The degree of variability between theoretical and empirical nanofluid viscosity model predictions and relevant experimental data is examined in this work. Results confirm a high degree of variability in the compared data; with some observed inconsistencies in the model formulations and the predicted data, consequently, a range of constitutive factors need to be incorporated into the models in order to accurately predict the rheological behavior of nanofluids in different use conditions. Notably, conducting broad theoretical studies and empirical investigations into the rheological behavior of nanofluids incorporating the fundamental parametric variables can plausibly lead to near-generalized models.

References

References
1.
Hosseini
,
S. M.
,
Moghadassi
,
A. R.
, and
Henneke
,
D. E.
,
2010
, “
A New Dimensionless Group Model for Determining the Viscosity of Nanofluids
,”
J. Therm. Anal. Calorim.
,
100
(
3
), pp.
873
877
.10.1007/s10973-010-0721-0
2.
Dzido
,
G.
,
Chmiel-Kurowska
,
K.
,
Gierczycki
,
A.
, and
Jarz¸bski
,
A. B.
,
2009
, “
Application of Klein's Equation for Description of Viscosity of Nanofluid
,”
Comput. Aided Chem. Eng.
,
26
, pp.
955
960
.10.1016/S1570-7946(09)70159-2
3.
Ho
,
C. J.
,
Chen
,
M. W.
, and
Li
,
Z. W.
,
2008
, “
Numerical Simulation of Natural Convection of Nanofluid in a Square Enclosure: Effects Due to Uncertainties of Viscosity and Thermal Conductivity
,”
Int. J. Heat Mass Transfer
,
51
(
17–18
), pp.
4506
4516
.10.1016/j.ijheatmasstransfer.2007.12.019
4.
Krieger
,
I. M.
, and
Dougherty
,
T. J.
,
1959
, “A Mechanism for Non-Newtonian Flow in Suspensions of Rigid Spheres,”
Trans. Soc. Rheol.
,
3
(1), pp.
137
152
.10.1122/1.548848
5.
Keblinski
,
P.
,
Phillpot
,
S. R. E.
,
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
,
45
(
4
), pp.
855
863
.10.1016/S0017-9310(01)00175-2
6.
Nguyen
,
C. T.
,
Desgranges
,
F.
,
Roy
,
G.
,
Galanis
,
N.
,
Maré
,
T.
,
Boucher
,
S.
, and
Mintsa
,
H. A.
,
2007
, “
Temperature and Particle-Size Dependent Viscosity Data for Water-Based Nanofluids–Hysteresis Phenomenon
,”
Int. J. Heat Fluid Flow
,
28
(6), pp.
1492
1506
.10.1016/j.ijheatfluidflow.2007.02.004
7.
Choi
,
S. U. S.
, and
Eastman
,
J. A.
,
1995
, “
Enhancing Thermal Conductivity of Fluid With Nanoparticles
,”
International Mechanical Engineering Congress and Exhibition
,
San Francisco, CA
, Nov. 12–17.
8.
Wang
,
L. Q
., ed.,
2009
,
Advances in Transport Phenomena
, ADVTRANS 1,
Springer-Verlag
,
Berlin, Heidelberg, Germany
, pp.
135
177
.
9.
Venerus
,
D. C.
,
Buongiorno
,
J.
,
Christianson
,
R.
,
Townsend
,
J.
,
Bang
,
I. C.
,
Chen
,
G.
,
Chung
,
S. J.
,
Chyu
,
M.
,
Chen
,
H.
,
Ding
,
Y.
,
Dubois
,
F.
,
Dzido
,
G.
,
Funfschilling
,
D.
,
Galand
,
Q.
,
Gao.
,
J.
,
Hong
,
H.
,
Horton
,
M.
,
Hu
,
L.
,
Iorio
,
C. S.
,
Jarzebski
,
A. B.
,
Jiang.
,
Y.
,
Kabelac
,
S.
,
Mark
,
K. A.
,
Kim
,
C.
,
Kim
,
J.
,
Kim
,
S.
,
McKrell
,
T.
