Critical Evaluation of Anomalous Thermal Conductivity and Convective Heat
Transfer Enhancement in Nanofluids
By
MASSACHUSETTS INSTITUTE
OF TECHOLOGY
Naveen Prabhat
DEC 0 9 2010
B.Tech., Mechanical Engineering (2008)
Indian Institute of Technology Bombay
LIBRARIES
ARCHIVES
SUBMITTED TO THE DEPARTMENT OF NUCLEAR SCIENCE AND ENGINEERING
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE IN NUCLEAR SCIENCE AND ENGINEERING
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
JUNE 2010
02010 Massachusetts Institute of Technology
All rights reserved
Signature of Author:
Naveen Prabhat
Department of Nuclear Science and Engineering
05/13/2010
Certified by:
Jacopo Buongiorno
Carl . Soderberg Professor of Power Engineering
Associate rofessor of Nuclear Science and Engineering
Thesis Supervisor
Certified by:
Lin-Wen Hu
Associate Director, N clear Reactor Laboratory
Thesis
-Supervisor
Accepted by:
Jacquelyn C.Yanch
Professor of Nuclear Science and Engineering
Chair Department Committee on Graduate Students
Critical Evaluation of Anomalous Thermal Conductivity and Convective Heat
Transfer Enhancement in Nanofluids
By
Naveen Prabhat
Submitted to the Department of Nuclear Science and Engineering
on May 13, 2010 in Partial Fulfillment of the requirements for the Degree of
Master of Science in Nuclear Science and Engineering
ABSTRACT
While robust progress has been made towards the practical use of nanofluids, uncertainties remain
concerning the fundamental effects of nanoparticles on key thermo-physical properties. Nanofluids have
higher thermal conductivity and single-phase heat transfer coefficients than their base fluids. The
possibility of very large thermal conductivity enhancement in nanofluids and the associated physical
mechanisms are a hotly debated topic, in part because the thermal conductivity database is sparse and
inconsistent. This thesis reports on the International Nanofluid Property Benchmark Exercise (INPBE) in
which the thermal conductivity of identical samples of colloidally stable dispersions of nanoparticles, or
'nanofluids', was measured by over 30 organizations worldwide, using a variety of experimental
approaches, including the transient hot wire method, steady-state methods and optical methods. The
nanofluids tested were comprised of aqueous and non-aqueous basefluids, metal and metal oxide
particles, near-spherical and elongated particles, at low and high particle concentrations. The data
analysis reveals that the data from most organizations lie within a relatively narrow band (± 10% or less)
about the sample average, with only few outliers. The thermal conductivity of the nanofluids was found
to increase with particle concentration and aspect ratio, as expected from classical theory. The effective
medium theory developed for dispersed particles by Maxwell in 1881, and recently generalized by Nan et
al., was found to be in good agreement with the experimental data.
The nanofluid literature contains many claims of anomalous convective heat transfer
enhancement in both turbulent and laminar flow. To put such claims to the test, we have performed a
critical detailed analysis of the database reported in 12 nanofluid papers (8 on laminar flow and 4 on
turbulent flow). The methodology accounted for both modeling and experimental uncertainties in the
following way. The heat transfer coefficient for any given data set was calculated according to the
established correlations (Dittus-Boelter's for turbulent flow and Shah's for laminar flow). The
uncertainty in the correlation input parameters (i.e. nanofluid thermo-physical properties and flow rate)
was propagated to get the uncertainty on the predicted heat transfer coefficient. The predicted and
measured heat transfer coefficient values were then compared to each other. If they differed by more than
their respective uncertainties, we called the deviation anomalous. According to this methodology, it was
found that in nanofluid laminar flow in fact there seems to be anomalous heat transfer enhancement in the
entrance region, while the data are in agreement (within uncertainties) with the Shah's correlation in the
fully developed region. On the other hand, the turbulent flow data could be reconciled (within
uncertainties) with the Dittus-Boelter's correlation, once the temperature dependence of viscosity was
included in the prediction of the Reynolds number. While this finding is plausible, it could not be directly
confirmed, because most papers do not report information about the temperature dependence of the
viscosity for their nanofluids.
Thesis Supervisor: Jacopo Buongiorno
Title: Associate Professor of Nuclear Science and Engineering
ACKNOWLEDGEMENTS
Foremost, I would like to express my sincere gratitude to my advisor Professor Jacopo
Buongiorno for his continuous support of my SM study and research, for his patience,
motivation, enthusiasm, and immense knowledge. His guidance helped me in all the time of
research and writing of this thesis. He has been resourceful and supportive whenever I needed
any help during my tenure as a Master student at MIT.
Besides my advisor, I would like to thank my thesis co-supervisor Dr. Lin-Wen Hu for her help
and suggestions in my research work. Her suggestions and help have been very valuable and
important in my research work. I also thank Dr. Tom McKrell for his help during the preparation
of INPBE workshop presentation and also for his valuable suggestions during group meetings.
I would also like to thank Dr. Jessica Townsend and Dr. Yuriy V. Tolmachev for their valuable
and significant contribution to the analysis of INPBE results.
My sincere thanks also goes to my fellow research group mates for their valuable contributions
and suggestions for my research work and also coordinating with me in various research related
events. I would like to thank Eric Forrest, Hyungdae Kim, Bao Truong, Bren Phillips and Vivek
Inder Sharma.
I would also like to thank my friends at MIT: Prithu Sharma, Rahul Goel, Stefano Passerini,
Aditya Bhakta, Mark Minton, Vaibhav Somani, Asha Parekh, Hitesh Chelawat, Wei-shan
Chiang, Nicolas Stauff, Koroush Shrivan and Bren Phillips for being supportive during my stay
at MIT and making it easy for me to adjust to the new culture and having fun at the same time.
Last but not the least, I would like to thank my family: my father Pramod Kumar Varshney,
sister Priyanka Prabhat and good friend Manisha Nadir for supporting me morally and
spiritually.
Contents
List of Symbols........................................................................--
- -
5
.....................................
6
1.
Intro ductio n .. . . . . .....................................................................................................
2.
Analysis of Abnormal Thermal Conductivity Enhancement for Nanofluids .....................................
3.
4.
.......---..
10
. ---.................. 10
2 .1.
M ethodology ..................................................................................
2.2.
T est nanofluids.........................................................................................
24
2.3.
Therm al conductivity data ..................................................................................................
29
2.4.
Comparison of data to effective medium theory................................................................
44
2.5
Comparison of data with other theoretical models..................................................45
Analysis of Anomalous Convective Heat Transfer Enhancement in Nanofluids..............................
55
3 .1
M eth o do lo gy ........................................................................................................................................
55
3.2
Error A nalysis..............................................................................................
59
3.3.
Experimental Studies Analyzed.........................................................................................
70
3.4.
Interpretation of Results.....................................................................................................
90
C on c lu sion ................................................................................................................................................-----..
97
REFERENCES......................................................................................100
APPENDIX A...........................................................................................
APPENDIX B............................................................................................
112
... 116
4
List of Symbols
kP
kg/(s. m)
W/(m. K)
kg/m 3
J/(kg. K)
kg /(s. m)
W/(m.K)
J/(kg. K)
W/(m. K)
PP
kg/m
Cp,
CPP
h
D
L
J/(kg. K)
yP
k
P
C,
kf
CP
Nu
Re
Pe
3
W/m 2K
m
m
dimensionless
dimensionless
dimensionless
dimensionless
Viscosity of nanofluids
Thermal Conductivity of nanofluids
Density of nanofluids
Specific heat of nanofluid
Viscosity of basefluid
Thermal conductivity of basefluid
Specific heat of basefluid
Thermal Conductivity of nanoparticles
Density of nanoparticles
Specific heat of nanoparticles
Heat Transfer Coefficient
Diameter of tube
Length of tube
Volume fraction of nanoparticle
Nusselt number
Reynolds number
Peclet number
1.
Introduction
Nanofluids are engineered colloidal dispersions of nanoparticles in base fluids such as water, oils or
refrigerants. The nanoparticles can be metals such as copper, silver, gold or metal oxides such as
alumina, zirconia, silica or various forms of carbon such as diamond, carbon nanotubes, graphite
etc.
One of the advantages of using nanoparticles over micro-sized particles is that they do not clog the system
and are expected to more closely mirror the behavior of molecules of the fluid. Erosion effects and
settling will also decrease with the use of nanoparticles instead of micro-sized particles. Nanofluids
research to date has examined fluids with particles of various types, including chemically stable metals,
metal oxides, and carbon [1].
