, Z. -F.
, 2003, “A Fractal Model for Predicting the Effective Thermal Conductivity of Liquid With Suspension of Nanoparticles
,” Int. J. Heat Mass Transfer
0017-9310, 46
, pp. 2665
–2672
.84.
Xuan
, Y.
, Li
, Q.
, and Hu
, W.
, 2004, “Aggregation Structure and Thermal Conductivity of Nanofluids
,” AIChE J.
0001-1541, 49
, pp. 1038
–1043
.85.
Prasher
, R.
, Phelan
, P. E.
, and Bhattacharya
, P.
, 2006, “Effect of Aggregation Kinetics on the Thermal Conductivity of Nanoscale Colloidal Solutions (Nanofluid)
,” Nano Lett.
1530-6984, 6
, pp. 1529
–1534
.86.
Keblinski
, P.
, Prasher
, R.
, and Eapen
, J.
, 2008, “Thermal Conductance of Nanofluids: Is the Controversy Over?
,” J. Nanopart. Res.
1388-0764, 10
, pp. 1089
–1097
.87.
deGroot
, S. R.
, and Mazur
, P.
, 1984, Nonequilibrium Thermodynamics
, Dover
, New York
.88.
DeVera
, A. L.
, and Strieder
, W.
, 1977, “Upper and Lower Bounds on the Thermal Conductivity of a Random, Two-Phase Material
,” J. Phys. Chem.
0022-3654, 81
, pp. 1783
.89.
Carson
, J. K.
, Lovatt
, S. J.
, Tanner
, D. J.
, and Cleland
, A. C.
, 2005, “Thermal Conductivity Bounds for Isotropic Porous Materials
,” Int. J. Heat Mass Transfer
0017-9310, 48
, pp. 2150
–2158
.90.
Griesinger
, A.
, Hurler
, W.
, and Pietralla
, M.
, 1997, “A Photothermal Method With Step Heating for Measuring the Thermal Diffusivity of Anisotropic Solids
,” Int. J. Heat Mass Transfer
0017-9310, 40
, pp. 3049
–3058
.91.
Eapen
, J.
, Williams
, W. C.
, Buongiorno
, J.
, Hu
, L. -W.
, Yip
, S.
, Rusconi
, R.
, and Piazza
, R.
, 2007, “Mean-Field Versus Microconvection Effects in Nanofluid Thermal Conduction
,” Phys. Rev. Lett.
0031-9007, 99
, p. 095901
.92.
Torquato
, S.
, and Rintoul
, M. D.
, 1995, “Effect of Interface on the Properties of Composite Media
,” Phys. Rev. Lett.
0031-9007, 75
, pp. 4067
–4070
.93.
Raghavan
, K.
, Foster
, K.
, Motakabbir
, K.
, and Berkowitz
, M.
, 1991, “Structure and Dynamics of Water at the Pt(111) Interface: Molecular Dynamics Study
,” J. Chem. Phys.
0021-9606, 94
, pp. 2110
–2117
.94.
Reedijk
, M. F.
, Arsic
, J.
, Hollander
, F. F. A.
, de Vries
, S. A.
, and Vlieg
, E.
, 2003, “Liquid Order at the Interface of KDP Crystals With Water: Evidence for Icelike Layers
,” Phys. Rev. Lett.
0031-9007, 90
, p. 066103
.95.
Mo
, H.
, Evmenenko
, G.
, and Dutta
, P.
, 2005, “Ordering of Liquid Squalane Near a Solid Surface
,” Chem. Phys. Lett.
0009-2614, 415
, pp. 106
–109
.96.
Yu
, C. -J.
, Richter
, A. G.
, Kmetko
, J.
, Dugan
, S. W.
, Datta
, A.
, and Dutta
, P.
, 2001, “Structure of Interfacial Liquids: X-Ray Scattering Studies
,” Phys. Rev. E
1063-651X, 63
, p. 021205
.97.
Eapen
, J.
, Li
, J.
, and Yip
, S.
, 2007, “Beyond the Maxwell Limit: Thermal Conduction in Nanofluids With Percolating Fluid Structures
,” Phys. Rev. E
1063-651X, 76
, p. 062501
.98.
Xue
, L.
, Keblinski
, P.
, Phillpot
, S. R.
, Choi
, S. U. S.
, and Eastman
, J. A.
, 2004, “Effect of Liquid Layering at the Liquid-Solid Interface on Thermal Transport
,” Int. J. Heat Mass Transfer
0017-9310, 47
, pp. 4277
–4284
.99.