,
Ni
,
R.
,
Philip
,
J.
,
Prabhat
,
N.
,
Song
,
P.
,
Vaerenbergh
,
S. V.
,
Wen
,
D.
,
Witharana
,
S.
,
Zhao
,
X.
, and
Zhou
,
S.
,
2010
, “
Viscosity Measurements
,”
Appl. Rheol.
,
20
(
4
), pp.
1
7
.
10.
Yanjiao
,
L.
,
Zhou
,
J.
,
Tung
,
S.
,
Schneider
,
E.
, and
Xi
,
S.
,
2009
, “
A Review on Development of Nanofluid Preparation and Characterization
,”
Powder Technol.
,
196
(2), pp.
89
101
.10.1016/j.powtec.2009.07.025
11.
Masoumi
,
N.
,
Sohrabi
,
N.
, and
Behzadmehr
,
A.
,
2009
, “
A New Model for Calculating the Effective Viscosity of Nanofluids
,”
J. Phys. D: Appl. Phys.
,
42
(5), p.
055501
.10.1088/0022-3727/42/5/055501
12.
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
,
50
(
21–22
), pp.
4331
4341
.10.1016/j.ijheatmasstransfer.2007.01.064
13.
Okhio
,
C.
,
Hodges
,
D.
, and
Black
,
J.
,
2010
, “
Review of Literature on Nanofluid
,”
Multidiscip. J. Sci. Technol., J. Sel. Areas Nanotechnol. (JSAN)
, pp.
1
8
.
14.
Hosseini
,
M.
, and
Ghader
,
S.
,
2010
, “
A Model for Temperature and Particle Volume Fraction Effect on Nanofluid Viscosity
,”
J. Mol. Liq.
,
153
(
2–3
), pp.
139
145
.10.1016/j.molliq.2010.02.003
15.
Chen
,
H.
,
Ding
,
Y.
,
Lapkin
,
A.
, and
Fan
,
X.
,
2009
, “
Rheological Behaviour of Ethylene Glycol–Titanate Nanotube Nanofluids
,”
J. Nanopart. Res.
,
11
(
6
), pp.
1513
1520
.10.1007/s11051-009-9599-9
16.
Renon
,
H.
, and
Prausnitz
,
J. M.
,
1968
, “
Local Composition in Thermodynamics Excess Functions for Liquid Mixtures
,”
J. AIChE
,
14
(
1
), pp.
135
144
.10.1002/aic.690140124
17.
Schmidt
,
A. J.
,
Chiesa
,
M.
,
Torchinsky
,
D. H.
,
Jeremy
,
A.
,
Boustani
,
A.
,
McKinley
,
G. H.
,
Nelson
,
K. A.
, and
Johnson
,
G. C.
,
2008
, “
Experimental Investigation of Nanofluid Shear and Longitudinal Viscosities
,”
Appl. Phys. Lett.
92
(24), p.
244107
.10.1063/1.2945799
18.
Wong
,
K. V.
, and
Leon
,
O.
,
2010
, “
Applications of Nanofluids: Current and Future
,”
Adv. Mech. Eng.
,
5
, p.
519659
.
19.
Vékás
,
L.
,
Marinică
,
O.
,
Susan-Resiga
,
D.
,
Stoian
,
F. D.
, and
Bica
,
D.
,
2004
, “
Magnetic and Flow Properties of High Magnetization Nanofluids
,”
Proceedings of the 6th International Conference on Hydraulic Machinery and Hydrodynamics
,
Timisoara, Romania
, Oct. 21–22.
20.
Yu
,
W.
,
Xie
,
H.
,
Li
,
Y.
, and
Chen
,
L.
,
2011
, “
Experimental Investigation on Thermal Conductivity and Viscosity of Aluminum Nitride Nanofluid
,”
Particuology
,
9
(
2
), pp.
187
191
.10.1016/j.partic.2010.05.014
21.
Prasher
,
R.
,
Song
,
D.
,
Wang
,
J.