The most important factor which has called upon the attention of engineering community towards
nanofluids is their improved heat transfer characteristics over base fluids. Nanofluids were first named
and proposed as a new method of enhancing heat transfer in fluid-cooled systems by Choi in 1995 [2]
Even at very low concentration of nanoparticles, some believe that, nanofluids can show very high
enhancement in the heat transfer capabilities with respect to the basefluid. This may make them useful to
many practical applications involving fluid based heat transfer like cooling of automobiles, electronic
circuits and transformers.
In spite of the attention received by this field, uncertainties concerning the fundamental effects of
nanoparticles on thermo-physical properties of solvent media remain.
Thermal conductivity is the
property that has catalyzed the attention of the nanofluids research community the most. As dispersions
of solid particles in a continuous liquid matrix, nanofluids are expected to have a thermal conductivity
that obeys the effective medium theory developed by Maxwell over 100 years ago 3. Maxwell's model for
spherical and well-dispersed particles culminates in a simple equation giving the ratio of the nanofluid
thermal conductivity (k) to the thermal conductivity of the basefluid (k):
k
k1
k,+2k,+2#(k,-k1 )
k,+2kf-#6(k,-kf)
where k, is the particle thermal conductivity and
# is the particle volumetric
(1)
fraction. Note that the model
predicts no explicit dependence of the nanofluid thermal conductivity on the particle size or temperature.
Also, in the limit of k>>kf and
by
kf
# <<1, the dependence on particle loading is expected to be
linear, as given
1+ 3#. However, several deviations from the predictions of Maxwell's model have been reported,
including:
e A strong thermal conductivity enhancement beyond that predicted by Eq. (1) with a non-linear
dependence on particle loading4 4 0
9,11-19
" A dependence of the thermal conductivity enhancement on particle size and shape
" A dependence of the thermal conductivity enhancement on fluid temperature14,20-22
To explain these unexpected and intriguing findings, several hypotheses were recently formulated. For
example, it was proposed that:
*
Particle Brownian motion agitates the fluid, thus creating a micro-convection effect that increases
energy transport23 2 7
e
Clusters or agglomerates of particles form within the nanofluid, and heat percolates preferentially
28 33
along such clusters -
"
Basefluid molecules form a highly-ordered high-thermal-conductivity layer around the particles,
2 8 32 3 4 5
thus augmenting the effective volumetric fraction of the particles , , ,3
Experimental confirmation of these mechanisms has been weak; some mechanisms have been openly
questioned.
For example, the micro-convection hypothesis has been shown to yield predictions in
conflict with the experimental evidence19' 36 . In addition to theoretical inconsistencies, the nanofluid
thermal conductivity data are sparse and inconsistent, possibly due to (i) the broad range of experimental
approaches that have been implemented to measure nanofluid thermal conductivity (e.g., transient hot
wire, steady-state heated plates, oscillating temperature, thermal lensing), (ii) the often-incomplete
characterization of the nanofluid samples used in those measurements, and (iii) the differences in the
synthesis processes used to prepare those samples, even for nominally similar nanofluids. In summary,
the possibility of very large thermal conductivity enhancement in nanofluids beyond Maxwell's
prediction and the associated physical mechanisms are still a hotly debated topic.
There have also been several experimental studies which have shown that adding nanoparticles to a
fluid enhances the convective heat transfer. A literature search was conducted for publications on
nanofluids convective heat transfer; the search yielded over 40 journal papers [54-103].
Most of the
published studies report that addition of nanoparticles to base fluids enhances the convective heat transfer
capabilities.
Not all of these studies, however, take into account the change in the properties of the
basefluids due to the addition of nanoparticles when predicting the behavior of nanofluids, which is then
compared to the experimental values. Some studies [93-103] have reported abnormally high
enhancements in the convective heat transfer of nanofluids which could not be predicted by the
conventional heat transfer correlations. The research conducted at MIT [54-55], on the other hand, shows
that if the properties of the nanofluids are properly accounted for in calculating the governing
dimensionless numbers (Re, Pr and Nu), the existing correlations for convective heat transfer accurately
predict the heat transfer coefficient enhancements seen with nanofluids.
In summary, the nanofluid
convective heat transfer database would seem to be inconsistent, and the question of whether truly
abnormal convective heat transfer enhancement is achievable with nanofluids remains open.
Some experimental studies report enhancements in convective heat transfer which could not be explained
by existing correlations, such as the Dittus-Boelter correlation for convective heat transfer in fullydeveloped turbulent flow:
Nu = 0.023 Re" Pr 0 4
h = 0.023 Re0 8
C
0.
k
D
0.4
= 0.023
coko.60.sgo.
p D.
,
(2)
where, h, p, u and k are the convective heat transfer coefficient, density, viscosity and thermal conductivity
of the nanofluid respectively. D and V are the diameter of the pipe and the velocity of the nanofluid
respectively. Similar correlation for constant heat flux laminar flow which reproduces the complex
analytical solution for local Nusselt number to within 1% [57]:
Nu =1.302(x)
x*
- 0.5
0.0015
y(3)
Nu = 4.364 + 0.263(x+ ).506 e-
41
(x+ /2)
+
> 0.0015
. (x /D)
whrN=hD
x
=
distance,
where, Nu=-hDand the dimensionless
Re Pr
k
In light of the above considerations, the studies of thermal conductivity and convective heat transfer
coefficient of nanofluids are of great interest to us. They have been discussed separately in Chapter-2 and
Chapter-3. The final conclusions have been given in the conclusion chapter at the end of the thesis.
Analysis of Anomalous Thermal Conductivity Enhancement
2.
At the first scientific conference centered on nanofluids (Nanofluids: Fundamentals and Applications,
September 16-20, 2007, Copper Mountain, Colorado), it was decided to launch an international nanofluid
property benchmark exercise (INPBE), to resolve the inconsistencies in the database and help advance the
debate on nanofluid properties. As a part of the INPBE, 31 organizations around the world measured
properties of standard nanofluid samples that were manufactured and shipped to them by a supplier. MIT
led the effort and part of this thesis project was devoted to supporting INPBE. Therefore, this thesis
dissertation reports on the INPBE effort on the thermal conductivity data.
2.1.
Methodology
The exercise's main objective was to compare thermal conductivity data obtained by different
organizations for the same samples. Four sets of test nanofluids were procured (see Section 2.2). To
minimize spurious effects due to nanofluid preparation and handling, all participating organizations were
given identical samples from these sets, and were asked to adhere to the same sample handling protocol.
The main points of the protocol were:
1. Complete all measurements within one month of the delivery date.
2.
Store all samples in a cool, dry and dark environment until the measurements are completed.
3. Do not sonicate the samples or mix the samples by other means.
4. Do not add surfactants or other chemicals to the samples.
The exercise was 'semi-blind', as only minimal information about the samples was given to the
participants at the time of sample shipment. The minimum requirement to participate in the exercise was
to measure and report the thermal conductivity of at least one test nanofluid at room temperature.
However, participants could also measure (at their discretion) thermal conductivity at higher temperature
and/or various other nanofluid properties, including (but not necessarily limited to) viscosity, density,
specific heat, particle size and concentration. The data were then reported in a standardized form to the
exercise coordinator at the Massachusetts Institute of Technology (MIT) and posted, unedited, at the
INPBE website (http://mit.edu/nse/nanofluids/benchmark/index.html).
The complete list of organizations
that participated in INPBE, along with the data they contributed, is reported in Table I. INPBE climaxed
in a workshop, held on January 29-30 in Beverly Hills, California, where the results were presented and
discussed by the participants. The workshop presentations can also be found at the INPBE website.
Table I Participating organizations in and data generated for INPBE.