Evans
, W.
, Fish
, J.
, and Keblinski
, P.
, 2007, “Thermal Conductivity of Ordered Molecular Water
,” J. Chem. Phys.
0021-9606, 126
, p. 154504
.100.
Mo
, H.
, Evmenenko
, G.
, Kewalramani
, S.
, Kim
, K.
, Ehrlich
, S. N.
, and Dutta
, P.
, 2006, “Observation of Surface Layering in a Nonmetallic Liquid
,” Phys. Rev. Lett.
0031-9007, 96
, p. 096107
.101.
Wang
, X. -Q.
, and Mujumdar
, A. S.
, 2007, “Heat Transfer Characteristics of Nanofluids: A Review
,” Int. J. Therm. Sci.
1290-0729, 46
, pp. 1
–19
.102.
Keblinski
, P.
, and Cahill
, D. G.
, 2005, “Comment on “Model for Heat Conduction in Nanofluids”
,” Phys. Rev. Lett.
0031-9007, 95
, p. 209401
.103.
Bastea
, S.
, 2005, “Comment on “Model for Heat Conduction in Nanofluids”
,” Phys. Rev. Lett.
0031-9007, 95
, p. 019401
.104.
He
, P.
, and Qiao
, R.
, 2008, “Self-Consistent Fluctuating Hydrodynamics Simulations of Thermal Transport in Nanoparticle Suspensions
,” J. Appl. Phys.
0021-8979, 103
, p. 094305
.105.
Morozov
, K. I.
, 2002, On the Theory of the Soret Effect in Colloids
, W.
Köhler
and S.
Wiegand
, eds., Springer-Verlag
, Berlin
.106.
Piazza
, R.
, 2004, “‘Thermal Forces’: Colloids in Temperature Gradients
,” J. Phys.: Condens. Matter
0953-8984, 16
, pp. S4195
–S4211
.107.
Keblinski
, P.
, Phillpot
, S. R.
, Choi
, S. U. S.
, and Eastman
, J. A.
, 2002, “Mechanisms of Heat Flow in Suspensions of Nano-Sized Particles (Nanofluids)
,” Int. J. Heat Mass Transfer
0017-9310, 45
, pp. 855
–863
.108.
Nie
, C.
, Marlow
, W. H.
, and Hassan
, Y. A.
, 2008, “Discussion of Proposed Mechanisms of Thermal Conductivity Enhancement in Nanofluids
,” Int. J. Heat Mass Transfer
0017-9310, 51
, pp. 1342
–1348
.109.
Hass
, K. C.
, Schneider
, W. F.
, Curioni
, A.
, and Andreoni
, W.
, 1998, “The Chemistry of Water on Alumina Surfaces: Reaction Dynamics From First Principles,”
,” Science
0036-8075, 282
, pp. 265
–268
.110.
Gmachowski
, L.
, 2002, “Aggregate Restructuring and Its Effect on the Aggregate Size Distribution
,” Colloids Surf., A
0927-7757, 207
, pp. 271
–277
.111.
Kim
, J.
, and Kramer
, T. A.
, 2006, “Improved Orthokinetic Coagulation Model for Fractal Colloids: Aggregation and Breakup
,” Chem. Eng. Sci.
0009-2509, 61
, pp. 45
–53
.112.
Wiltzius
, P.
, 1987, “Hydrodynamic Behavior of Fractal Aggregates
,” Phys. Rev. Lett.
0031-9007, 58
, pp. 710
–713
.113.
Hess
, W.
, Frisch
, H. L.
, and Klein
, R.
, 1986, “On the Hydrodynamic Behavior of Colloidal Aggregates
,” Z. Phys. B: Condens. Matter
0722-3277, 64
, pp. 65
–67
.114.
Buongiorno
, J.
, 2006, “Convective Transport in Nanofluids
,” ASME J. Heat Transfer
0022-1481, 128
, pp. 240
–250
.115.
Goldhirsch
, I.
, and Ronis
, D.
, 1983, “Theory of Thermophoresis. I. General Considerations and Mode-Coupling Analysis
,” Phys. Rev. A
1050-2947, 27
, pp. 1616
–1634
.116.
Lin
, F.
, Bhatia
, G. S.
, and Ford
, J. D.
, 1993, “Thermal Conductivities of Powder-Filled Epoxy Resins
,” J. Appl. Polym. Sci.