, and
Phelan
,
P. E.
,
2006
, “
Measurements of Nanofluid Viscosity and Its Implications for Thermal Applications
,”
Appl. Phys. Lett.
,
89
(13), p.
133108
.10.1063/1.2356113
22.
Pastoriza-Gallego
,
M. J.
,
Casanova
,
C.
,
Legidoa
,
J. L.
, and
Piñeiro
,
M. M.
,
2011
, “
CuO in Water Nanofluid: Influence of Particle Size and Polydispersity on Volumetric Behaviour and Viscosity
,”
Fluid Phase Equilib.
,
300
(1--2), pp.
188
196
.10.1016/j.fluid.2010.10.015
23.
Garg
,
J.
,
Poudel
,
B.
,
Chiesa
,
M.
,
Gordon
,
J. B.
,
Ma
,
J. J.
,
Wang
,
J. B.
,
Ren
,
Z. F.
,
Kang
,
W. 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.
,
103
(7), p.
074301
.10.1063/1.2902483
24.
Tavman
,
I.
,
Turgut
,
A.
,
Chirtoc
,
M.
,
Schuchmann
,
H. P.
, and
Tavman
,
S.
,
2008
, “
Experimental Investigation of Viscosity and Thermal Conductivity of Suspensions Containing Nanosized Ceramic Particles
,”
Arch. Mater. Sci. Eng.
,
34
(
2
), pp.
99
104
.
25.
Batchelor
,
G. K.
,
1977
, “
The Effect of Brownian Motion on the Bulk Stress in a Suspension of Spherical Particles
,”
J. Fluid Mech.
,
83
(
1
), pp.
97
117
.10.1017/S0022112077001062
26.
Namburu
,
P. K.
,
Kulkarni
,
D. P.
,
Misra
,
D.
, and
Das
,
D. K.
,
2007
, “
Viscosity of Copper Oxide Nanoparticles Dispersed in Ethylene Glycol and Water Mixture
,”
Exp. Therm. Fluid Sci.
,
32
(
2
), pp.
397
402
.10.1016/j.expthermflusci.2007.05.001
27.
Chen
,
H.
,
Ding
,
Y.
, and
Tan
,
C.
,
2007
, “
Rheological Behaviour of Nanofluids
,”
New J. Phys.
,
9
, p.
367
.10.1088/1367-2630/9/10/367
28.
Zhou
,
S.
,
Ni
,
R.
, and
Funfschilling
,
D.
,
2010
, “
Effects of Shear Rate and Temperature on Viscosity of Alumina Polyalphaolefins Nanofluids
,”
J. Appl. Phys.
,
107
(5), p.
054317
.10.1063/1.3309478
29.
Tammann
,
G.
, and
Hesse
,
W.
,
1926
, “
Die Abhängigkeit der Viscosität von der Temperatur bie unterkühlten Flüssigkeiten
,”
Z. Anorg. Allg. Chem.
,
156
(
1
), pp.
245
247
.10.1002/zaac.19261560121
30.
Paul
,
C. W.
, and
Cotts
,
P. M.
,
1986
, “
Effects of Aggregation and Solvent Quality on the Viscosity of Semidilute Poly(vinylbutyra1) Solutions
,”
Macromolecules
,
19
(
3
), pp.
692
699
.10.1021/ma00157a036
31.
Chandrasekar
,
M.
,
Suresh
,
S.
, and
Chandra
,
B. A.
,
2010
, “
Experimental Investigations and Theoretical Determination of Thermal Conductivity and Viscosity of Al2O3/Water Nanofluid
,”
Exp. Therm. Fluid Sci.
,
34
(
2
), pp.
210
216
.10.1016/j.expthermflusci.2009.10.022
32.
Murshed
,
S. M. S.
,
Leong
,
K. C.
, and
Yang
,
C.
,
2008
, “
Investigations of Thermal Conductivity and Viscosity of Nanofluids
,”
Int. J. Therm. Sci.
,
47
(
5
), pp.
560
568
.10.1016/j.ijthermalsci.2007.05.004
33.
Tsai
,
T.