Organization/ Contactperson
Generateddatafor
Experimental method afor
thermal conductivity
Set I
Set 2
Set 3
Set 4
TC
TC
TC
TC, V
TC, V
measurement (Ref)
Argonne National Laboratory / E. V. Timofeeva
KD2 Pro
CEA / C. Reynaud
Steady-state coaxial cylinders
Chinese University of Hong Kong / S.-Q. Zhou
Steady state parallel plate
DSO National Laboratories / L. G. Kieng
Supplied nanofluid samples
ETH Zurich and IBM Research / W. Escher
THW and parallel hot plates f
Helmut-Schmidt University Armed Forces / S. Kabelac
Guarded hot plate
Illinois Institute of Technology / D. Venerus
Forced Rayleigh scattering
Indian Institute of Technology, Kharagpur / I. Manna
KD2 Pro
C
TC
V
d
e
TC
d
g
TC
TC
TC
TC, V
TC, V
TC, V
TC
TC
TC, V
TC
TC
TC
TC
TC
Indian Institute of Technology, Madras / T. Sundararajan, S. THW l
K. Das
Indira Gandhi Centre for Atomic Research / J. Philip
THWd ! KD2
TC
TC
TC
Kent State University / Y. Tolmachev
KD2 Pro
TC
TC, V
TC
Korea Aerospace University / S. P. Jang
THW'
Korea Univ. / C. Kim
THW
METSS Corp. / F. Botz
TC
TC
TC, V
TC, V
TC, V
THW d
TC
TC
TC
MIT / J. Buongiorno, L.W. Hu, T. McKrell
THW 3
TC
TC
TC
MIT / G. Chen
THW k
TC
TC, V
Nanyang Technological University / K. C. Leong
THW '
TC
NIST / M. A Kedzierski
KD2 Pro
TC, V, D
d
m
TC
V, D
North Carolina State University - Raleigh / J. Eapen
Contributed to data analysis
Olin College of Engineering / R. Christianson, J. Townsend
THW"
TC, V
TC
Queen Mary University of London / D. Wen
THW
TC, V
TC
d
TC
V, D
V, D
TC
TC
RPI / P. Keblinski
Contributed to data analysis
SASOL of North America / Y. Chang
Supplied nanofluid samples
Silesian University of Technology / A. B. Jarzebski, G. Dzido
THW
South Dakota School of Mines and Technology / H. Hong
Hot Disk P
Stanford University / P. Gharagozloo, K. Goodson
IR thermometry
Texas A&M University / J. L. Alvarado
KD2 Pro
Ulsan National Institute of Science and Technology; Tokyo
KD2 Pro
q
TC, V
TC, V
TC
TC
TC
TC
TC
TC
TC
TC
TC
TC
TC
TC,V
TC,V
TC,V
TC,V
TC, V, D
TC, V, D
Institute of Technology / I. C. Bang, J. H. Kim
Universite Libre de Bruxelles, University of Naples / C. S. Modified hot wall technique
Iorio
Parallel plates
University of Leeds / Y. Ding
KD2 and parallel hot plates t
TC, V
TC
TC, V
University of Pittsburgh / M. K. Chyu
Unitherms 2022 (Guarded heat
TC
TC
TC, V
flow meter)
TC,V
University of Puerto Rico - Mayaguez / J. G. Gutierrez
a
THW "
TC
TC
THW = transient hot wire; KD2 and KD2 Pro (information about these devices at
http://www.decagon.com/thermal/instrumentation/instruments.php); UnithermTM 2022 (information about this device
athttp://anter.com/2022.htm)
b
TC = thermal conductivity
J. Glory, M. Bonetti, M. Helezen, M. Mayne-L'Hermite, C. Reynaud, J. Appl. Phys.,103, 094309 (2008).
d
A publication with detailed information about this apparatus is not available
V = viscosity
N. Shalkevich, W. Escher, T. Buergi, B. Michel, L. Si-Ahmed and D. Poulikakos, Langmuir, DOI: 10.1021/la9022757 (2009).
g
D. C. Venerus, M. S. Kabahdi, S. Lee and V. Perez-Luna, J. Appl. Phys., 100, 094310 (2006).
h
H. E. Patel, T. Sundararajan and S. K. Das, J. Nanoparticle Research, Vol 10(1), 87-97 (2008).
J.-H. Lee, K. S. Hwang, S. P. Jang, B. H. Lee, J. H. Kim, S. U. S.. Choi, C. J. Choi, Int. J. Heat Mass Transfer, Vol. 51, 2651-2656 (2008).
R. Rusconi, W. C. Williams, J. Buongiorno, R. Piazza, L. W. Hu, Int. J. Thermophysics, Vol. 28, No. 4, 1131-1146 (2007).
k
J. Garg, B. Poudel, M. Chiesa, J. B. Gordon, J. J. Ma, J. B. Wang, Z. F. Ren, Y. T. Kang, H. Ohtani, J. Nanda, G. H. McKinley,
G. Chen,
J. Appl. Phys., 103, 074301 (2008).
S. M. S. Murshed, Leong K. C., and Yang C., Int. J. Thermal Sciences, 44, 367-373 (2005).
D = density
J. Townsend, Christianson R.,
1 7th
Symposium on Thermophysical Properties, Paper #849, Boulder, CO, June 21 - 16 (2009).
Jarzebski, M. Palica, A. Gierczycki, K. Chmiel-Kurowska, G. Dzido, Internal Report, BW-459/RCh6/2007/6, Silesian Univ.
of Technol.,
Gliwice (2007).
Wright, D. Thomas, H. Hong, L. Groven, J. Puszynski, D. Edward, X. Ye , S. Jin, Appl. Phys. Lett., 91, 173116 (2007).
q
P. E. Gharagozloo and K. E. Goodson, Appl. Phys. Lett. 93, 103110 (2008).
S. Van Vaerenbergh, T. Mare C. Tam Nguyen, A. Guerin, VIII-eme Colloque Interuniversitaire Franco-Queb6cois sur la Thermique des
Systbmes, May 28-30, Montreal, Canada (2007).
s
C. H. Li and G. P. Peterson, J. Appl. Phys., 99, 084314 (2006).
D. Wen and Ding Y., Transactions of IEEE on Nanotechnology, 5, 3, 220-227 (2006).
"
J. G. Gutierrez, and R. Rodriguez, IMECE2007-43365, Proc. 2007 ASME Int. Mech. Eng. Congress and Expo, Nov 11-15, Seattle,
Washington, USA (2007).
Table II Characteristics of the Set 1 samples
Sample
a
Loading
Particle size
IIT
Sasol
MIT
80x10 nm (nominal nanorod size),
60-64 nm
n/a
n/a
n/a
n/a
1% vol.
0.7 to 0.8 % vol f
10 nm (nominal particle size)
g
75-88nm
4
3% vol.
1.9 to 2.2 % vol f
10 nm (nominal particle size)
g
99-112nm
5
1%vol.
0.7 to 0.8 % vol f
80x10 nm (nominal nanorod size)
g
70-11 Onm
6
3% vol.
2.0 to 2.3 %vol f
80x10 nm (nominal nanorod size)
g
100-1 l5nm
7
n/a
n/a
n/a
n/a
n/a
Sasol
MIT
1
1% vol.
1.2 to 1.3 % vol
2
n/a*
3
a
4
d
b
131-134nm
Range of values is given to account for expected hydration range of alumina (boehmite). Boehmite's chemical formula is Al 2O 3 nH 20,
where n = 1 to 2. The hydrate is bound and cannot be dissolved in water. In most boehmites there is 70 to 82 wt% A120 3 per gram of
powder. Boehmite density is 3.04 g/cm 3.
b
Average size of dispersed phase, measured by dynamic light scattering (DLS). The range indicates the spread of six nominally-identical
measurements. DLS systemic uncertainty is of the order of ±10 nm. Malvern NanoS used to collect data.
Measurements by inductive coupled plasma (ICP)
d
Average size of dispersed phase, measured by DLS. The range indicates the spread of multiple nominally-identical measurements. DLS
systemic uncertainty is of the order of± 10 nm.
Not applicable
Measurements by neutron activation analysis (NAA)
g
Not available due to unreliability of DLS analyzer with PAO-based samples
Table III Characteristics of the Set 2 samples
Sample
Au loading
Stabilizer
Particle size
pH
concentration
(trisodium citrate)
1
DSO
MIT
0.0010 vol%
0.0009 vol% d
a
DSO
MIT *
IIT 4
DSO
MIT
20-30 nm
4-11 nm
14.8 nm ave
0.1 wt%
0.10 wt%
6.01
0.1 wt%
0.09
7.30
MIT
a
(10-22 nm)
2
Zero
Zero *n/a
n/a
n/a
wt
Measurements by inductive coupled plasma (ICP). ICP has an accuracy of 0.6% of the reported value for gold in the concentration range
of interest.
Number-weighted average size of particles, measured by DLS. The range indicates the spread of two nominally-identical measurements.
DLS systemic uncertainty is of the order of ± 10 nm.
Measurements by DLS. The values reported are the number-weighted average and the range at the full-width half maximum for six
measurements.
d
Assumed density of gold is 19.32 g/cm
3
Within the detection limit of ICP.