0021-8995, 49
, pp. 1901
–1908
.117.
Boudenne
, A.
, Ibos
, L.
, Fois
, M.
, Gehin
, E.
, and Majeste
, J. -C.
, 2004, “Thermophysical Properties of Polypropylene/Aluminum Composites
,” J. Polym. Sci., Part B: Polym. Phys.
0887-6266, 42
, pp. 722
–732
.118.
Tekce
, H. S.
, Kumlutas
, D.
, and Tavman
, I. H.
, 2007, “Effect of Particle Shape on Thermal Conductivity of Copper Reinforced Polymer Composites
,” J. Reinf. Plast. Compos.
0731-6844, 26
, pp. 113
–121
.119.
Xu
, Y.
, Chung
, D. D. L.
, and Mroz
, C.
, 2001, “Thermally Conducting Aluminum Nitride Polymer-Matrix Composites
,” Composites, Part A
1359-835X, 32
, pp. 1749
–1757
.120.
Agari
, Y.
, and Uno
, T.
, 1986, “Estimation of Thermal Conductivities of Filled Polymers
,” J. Appl. Polym. Sci.
0021-8995, 32
, pp. 5705
–5712
.121.
Cowling
, T. G.
, Gray
, P.
, and Wright
, P. G.
, 1963, “The Physical Significance of Formulae for the Thermal Conductivity and Viscosity of Gaseous Mixtures
,” Proc. R. Soc. London, Ser. A
0950-1207, 276
, pp. 69
–82
.122.
Pandey
, J. D.
, and Mishra
, R. K.
, 2005, “Theoretical Evaluation of Thermal Conductivity and Diffusion Coefficient of Binary Liquid Mixtures
,” Phys. Chem. Liq.
0031-9104, 43
, pp. 49
–57
.123.
Assael
, M. J.
, Charitidou
, E.
, and Wakeham
, W. A.
, 1989, “Absolute Measurements of the Thermal Conductivity of Mixtures of Alcohols With Water
,” Int. J. Thermophys.
0195-928X, 10
, pp. 793
–803
.124.
Li
, C. C.
, 1976, “Thermal Conductivity of Liquid Mixtures
,” AIChE J.
0001-1541, 22
, pp. 927
–930
.125.
Li
, Q.
, Xuan
, Y.
, and Wang
, J.
, 2005, “Experimental Investigations on Transport Properties of Magnetic Fluids
,” Exp. Therm. Fluid Sci.
0894-1777, 30
, pp. 109
–116
.126.
Jagannadham
, K.
, and Wang
, H.
, 2002, “Thermal Resistance of Interfaces in AlN-Diamond Thin Film Composites
,” J. Appl. Phys.
0021-8979, 91
, pp. 1224
–1235
.127.
Ge
, Z.
, Cahill
, D. G.
, and Braun
, P. V.
, 2006, “Thermal Conductance of Hydrophilic and Hydrophobic Interfaces
,” Phys. Rev. Lett.
0031-9007, 96
, p. 186101
.128.
Bryning
, M. B.
, Milkie
, D. E.
, Islam
, M. F.
, Kikkawa
, J. M.
, and Yodh
, A. G.
, 2005, “Thermal Conductivity and Interfacial Resistance in Single-Wall Carbon Nanotube Epoxy Composites
,” Appl. Phys. Lett.
0003-6951, 87
, p. 161909
.129.
Huxtable
, S. T.
, Cahill
, D. G.
, Shenogin
, S.
, Xue
, L.
, Ozisik
, R.
, Barone
, P.
, Usrey
, M.
, Strano
, M. S.
, Siddons
, G.
, Shim
, M.
, and Keblinski
, P.
, 2003, “Interfacial Heat Flow in Carbon Nanotube Suspension
,” Nature Mater.
1476-1122, 2
, pp. 731
–734
.130.
Nan
, C. -W.
, Liu
, G.
, Lin
, Y.
, and Li
, M.
, 2004, “Interface Effect on Thermal Conductivity of Carbon Nanotube Composites
,” Appl. Phys. Lett.
0003-6951, 85
, pp. 3549
–3551
.131.
Wen
, D.
, and Ding
, Y.
, 2004, “Experimental Investigation Into Convective Heat Transfer of Nanofluids at the Entrance Region Under Laminar Flow Conditions
,” Int. J. Heat Mass Transfer
0017-9310, 47
, pp. 5181
–5188
.132.
Wen
, D.
, and Ding
, Y.