,
Kuo
,
L.
,
Chen
,
P.
, and
Yang
,
C.
,
2008
, “
Effect of Viscosity of Base Fluid on Thermal Conductivity of Nanofluids
,”
Appl. Phys. Lett.
,
93
(23), p.
233121
.10.1063/1.3046732
34.
He
,
Y.
,
Jin
,
Y.
,
Chen
,
H.
,
Ding
,
Y.
,
Cang
,
D.
, and
Lu
,
H.
,
2007
, “
Heat Transfer and Flow Behaviour of Aqueous Suspensions of TiO2 Nanoparticles (Nanofluids) Flowing Upward Through a Vertical Pipe
,”
Int. J. Heat Mass Transfer
,
50
(11–12), pp.
2272
2281
.10.1016/j.ijheatmasstransfer.2006.10.024
35.
Putnam
,
P. A.
,
Cahill
,
D. G.
,
Braun
,
P. V.
,
Ge
,
Z.
, and
Shimmin
,
R. G.
,
2006
, “
Thermal Conductivity of Nanoparticle Suspensions
,”
J. Appl. Phys.
,
99
(8), p.
084308
.10.1063/1.2189933
36.
Xie
,
H.
,
Chen
,
L.
, and
Wu
,
Q.
,
2008
, “
Measurements of the Viscosity of Suspensions (Nanofluids) Containing Nanosized Al2O3 Particles
,”
High Temp.-High Pressure
,
37
(
2
), pp.
127
135
.
37.
Einstein
,
A.
,
1906
, “
Eineneuebestimmung der molekuldimensionen
,”
Ann. Phys.
324(2), pp. 289–306.10.1002/andp.19063240204
38.
Anoop
,
K. B.
,
Kabelac
,
S.
,
Sundararajan
,
T.
, and
Das
,
S. K.
,
2009
, “
Rheological and Flow Characteristics of Nanofluids: Influence of Electroviscous Effects and Particle Agglomeration
,”
J. Appl. Phys.
,
106
(3), p.
034909
.10.1063/1.3182807
39.
Farris
,
R. D.
,
1968
, “Prediction of the Viscosity of Multimodal Suspensions From Unimodal Viscosity Data,”
Trans. Soc. Rheol.
,
12
(
2
), p.
281
.10.1122/1.549109
40.
Muralidharan
,
G.
, and
Runkana
,
V.
,
2009
, “Rheological Modeling of Spherical Polymeric Gels and Dispersions Incorporating the Influence of Particle Size Distribution and Surface Forces,”
Ind. Eng. Chem. Res.
,
48
(
19
), pp.
8805
8811
.10.1021/ie801736q
41.
Larson
,
R. G.
,
1999
,
The Structure and Rheology of Complex Fluids
,
Oxford University
,
Oxford, UK
.
42.
Frankel
,
N. A.
, and
Acrivos
,
A.
,
1967
, “
On the Viscosity of a Concentrated Suspension of Solid Spheres
,”
Chem. Eng. Sci
,
22
(
6
), pp.
847
853
.10.1016/0009-2509(67)80149-0
43.
Graham
,
A. L.
,
1981
, “
On the Viscosity of Suspension of Solid Spheres
,”
Appl. Sci. Res.
,
37
(
3–4
), pp.
275
286
.10.1007/BF00951252
44.
Servais
,
C.
,
Jones
,
R.
, and
Roberts
,
I.
,
2002
, “
The Influence of Particle Size Distribution on the Processing of Food
,”
J. Food Eng.
,
51
(
3
), pp.
201
208
.10.1016/S0260-8774(01)00056-5
45.
Brinkman
,
H. C.
,
1952
, “
The Viscosity of Concentrated Suspensions and Solution
,”
J. Chem. Phys.
,
20
(4), pp.
571
581
.10.1063/1.1700493
46.
Lundgren
,
T. S.
,
1972
, “
Slow Flow Through Stationary Random Beds and Suspensions of Spheres
,”
J. Fluid Mech.
,
51
(2), pp.