Not applicable
Table IV Characteristics of the Set 3 samples
Sample
1
Silica (Si0 2) loading
Na 2SO 4 concentration
Grace
MIT
Grace
49.8 wt%
43.6 wt%
31.1 vol% c
26.0 vol%'
a
MIT
Particle size
a
0.1-0.2 wt% of 0.27 wt% of Na
pH
Grace
MIT b
Grace
MIT
22 nm
20-40
8.9
9.03
n/a
n/a
Na
2d
a
a
n/a
nm
n/a
n/a
n/a
a
Measured by inductive coupled plasma (ICP). ICP has an accuracy of 0.6% of the reported value.
b
Number-weighted average size of particles, measured by dynamic light scattering (DLS).
The range indicates the spread of three
nominally-identical measurements. DLS systemic uncertainty is of the order of ±10 nm.
Assumed density of silica (Si0 2) is 2.2 g/cm 3
d
Sample 2 is simply de-ionized water, which was assumed to be the basefluid sample, but was not actually sent to the participants.
Not applicable
Table V Characteristics of the Set 4 samples.
Sample
UPRM
1
0.17 vol%
MIT
b
Particle size
Particle composition
Particle loading
0.16 vol%
c
UPRM
MIT
Mn 2 -Znv2-Fe 2 d
Mn ~ 15 at%,
a
pH
UPRM
MIT
MIT
7.4mm *
6-11 nm f
15.2
n/a
n/a
15.1
Zn - 14 at%,
Fe - 71 at%
2
n/a 9
n/a
n/a
n/a
a
Atomic fraction of metals measured by Energy Dispersive X-ray Spectroscopy (EDS).
b
Determined from magnetic measurements
C
Measurements by inductive coupled plasma (ICP). Assumed density of 4.8 g/cm 3 for Mn-Zn ferrite. ICP has an accuracy of 0.6% of the
reported value.
d
The molar fraction of Mn and Zn was determined from stoichiometric balance.
*
Average magnetic particle diameter
Number-weighted average size of particles, measured by dynamic light scattering (DLS).
The range indicates the spread of four
nominally-identical measurements. DLS systemic uncertainty is of the order of± 10 nm.
g
Not applicable
Table VI Summary of INPBE results
Sample #
Sample description
thermal
Measured
Measured
Predicted
thermal
thermal
conductivity ratio '
conductivity b
conductivity
a
k/kf
ratio b
(W/m-K)
Lower
Upper
bound
bound
k/k
Sample 1
Alumina nanorods (80x10 nm), 1% vol. in water
0.627 ± 0.013
1.036± 0.004
1.024
1.086
Sample 2
De-ionized water
0.609 ±0.003
n/a d
n/a
n/a
Sample 3
Alumina nanoparticles (10 nm), 1%vol. in PAO + surfactant
0.162 ± 0.004
1.039 ± 0.003
1.027
1.030
Sample 4
Alumina nanoparticles (10 nm), 3 % vol. in PAO + surfactant
0.174 ±0.005
1.121 ±0.004
1.083
1.092
Set 1
Sample 5
Alumina nanorods (80x10 nm), 1%vol. in PAO + surfactant
0.164 ± 0.005
1.051 ± 0.003
1.070
1.116
Sample 6
Alumina nanorods (80x10 nm), 3% vol. in PAO + surfactant
0.182 ± 0.006
1.176 ± 0.005
1.211
1.354
Sample 7
PAO + surfactant
0.156 ±0.005
n/a
n/a
n/a
Sample 1
Gold nanoparticles (10 nm), 0.001% vol. in water + stabilizer
0.613 ± 0.005
1.007 ± 0.003
1.000
1.000
Sample 2
Water + stabilizer
0.604 ±0.003
n/a
n/a
n/a
Sample 1
Silica nanoparticles (22 nm), 31% vol. in water + stabilizer
0.729 ± 0.007
1.204 ± 0.010
1.008
1.312
Sample 2
De-ionized water
0.604 ±0.002
n/a
n/a
n/a
Sample 1
Mn-Zn ferrite nanoparticles (7 nm), 0.17% vol. in water +
0.459 ± 0.005
1.003 ± 0.008
1.000
1.004
0.455 ±0.005
n/a
n/a
n/a
Set 2
Set 3
stabilizer
Set 4
Sample 2
Water + stabilizer
a
Nominal values for nanoparticle concentration and size
b
Sample average and standard error of the mean
Calculated with the assumptions in Appendix B
d
Not applicable
2.2.
Test nanofluids
To strengthen the generality of the INPBE results, it was desirable to select test nanofluids with a broad
diversity of parameters; for example, we wanted to explore aqueous and non-aqueous basefluids, metallic
and oxidic particles, near-spherical and elongated particles, and high and low particle loadings. Also,
given the large number of participating organizations, the test nanofluids had to be available in large
quantities (> 2 L) and at reasonably low cost.
Accordingly, four sets of test samples were procured. The providers were Sasol (Set 1), DSO National
Labs (Set 2), W. R. Grace & Co. (Set 3) and the University of Puerto Rico at Mayaguez (Set 4). The
providers reported information regarding the particle materials, particle size and concentration, basefluid
material, the additives/stabilizers used in the synthesis of the nanofluid, and the material safety data
sheets. Said information was independently verified, to the extent possible, by the INPBE coordinators
(MIT and Illinois Institute of Technology, IIT), as reported in the next sections. Identical samples were
shipped to all participating organizations.
2.2.1.
Set 1
The samples in Set 1 were supplied by Sasol. The numbering for these samples is as follows:
(1)
Alumina nanorods in de-ionized water
(2)
De-ionized water. (basefluid sample)
(3)
Alumina nanoparticles (first concentration) in Polyalphaolefins lubricant (PAO) + surfactant
(4)
Alumina nanoparticles (second concentration) in PAO + surfactant
(5)
Alumina nanorods (first concentration) in PAO + surfactant
(6)
Alumina nanorods (second concentration) in PAO + surfactant
(7)
PAO + surfactant. (basefluid sample)
The synthesis methods have not been published, so a brief summary is given here. For sample 1, alumina
nanorods were simply added to water and dispersed by sonication. Sample 2, de-ionized water, was not
actually sent to the participants. The synthesis of samples 3-7 involved three steps. First, the basefluid
was created by mixing PAO (SpectraSyn- 10 by Exxon Oil) and 5% wt. dispersant (Solsperse 21000 by
Lubrizol Chemical), and heating and stirring the mixture at 70'C for two hours, to ensure complete
dissolution of the dispersant.
Second, hydrophilic alumina nanoparticles or nanorods (in aqueous
dispersion) were coated with a mono-layer of hydrophobic linear alkyl benzene sulfonic acid and then
spray dried. Third, the dry nanoparticles or nanorods were dispersed into the basefluid.
(a)
(b)
Figure 1. Set 1 - TEM pictures of samples 1 (a) and 3 (b), respectively. The nanorod dimensions in
sample 1 are in reasonable agreement with the nominal size (80x10nm) stated by Sasol. However,
smaller particles of lower aspect ratio are clearly present along with the nanorods. TEM pictures of
PAO-based samples have generally been of lower quality. However, the nanoparticles in sample 3
appear to be roughly spherical and of approximate diameter 10-20 nm, thus consistent with the nominal
size of 10 nm stated by Sasol.
Table 1I reports the information received by Sasol along with the results of some measurements done at
MIT and IIT. Figure 1 shows transmission electron microscopy (TEM) images for samples 1 and 3.
TEM images for samples 4-6 are not available.
2.2.2. Set 2
The samples in Set 2 were supplied by Dr. Lim Geok Kieng of DSO National Laboratories in Singapore.
The numbering for these samples is as follows:
Gold nanoparticles in de-ionized water and trisodium citrate stabilizer.
De-ionized water + sodium citrate stabilizer. (basefluid sample)
Figure 2. Set 2 - TEM pictures of sample 1. The nanoparticles are roughly spherical and of
diameter <20 nm, thus somewhat smaller than the nominal size of 20-30 nm stated by DSO
National Labs.
The nanofluid sample was produced according to a one-step 'citrate method', in which 100 mL of 1.18
mM gold(III) chloride trihydrate solution and 10 mL of 3.9 M trisodium citrate dehydrate solution were
mixed, brought to boil and stirred for 15 minutes. Gold nanoparticles formed as the solution was let cool
to room temperature. Table III reports the information received by DSO National Labs along with the
results of some measurements done at MIT. Figure 2 shows the TEM images for sample 1.