, 2006, “Natural Convective Heat Transfer of Suspensions of Titanium Dioxide Nanoparticles (Nanofluids)
,” IEEE Trans. Nanotechnol.
1536-125X, 5
, pp. 220
–227
.133.
Shaikh
, S.
, Lafdi
, K.
, and Ponnappan
, R.
, 2007, “Thermal Conductivity Improvement in Carbon Nanoparticle Doped PAO Oil: An Experimental Study
,” J. Appl. Phys.
0021-8979, 101
, p. 064302
.134.
Choi
, S. U. S.
, Zhang
, Z. G.
, Yu
, W.
, Lockwood
, F. E.
, and Grulke
, E. A.
, 2001, “Anomalous Thermal Conductivity Enhancement in Nanotube Suspensions
,” Appl. Phys. Lett.
0003-6951, 79
, pp. 2252
–2254
.135.
Hwang
, Y.
, Lee
, J. K.
, Lee
, C. H.
, Jung
, Y. M.
, Cheong
, S. I.
, Lee
, C. G.
, Ku
, B. C.
, and Jang
, S. P.
, 2007, “Stability and Thermal Conductivity Characteristics of Nanofluids
,” Thermochim. Acta
0040-6031, 455
, pp. 70
–74
.136.
Wen
, D.
, and Ding
, Y.
, 2004, “Effective Thermal Conductivity of Aqueous Suspensions of Carbon Nanotubes (Carbon Nanotube Nanofluids)
,” J. Thermophys. Heat Transfer
0887-8722, 18
, pp. 481
–485
.137.
Williams
, W.
, Buongiorno
, J.
, and Hu
, L. -W.
, 2008, “Experimental Investigation of Turbulent Convective Heat Transfer and Pressure Loss of Alumina/Water and Zirconia/Water Nanoparticle Colloids (Nanofluids) in Horizontal Tubes
,” ASME J. Heat Transfer
0022-1481, 130
, p. 042412
.138.
Williams
, W. C.
, 2006, “Experimental and Theoretical Investigations of Transport Phenomena in Nanoparticle Colloids (Nanofluids)
,” Ph.D. thesis, Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA.139.
Bertolini
, D.
, and Tani
, A.
, 1997, “Thermal Conductivity of Water: Molecular Dynamics and Generalized Hydrodynamics Results
,” Phys. Rev. E
1063-651X, 56
, pp. 4135
–4151
.140.
Li
, L.
, and Chung
, D. D. L.
, 1994, “Thermally Conducting Polymer-Matrix Composites Containing Both AIN Particles and SIC Whiskers
,” J. Electron. Mater.
0361-5235, 23
, pp. 557
–564
.141.
National Institute of Standards and Technology (NIST)
, “Fluid Properties
,” http://webbook.nist.gov/chemistry/fluid/http://webbook.nist.gov/chemistry/fluid/142.
Rusconi
, R.
, Williams
, W.
, Buongiorno
, J.
, Piazza
, R.
, and Hu
, L. -W.
, 2007, “Numerical Analysis of Convective Instabilities in a Transient Short-Hot-Wire Setup for Measurement of Liquid Thermal Conductivity
,” Int. J. Thermophys.
0195-928X, 28
, pp. 1131
–1146
.143.
2007, “
CRC Handbook of Chemistry and Physics
,” http://www.hbcpnetbase.comhttp://www.hbcpnetbase.com144.
Kwak
, K.
, and Kim
, C.
, 2005, “Viscosity and Thermal Conductivity of Copper Oxide Nanofluid Dispersed in Ethylene Glycol
,” Korea-Aust. Rheol. J.
1226-119X, 17
, pp. 35
–40
.145.
“
The A-Z of Materials
,” http://www.azom.comhttp://www.azom.com146.
Weidenfeller
, B.
, Höfer
, M.
, and Schilling
, F.
, 2002, “Thermal and Electrical Properties of Magnetite Filled Polymers
,” Composites, Part A
1359-835X, 33
, pp. 1041
–1053
.147.
Bozorth
, R. M.
, 1978, Ferromagnetism
, IEEE
, New York
.148.
Yu
, R. C.
, Tea
, N.
, Salamon
, M. B.
, Lorents
, D.
, and Malhotra
, R.
, 1992, “Thermal Conductivity of Single Crystal C60
,” Phys. Rev. Lett.
0031-9007, 68
, pp. 2050
–2053
.Copyright © 2010
by American Society of Mechanical Engineers
You do not currently have access to this content.