273
299
.10.1017/S002211207200120X
47.
Doi
,
M.
, and
Edwards
,
S. F.
,
1978
, “
Dynamics of Rod-like Macromolecules in Concentrated Solution
,”
J. Chem. Soc., Faraday Trans.
, Part 2,
2
(
74
), pp.
918
932
.10.1039/F29787400918
48.
Cheng
,
N.-S.
, and
Law
,
A. W.-K.
,
2003
, “
Exponential Formula for Computing Effective Viscosity
,”
Powder Technol.
,
129
(
1–3
), pp.
156
160
.10.1016/S0032-5910(02)00274-7
49.
Powell
,
R. E.
,
Roseveare
,
W. E.
, and
Henry
,
E.
,
1941
, “
Diffusion, Thermal Conductivity, and Viscous Flow of Liquids
,”
Ind. Eng. Chem.
,
33
(
4
), pp.
430
435
.10.1021/ie50376a003
50.
Renon
,
H.
, and
Prausnitz
,
J. M.
,
1968
, “
Local Composition in Thermodynamics Excess Functions for Liquid Mixtures
,”
AIChE J.
,
14
(
1
), pp.
135
144
.10.1002/aic.690140124
51.
Abu-Nada
,
E.
,
2009
, “
Effects of Variable Viscosity and Thermal Conductivity of Al2O3–Water Nanofluid on Heat Transfer Enhancement in Natural Convection
,”
Int. J. Heat Fluid Flow
,
30
(
4
), pp.
679
690
.10.1016/j.ijheatfluidflow.2009.02.003
52.
Noni
,
A.
,
Garcia
,
D. E.
, and
Hotza
,
D.
,
2002
, “A Modified Model for the Viscosity of Ceramic Suspensions,”
Ceram. Int.
,
28
(7), pp.
731
735
.10.1016/S0272-8842(02)00035-4
53.
Brenner
,
H.
, and
Condiff
,
D. W.
,
1974
, “
Transport Mechanics in Systems of Orientable Particles. IV. Convective Transport
,”
J. Colloid Interface Sci.
,
47
(
1
), pp.
199
264
.10.1016/0021-9797(74)90093-9
54.
Kulkarni
,
D. P.
,
Das
,
D. K.
, and
Chukwu
,
G. A.
,
2006
, “
Temperature Dependent Rheological Property of Copper Oxide Nanoparticles Suspension
,”
J. Nanosci. Nanotechnol.
,
6
(
4
), pp.
1150
1154
.10.1166/jnn.2006.187
55.
Lu
,
W. Q.
, and
Fan
,
Q. M.
,
2008
, “
Study for the Particle's Scale Effect on Some Thermophysical Properties of Nanofluids by a Simplified Molecular Dynamics Method
,”
Eng. Anal. Boundary Elem.
,
32
(4), pp.
282
289
.10.1016/j.enganabound.2007.10.006
56.
Kwek
,
D.
,
Crivoi
,
A.
, and
Duan
,
F.
,
2010
, “
Effects of Temperature and Particle Size on the Thermal Property Measurements of Al2O3-Water Nanofluids
,”
J. Chem. Eng. Data
,
55
(
12
), pp.
5690
5695
.10.1021/je1006407
57.
Doi
,
M.
, and
Edwards
,
S. F.
,
1978
, “
Dynamics of Rod-Like Macromolecules in Concentrated Solution
,”
J. Chem. Soc., Faraday Trans.
, Part 1,
2
(
74
), pp.
560
570
.10.1039/F29787400560
58.
White
,
F. M.
,
1991
,
Viscous Fluid Flow
,
McGraw-Hill
,
New York
.
59.
Maiga
,
S. E. B.
,
Nguyen
,
C. T.
,
Galanis
,
N.
, and
Roy
,
G.
,
2004
, “
Heat Transfer Behaviours of Nanofluids in a Uniformly Heated Tube
,”
Superlattices Microstruct.
,
35
(3–6), pp.
543
557
.10.1016/j.spmi.2003.09.012
You do not currently have access to this content.