2.2.3.
Set 3
Set 3 consisted of a single sample, supplied by W. R. Grace & Co.:
(1) Silica mono-dispersed spherical nanoparticles and stabilizer in de-ionized water
uh
Figure 3. Set 3 - TEM pictures of sample 1. The nanoparticles are roughly spherical and of
diameter 20-30 nm, thus consistent with the nominal size of 22 nm stated by Grace.
The silica particles were synthesized by ion exchange of sodium silicate solution in a proprietary process.
A general description of this process can be found in the literature43 . Grace commercializes this nanofluid
as Ludox TM-50, and indicated that the nanoparticles are stabilized by making the system alkaline, the
base being deprotonated silanol (SiO~) groups on the surface with Na' as the counterion (0.1-0.2 wt% of
Na ions). The dispersion contains also 500 ppm of a proprietary biocide. Grace stated that it was not
possible to supply a basefluid sample with only water and stabilizer "because of the way the particles are
made". Given the low concentration of the stabilizer and biocide, de-ionized water was assumed to be the
basefluid sample, and designated 'sample 2', though it was not actually sent to the participants. Table IV
reports the information received by Grace along with the results of some measurements done at MIT.
Figure 3 shows the TEM images for the Set 3 sample.
2.2.4. Set 4
The samples in Set 4 were supplied by Dr. Jorge Gustavo Gutierrez of the University of Puerto Rico 44
Mayaguez (UPRM). A chemical co-precipitation method was used to synthesize the particles . The Set
4 sample numbering is as follows:
(1)
Mn-Zn ferrite (Mn/-Zn/-Fe 20 4) particles in solution of stabilizer and water.
(2)
Solution of stabilizer (25 wt %) and water (75 wt %). (basefluid sample)
I 1
l
v
v
Iv
v
111 11At !.''11"
l
liv
cv'
K FOCIt
Figure 4. Set 4 - TEM pictures of sample 1. The nanoparticles have irregular shape and approximate size
<20 nm, thus consistent with the nominal size of -7 nm stated by UPRM.
The stabilizer is Tetramethylammonium hydroxide, or (CH 3)4NOH.
Table V reports the information
received by UPRM along with the results of some measurements done at MIT. Figure 4 shows the TEM
images for sample 1.
2.3.
Thermal conductivity data
The thermal conductivity data generated by the participating organizations are shown in Figures 5 through
17, one for each sample in each set.
In these figures the data are anonymous, i.e., there is no
correspondence between the organization number in the figures and the organization list in Table I. The
data points indicate the mean value for each organization, while the error bars indicate the standard
deviation calculated using the procedure described in Appendix A. The sample average, i.e., the average
of all data points, is shown as a solid line, and the standard error of the mean is denoted by the dotted
lines to facilitate visualization of the data spread. The standard error of the mean is typically much lower
than the standard deviation because it takes into account the total number of measurements made to arrive
at the sample average. Each measurement technique is denoted by a different symbol, and averages for
each of the measurement techniques are shown. The measurement techniques were grouped into four
categories: the KD2 Thermal Properties Analyzer (Decagon), custom transient hot wire (THW), steady
state parallel plate, and other techniques. Outliers (determined using Peirce's criterion) are shown as filled
data points and were not included in either the technique or ensemble averages.
It can be seen that for all water-based samples in all four sets most organizations report values of the
thermal conductivity that are within ±5% of the sample average. For the PAO-based samples the spread
is a little wider, with most organizations reporting values that are within ± 10% of the sample average. A
note of caution is in order: while all data reported here are nominally for room temperature, what
constitutes 'room temperature' varies from organization to organization. The data shown in Figures 5
through 17 include only measurements conducted in the range 20 - 30 'C.
Over this range of
temperatures, the thermal conductivity of the test fluids is expected to vary minimally; for example, the
water thermal conductivity varies by less than 2.5%. Where deionized water was the basefluid (Figures 6
and 15), the range of nominal thermal conductivity of water for 20 - 30 *C is shown as a red band plotted
on top of the measured data.
Figures 18 through 25 show the thermal conductivity 'enhancement' for all nanofluid samples, i.e., the
ratio of the nanofluid thermal conductivity to the basefluid thermal conductivity. For each organization,
the data point represents the ratio of the mean thermal conductivities of the nanofluid and basefluid, while
the error bars represent the standard deviation calculated according to the procedure described in
Appendix A. If a participating organization did not measure the basefluid thermal conductivity in their
laboratory, a calculation of enhancement was not made. Again, the sample average is shown as a solid
line along with the standard error of the mean, and outliers are indicated by filled data points. Note that
there is reasonable consistency (within ±5%) in the thermal conductivity ratio data among most
organizations and for all four sets, including water-based and PAO-based samples.
The INPBE database is summarized in Table VI. Comparing the data for samples 3, 4, 5 and 6 in Set 1, it
is noted that, everything else being the same, the thermal conductivity enhancement is higher at higher
particle concentration, and higher for elongated particles than for near-spherical particles. Comparing the
data for samples 1 and 5 in Set 1, it is noted that the thermal conductivity enhancement is somewhat
higher for the PAO basefluid than for water. The Set 2 data suggest that the thermal conductivity
enhancement is negligible, if the particle concentration is very low, even if metal particles of high thermal
conductivity are used. On the other hand, the Set 3 data suggest that a robust enhancement can be
achieved, if the particle concentration is high, even if the particle material has a modest thermal
conductivity. All these trends are expected, based on the effective medium theory, as will be discussed in
section 2.4.
2.3.1. Effects of the Experimental Approach on the Thermal Conductivity Measurements
Table I reports the experimental techniques used by the various organizations to measure thermal
conductivity, and provides, when available, a reference where more information about those techniques
can be found. Transient, steady-state, and optical techniques were used to measure thermal conductivity.
There are transient measurement techniques that require the immersion of a dual heating and sensing
element in the sample, such as the transient hot wire (THW) and transient hot disk techniques. The THW
technique is based on the relationship between the thermal response of a very small (< 100 m) diameter
wire immersed in a fluid sample to a step change in heating and the thermal conductivity of the fluid
sample [39].
The THW technique was used by over half of the participating organizations, many of
which used a custom built apparatus. The KD2 Thermal Properties Analyzer made by Decagon, an offthe-shelf device that is based on the THW approach, was also used. The transient hot disk technique is
similar to the THW technique, except that the heater/sensor is a planar disk coated in Kapton [40]. In
steady-state techniques such as the parallel plate [41] and co-axial cylinder [42] methods, heat is
transferred between two plates (or co-axial cylinders) sandwiching the test fluid. Measurement of the
temperature difference and heat transfer rate across the fluid can be used to determine the thermal
conductivity via Fourier's law. The thermal comparator method, also a steady-state method, measures the
voltage difference between a heated probe in point contact with the surface of the fluid sample and a
reference, which can be converted to thermal conductivity using a calibration curve of samples of known
conductivity [43]. In the forced Rayleigh scattering method, an optical grating is created in a sample of
the fluid using the intersection of two beams from a high-powered laser. The resulting temperature
change causes small-scale density changes that create a refraction index grating that can be detected using
another laser. The relaxation time of the refraction index grating is related to the thermal diffusivity of
the fluid, from which the thermal conductivity can be evaluated [44].
The measurement techniques were grouped into KD2, Custom THW, Parallel Plate, and Other (which
include thermal comparator, hot disk, Forced Rayleigh Scattering, and co-axial cylinders).
Thermal
conductivity and enhancement data for each group of measurement techniques is shown in Figures 5 - 25.
For each of the four measurement technique groupings, the average thermal conductivity is shown on the
plot and is indicated by the solid line.
In the custom THW data on Figure 5 and 6, there is one
measurement that is well above the average in both figures. This was the only THW apparatus with an
uninsulated wire. Typically an insulated wire is used in this method to reduce the current leakage into the
fluid. The higher thermal conductivity measured here may be a result of that effect. Excepting the
outliers, all the measurement techniques show good agreement for deionized water (Figures 6 and 15).
For the PAO basefluid (Figure 11) the uninsulated hot wire measurement (Organization 14) is no longer
an outlier. PAO is not as electrically conductive as water, and the current leakage effect should be less of
an issue for this fluid.
As described in Appendix A, a Fixed Effects Model was used to determine whether differences in the data
from different measurement techniques are statistically significant. Because of the low number of data
points in the Parallel Plate and Other categories, only the KD2 and Custom Hot Wire techniques were
compared. For all the samples in Sets 1, 2 and 3, the KD2 thermal conductivity average is lower than the
Custom THW average. The Fixed Effects Model shows that this is a statistically significant difference for
samples 1, 3, 4, 6, 7, in Set 1, and sample 2 in Set 3. In Set 4, the KD2 average is higher than the Custom
THW, but this difference is statistically significant only for Sample 2 (the water+stabilizer basefluid for
the ferrofluid). It is not clear why the KD2 measurements are lower than the THW measurements for all
fluids except those in Set 4. Finally, in most cases, there is less scatter in the KD2 data for the PAO-based
nanofluids than the water-based nanofluids. This may be due to the higher viscosity of the PAO which
counteracts thermal convection during the 30 second KD2 heating cycle.
It is difficult to make specific conclusions about thermal conductivity measurements using the parallel
plate technique due to the low number of data points and the amount of scatter for some samples (see
Figures 12 - 14). Additional measurements would be needed to determine if there is a systematic
difference between the parallel plate technique and other techniques.
Although the thermal conductivity data show some clear differences in measurement technique, these
differences become less apparent once the data are normalized with the basefluid thermal conductivities.
(Figures 18 - 25). A comparison of the KD2 and THW techniques was again performed using the Fixed
Effects Model. The only statistically significant difference between the two techniques was for Set 1,
Sample 4 (Figure 20), and the 3% volume fraction alumina-PAO nanofluid.
This study shows that the choice of measurement technique can affect the measured value of thermal
conductivity, but if the enhancement is the parameter of interest, the measurement technique is less
important, at least for the KD2 and THW techniques. Therefore, to ensure accurate determinations of
nanofluid thermal conductivity enhancement using these techniques, it is important to measure both the
basefluid and nanofluid thermal conductivity using the same technique and at the same temperature.
Set 1: Sample 1
0.75
E 0.7
'5 0.65
0
0.6
0 KD2
A Parallel Plate
Sample Avg.
0.55
.5
--
C Custom THW
O Other
--- Sample Avg. + SE
Sample Avg. - SE
0.5
0
1 2 3 4 5 6 7 8 9 1011121314151617 18 19 202122 23 2425 26 27 28 29 303132
Organization
Figure 5. Thermal conductivity data for sample 1, Set 1.
Set 1: Sample 2
0.75
0 KD2
A Parallel Plate
Sample Avg.
Sample Avg. - SE
.
0.65
(DI
0.6
a,
C Custom THW
0 Other
--- Sample Avg. + SE
NIST (20 - 30 C)
0.55
-
-
0.5
0
1 2
3 4
5 6 7
8 9 10111213 1415161718 19202122 23 24 25 26 27 28 29 303132
Organization
Figure 6. Thermal conductivity data for sample 2 (basefluid), Set 1.
Set 1: Sample 3
0.23
E
0 Custom THW
o KD2
0.22
0 Other
---- Samole Avg. + SE
* Parallel Plate
-Sample
Avg.
0.21
----- Sample Avg. - SE
0.2
5 0.19
8
0.18
C
0 0.17
_
0.16
_
--
0.15
_...----------
------ --
- ----
--- --- -----
-
--
-
-
- --
---
-
-----
-
-----------------------------------------------------
QD
0.14
0.13
0
1 2 3 4
5 6
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Organization
Figure 7. Thermal conductivity data for sample 3, Set 1.
Set 1: Sample 4
0.23
0.22
0.21
0.2
o KD2
Custom THW
O Other
------ Sample Avg. + SE
E
A Parallel Plate
-Sample
Avg.
--- ~- Sample Avg. - SE
0.19
0.18
0.17
4D
6
0.16
0.15
0.14
0.13
0 1 2 3 4 5 6 7 8
9 101112 131415161718 19 202122 23 24 25 26 27 28 29303132
Organization
Figure 8. Thermal conductivity data for sample 4, Set 1.
Set 1: Sample 5
0.22
o
D
Custom THW
* Other
--- Sample Avg. + SE
Avg. - SE
-Sample
KD2
A Parallel Plate
Sample Avg.
0.21
0.2
0.19
0.18
0.17
0.16
0.15
0.14
0.13
---
0.12
0
---
- ----
~--
5 6 7 8 9 10111213141516171819202122 23 2425 262728 29303132
1 2 3 4
Organization
Figure 9. Thermal conductivity data for sample 5, Set 1.
Set 1: Sample 6
0.25
o
0.23
KD2
A Parallel Plate
-Sample
Avg.
0.22
---
0.24
Custom THW
0 Other
-- Sample Avg. + SE
O
Sample Avg. - SE
0.21
0.2
0.19
---------------------------
----- - ------------------------
0.18
S
- D
A
---
--
-
-----
-------
0.17
0.16
0.15
0
1 2 3 4
5 6 7 8
9 10111213141516171819 20 21222324252627 282930 3132
Organization
Figure 10. Thermal conductivity data for sample 6, Set 1.
Set 1: Sample 7
0.22
0 Custom THW
o KD2
0.21
A Parallel Plate
Sample Avg.
0.2
0.19
0 Other
--- Sample Avg. + SE
--- Sample Avg. - SE
0.18
0.17
0.16
---.9
1
0.15
0.14
0.13
0.12
0
2 3 4
1
5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Organization
Figure 11. Thermal conductivity data for sample 7, Set 1.
Set 2: Sample 1
0
-
A
KD2
Parallel Plate
Sample Avg.
El Custom THW
0 Other
-- Sample Avg. + SE
-Sample
Avg. - SE
0.65
LIJ
----------------------------------------------
----------------------------------0
U
0.6
0.55
0
1 2 3 4 5 6 7 8 9 10111213141516171819 202122 23 24 25 26 27 28 29303132
Organization
Figure 12. Thermal conductivity data for sample 1, Set 2.
Set 2: Sample 2
E Custo m THW
o KD2
A Parallel Plate
Sample Avg.
-
0 Other
--- Samp le Avg. + SE
---- Sample Avg. - SE
0.65
- - (D
-o
-----------------
:*--I ---------------------------IF
--------------------A------------------------L----------------------
-
0.6
E
1,
0.55
-
0
--
1 2 3 4
-
5 6
7 8 9 10111213 1415 161718 19 202122 23 2425 26 27 28 29 303132
Organization
Figure 13. Thermal conductivity data for sample 2, Set 2.
Set 3: Sample 1
0.9
0.85
O KD2
A Parallel Plate
Sample Avg.
D
0
Custom THW
Other
--- Sample Avg. + SE
Avg. - SE -Sample
0.8
q
0
0.75
---------------------------------------------------------------------------------%,
----------------&---------------------------
(U
0.7
T
a,
I-
0.65
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Organization
Figure 14. Thermal conductivity data for sample 1, Set 3.
Set 3: Sample 2
0.75
E
o KD2
A Parallel Plate
Sample Avg.
0.7
Custom THW
O Other
--- Sample Avg. + SE
NIST (20 - 30 C)
U
---- Sample Avg. - SE
+
5 0.65
T
0
U
E
0.6
z
1
ML
146001
*1~
all
KW O
--------------
0.55
-
-
0.5
0
-
1 2 3 4 5 6 7 8 9 10111213141516171819 202122 23 2425 26 27 28 29303132
Organization
Figure 15. Thermal conductivity data for sample 2 (basefluid), Set 3.
Set 4: Sample 1
0.55
0.5
0.45
(D ~
~
--------------------------------------------------------------------Wl---i---------------------------~ ----- ~r
~
0.4
0
E 0.35
-C
o
O Custom THW
KD2
A Parallel Plate
0.3
-Sample
Avg.
.Sample
Avg. - SE
--
O Other
-----Sample Avg. + SE
0.25
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19202122 23 24 25 2627 28 29 303132
Organization
Figure 16. Thermal conductivity data for sample 1, Set 4.
Set 4: Sample 2
o
)-
0.
0.5
8
0.45
l Custom THW
KD2
A Parallel Plate
0.55
O Other
-Sample
Avg.
Sample
-- Avg. - SE
-
- -
---- Sample Avg. + SE
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - -
---------------; ------------M -------------------------------------
0
U
E
i
0.4
0.35
I0.3
-
0 1 2
3 4 5 6 7
-
8 9 10111213 1415161718 19202122 23 2425 262728 29 303132
Organization
Figure 17. Thermal conductivity data for sample 2 (basefluid), Set 4.
Set 1: Sample 1
1.1
1.05
1
0 KD2
0.95
A Parallel Plate
-Sample
Avg.
------ Sample Avg. - SE
0
Custom THW
0
Other
---- Sample Avg. + SE
0.9
0 1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829303132
Organization
Figure 18. Thermal conductivity enhancement data for sample 1, Set 1.
Set 1: Sample 3
1
E
5)
c
Custom THW
Other
---- Sample Avg. + SE
O KD2
A Parallel Plate
Sample Avg.
1.2
----
1.15
o
Sample Avg. - SE
UiL
I.1
UV
1.05
----------------------------
M
I
I I
M
4
---------
T ---EffE
--------------------------T-T--T i---------------------I-
0.95
0
1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829303132
Organization
Figure 19. Thermal conductivity enhancement data for sample 3, Set 1.
Set 1: Sample 4
O Custom THW
O KD2
A Parallel Plate
0 Other
---- Sample Avg. + SE
-Sample
Avg.
-----Sample Avg. - SE
E
.C
c
U
C
0
1.15
__MED___I
-- ------------------------_
T
--_-__---------------------------------
E
1.05
c
1
-.
-
--
__
_
_
__
_
_
__
_
0 1 2 3 4 5 6 7 8 9 10111213141516171819202122232425262728 29303132
Organization
Figure 20. Thermal conductivity enhancement data for sample 4, Set 1.
Set 1: Sample 5
E
1.15
{
(U
1.01
MID
HHEH A i E_=~E
,-;ggiiiiH-
LU
C
iii---i
--
o
KD2
-81
-
E
*c
_
__
0 Custom THW
A Parallel Plate
0.95
--
- -
-
_rT
0 Other
Sample Avg.
-----Sample Avg. + SE
---Sample Avg. - SE
0.9
0 1 2 3 4 5 6 7 8 9 1011121314151617181920212223 2425262728 29303132
Organization
Figure 21. Thermal conductivity enhancement data for sample 5, Set 1.
Set 1: Sample 6
1.35
o
E
C Custom THW
KD2
A Parallel Plate
1.3
0 Other
Sample Avg.
--- Sample Avg. - SE
M
1.25
-- Sample Avg. + SE
LU
-Z.~ 1.2
--
E)----------
-o
-
-
f-
1.15
0
R
E
1.1
1.05
0
1
2
3
4
5
6
7
8
9
29303132
2425262728
1011121314151617181920212223
Organization
Figure
22.
Thermal
conductivity
enhancement
data
for
sample
6,
Set
1.
Set 2: Sample 1
O KD2
E,
A Parallel Plate
Sample Avg.
---- Sample Avg. - SE
1.15
LU
O
Custom THW
0 Other
---- Sample Avg. + SE
-1.1
1.05
.E
1
-
0.95
.c
0.9
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Organization
Figure 23. Thermal conductivity enhancement data for sample 1, Set 2.
Set 3: Sample 1
1.35
0 KD2
Parallel Plate
-Sample
Avg.
--- Sample Avg. - SE
A
1.3
1.25
( Custom THW
0 Other
Sample Avg. + SE
------
----- - -
1.2
1.15
1.1
1.05
0
1 2 3 4 5 6
7 8 9 1011 12 13 14 15 16 17 18 192021 222324252627 28 293031 32
Organization
Figure 24. Thermal conductivity enhancement data for sample 1, Set 3.
Set 4: Sample 1
1.2
*
1.15
1.1
E
0
KD2
A Parallel Plate
-
Sample Avg.
---
Custom THW
Other
Sample Avg. + SE
----- Sample Avg. - SE
1.05
1
0.95
0.9
0 1 2 3 4 5 6 7 8 9 10111213 141516171819202122 23 2425262728 29303132
Organization
Figure 25. Thermal conductivity enhancement data for sample 1, Set 4.
Deviation from Effective Medium Theory
'
~~~ ----................
----
-------
|-----------
--------
-- Upper Bound of EMT
- -Lower Bound of EMT
0.05
0.1
0.2
0.15
Fractional Error
0.25
0.3
0.35
Figure 26. Percentage of all INPBE experimental data that are predicted by Nan et al.'s theory within the
error indicated on the x-axis.
43
Comparison of data to effective medium theory
2.4.
Equation (1) is valid for well-dispersed non-interacting spherical particles with negligible thermal
resistance at the particle/fluid interface. To include the effects of particle geometry and finite interfacial
resistance, Nan et al [45] generalized Maxwell's model to yield the following expression for the thermal
conductivity ratio:
k
kf
3 +#[2pA (1- Ll)+#33G - L33 A(4
3-#(2pA L 1 +#8
3 3L 33 )
where, for particles shaped as prolate ellipsoids with principal axes a
= a22
< a 33 :
2
L11 =
2(p
P
2
-1)
-
2
2(p 2 -1)
3/2
cosh' p
k" -k
p3
=
i-
,
L 3 3 =1-2LH
k
f
k, + L(ki - kf)
k-=
,
,
p=a33/au
y =(2+ 1/p)Rbdkf/(al,/2)
1+ yL1 k, / kf
and Rbd is the (Kapitza) interfacial thermal resistance. The limiting case of very long aspect ratio in Nan
et al.'s theory is bounded by the nanoparticle linear aggregation models proposed by Prasher et al.[3 1] and
Keblinski et al.[46]. Obviously, Eq. (4) reduces to Eq. (1) for spherical particles (p=1) and negligible
interfacial thermal resistance (Rbd=O), as it can be easily verified. Equation (4) predicts that, if k, > kf, the
thermal conductivity enhancement increases with increasing particle loading, increasing particle aspect
ratio and decreasing basefluid thermal conductivity, as observed for the data in INPBE Set 1. More
quantitatively, the theory was applied to the INPBE test nanofluids with the assumptions reported in
Appendix B. Figure 26 shows the cumulative accuracy information of the effective medium theory for all
the INPBE data. Two curves are shown: one for zero interfacial thermal resistance (upper bound), and
one for a typical value of the interfacial resistance, 10-8 m2 K/W [47-49]. It can be seen that all INPBE
data can be predicted by the lower bound theory with <17% error, while the upper bound estimate
predicts 90% of the data with <18% error.
The above data analysis demonstrates that our colloidally stable nanofluids exhibit thermal conductivity
in good agreement with the predictions of the effective medium theory for well-dispersed nanoparticles.
That is, no anomalous thermal conductivity enhancement was observed for the nanofluids tested in this
study. As such, resorting to the other theories proposed in the literature (e.g., Brownian motion, liquid
layering, aggregation) is not necessary for the interpretation of the INPBE database. It should be noted,
however, that the ranges of parameters explored in INPBE, while broad, are not exhaustive. For example,
only one nanofluid with metallic nanoparticles was tested, and only at very low concentration.
2.5.
Comparison of data with other theoretical models
The data obtained during INPBE was also compared with other theoretical models (except the effective
medium theory) which have been proposed based on different possible mechanisms of heat transfer. Since
the main aim of the study was to create a benchmark of properties of certain nanofluids and see if a
particular theoretical model is able to capture the effect of all the parameters which were varied across
different nanofluids used in this study, a comparison to various different theoretical models was
necessary. The theoretical models that were implemented can be broadly classified into three different
categories:
1. Static Models (Effective Medium Theories for spherical and non-spherical particles)
a. Maxwell's model for spherical nanoparticles [3]
k
1+2fl
kf
1-fl0
where,f# = [k]/(k, + 2kf) and
(5)
[k] = k, - kf
b. Maxwell's model for non-spherical nanoparticles (Nan et al [45])
k
kf
3+#[2pA8(1- LI)+#833 1 - L33)]
3-0(2AL 1 +#l33L33)
(6)
where, for particles shaped as prolate ellipsoids with principal axes a,, = a 22 < a 33 :
L
-
=
2(p 2 -1)
Al =
L33 =1-2L1
p
cosh-'p,,
2(p 2 _1)332
k' -k
L(
f
k + Li(kc -kf)
p= a 33 Ia/
y = (2+ 1/p)Rbdkf/(all/2)
k c=
yLk, / kf
I+
2. Dynamic Models: These models assume that there is a significant contribution of motion of
nanoparticles which produces convection effect enhancing the thermal conduction in nanofluids.
a. Prasher's Dynamic Model [25]
k
3
= (1 + ARe'PrO3 3 3 ) * ([kp(1+ 2a) + 2kf] + 20[kp(1 - a) - k
kf
[k,(1 + 2a) + 2kg] - 0[k,(1 - a) - kf]
-
(7)
where, A is a constant with value 4x1 04, m is 2.0 for water based nanofluids
= 2Rbkj where Rb is the interfacial surface resistance and d is the diameter of
nanoparticle. The
value of Rb was chosen to be 1x10-8 and 0 for predicting the lower and upper limit of thermal
conductivities respectively.
b. Jang and Choi Model [7]
k = kf (1 - 0) + knano 0 + 3C
kfRe2 PrO
(8)
p
knano = flk,
where, C1 is proportionality constant, df and d,
are diameter of basefluid molecule and
p where
Cm and vy are the random motion velocity of
nanoparticles respectively and Red,s =
Vfb
nanoparticles and dynamic viscosity of basefluid respectively.Cp=D,/1f where D,, and 1f are the
where kb is the
nanoparticle diffusion coefficient and mean free path in basefluid. Do= kb
Boltzmann constant. Mean free path was calculated using kinetic theory of gases. The value of C
was assumed to be 510000 andf = 0.01
3. Aggregation Models: These models assume an increase in the conduction due to aggregation of
nanoparticles in the fluid forming larger clusters which lead to high conduction
a. Prasher's Aggregate Model [31]
k
(ka + 2kf) + 20a(ka kf)
-(ka + 2kf)-0a(ka kf)
kf
=
(9)
where, ka and 0aare the effective thermal conductivity and volume fraction of aggregates
respectively.
(
ka = aknc3
3 +
Oc [2p(1
-
fl33(1
L11) -
i
__Oc(2fl11l11
-
)
L3
3
)]\
f 33L33)
)(10)
where, kne is the effective thermal conductivity of the aggregate sphere in the presence of the deadend particles only. ke is given by the Bruggeman model as given below:
(1 - Gae)(kf - kne) + On (k, - kne)
kf + 2kne
where,
0
Tc
(11)
kf + 2kne
is the volume fraction of particles with dead ends.
2
p
L
2(p2
-l1)
3_2
k-
0
p/ 0 int
-kf
k
kf+LI,(kfl -kf)
-
Oa =
p=R, /a
L33 =1-2L1
cosh-'p,
2(p2 -1)/23
,
nc =
0
int
-
-
c
kf+L
-kf
33 (knc -kf)
( )max = ( 0 P)1/(df-3)
where, Oint and 0, are the volume fraction of nanoparticles in the aggregate/cluster and nanofluid
respectively. Rg and a are the radii of the cluster and nanoparticles respectively. The aggregation
parameter p= (Rg/a) was varied from a minimum value of 2 to a maximum value of ( 0 ,)1/(df-3) to
obtain prediction of minimum and maximum thermal conductivity.
Section 2.4 discusses the comparison of INPBE data with the static models only. Plots shown in Figure 27
and 28 represent the comparison of the all the experimental data obtained during INPBE with the
Maxwell Model for spherical particles. Figure 2 shows that 90% of the data measured from experiments
was predicted by the Maxwell's model for spherical particles within 10% accuracy Figure 28 confirms the
same fact in a different way, it shows the comparison of theoretical estimation and experimental
measurements with 10% error bars and it is clear from the plot that most of the data is predicted within
10% of the measured values using the traditional Maxwell's model for predicting thermal conductivity.
A similar comparison was done with the modified Maxwell's model given by Nan et al [45] which takes
into account the non-spherical particles like nanorods. The comparison of the experimental measurements
with the estimation from the Nan et al have been discussed in Section 2.4. Hence in general the traditional
static thermal conductivity models seem to predict the thermal conductivity
Data was also compared with dynamic and aggregation models mentioned above. Dynamic models
analyzed for the INPBE samples included Prasher's Dynamic Model and Jang and Choi's dynamic
Model. These models assume that the motion of nanoparticles in a nanofluid is responsible for the
enhancement of thermal conductivity. A comparison of the experimental results obtained during INPBE
with the Prasher's Dynamic model has been shown in Figure 29 and Figure 30. It is clear from the plots
that only 30% of the experimental results were predicted within 10% accuracy by Prasher's Dynamic
model.
The comparison with Jang and Choi's Dynamic model is shown in Figure 31 and Figure 32. Figure 31
suggests that the model highly over predicts the results for certain experiments. These were found to be
samples with high concentration of nanoparticles. Figure 32 shows that around 70% of the experimental
values are predicted by the Jang and Choi's model within 10% experimental error. Hence it has been
observed that dynamic models in general seem to over predict the thermal conductivity of nanofluids
especially at higher concentration of nanoparticles.
Maxwell's Model for Spherical Particles
100
se
r
90
-
t
-
80
--
-
-
--
70
60
50
40
30
20
10
0
0.1
0
0.2
0.4
0.3
0.5
0.6
Fractional Error
0.7
0.8
0.9
1
Figure 27 Percentage of result plotted as a function of Fractional Error for Maxwell's Static model for spherical particles
Maxwell's Model for Spherical Particles
1.35-
---
1.3
---
Maxwell Static
with Spherical
1.25
Particles
-
-
45 degree line
1.2
--
1.15--
--
Error bar (-10%)
----
1.1
-
-----
Error bar (+10%)
---
1.05
--
1 0.95
0.95
1
1.05
1.1
1.15
1.2
Measured Value
1.25
1.3
1.35
Figure 28 Calculated Value from the Maxwell Static model is plotted against the measured values with 10% error bars
Prasher's Dynamic Model
100
90
80
70
50
8R40
304
1 0----------10
0.6
0.4
0.2
0
0.8
1.8
1.6
1.4
1.2
1
2.2
2
Fractional Error
Figure 29 Percentage of results plotted as a function of fractional error for Prasher's Dynamic Model
Prasher's Dynamic Model
3.25 +
QY Prasher's
2.75
Dynamic Model
-------
45 degree line
-
2.25
-
.-.-
-
Error bar (-10%)
.!
-
-
S 1.75
-
---
-Error bar (+10%)
1.25
0.75---
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
Measured Value
Figure 30 Calculated value from Prasher's Dynamic model vs Measured Values with 10% error bars
Jang and Choi Dynamic Model
100
90
80
70
-
S60
S50
440
30
20
10
0
0
0.2
0.1
0.3
0.5
0.4
0.6
0.7
0.9
0.8
1
Fractional Error
Figure 31 Calculated value from Jang and Choi's Dynamic model vs Measured Values with 10% error bars
Jang and Choi Dynamic Model
2.1
-
4
Jangand Choi
Dynamic Model
45 degree line
Error bar (-10%)
1.-
Error bar (+10%)
--
-1.5
-
0.9
0.9
1
1.1
1.2
1.3
Measured Value
Figure 32 Percentage of results plotted as a function of fractional error for Jang and Choi's Dynamic Model
Prasher's Aggregate Model
100
1
90
80
70
60
-E+-Praher's Aggregate
Model (Lower Limit)
I
50
40-
30
20
the ~~
10
1.3upr
~
~
~
~ upperr
~~liiLndrddosrprsniteupe)ii
oe
Prasher's Aggregate
(Lower Limit)
lModel
-Prasher's
AggregatePae
Pras
AggregateggModet
her'
Model (Upper Limit)
Model|(Upper Lirnit)
1.2
V~
45 degree lineI
1.1
- --
-
-
-
-
rror bar (-10%)
Figue 3plotedas
reult
Perentge oafuntio of raciona eror fr Pashr's ggrgateModlrlue otsreprsenath
9
-
0.9
0.9
Me reddots
upper
lmit andthe
rpresenttheAlowrelimi
Error bar (+10%)
-1
1.1
1.2
Measured Value
1.3
1.4
Figure 34 Percentage of results plotted as a function of fractional error for Prasher's Aggregate Model, blue dots represent the
upper limit and the red dots represent the lower limit
Similar comparison was done for aggregation model proposed by Prasher [31]. It is based on the
assumption that the agglomeration of nanoparticles leads to formation of clusters which lead to better
thermal conduction and lower the conduction resistance. The results were compared for a maximum and
minimum thermal conductivity value based on the maximum and minimum aggregation states. The
comparison has been shown in Figure 33 and Figure 34. The blue dots display the thermal conductivity at
lower aggregation state (hence lower limit) and the red dots represent the thermal conductivity at higher
aggregation state (hence upper limit). When used with a range of values for the aggregation parameter,
this model is effective at bounding the data at almost all concentration values. Almost all calculated
enhancement values lie within 10% of the corresponding measured values. Most of the results can be
predicted correctly at lower and intermediate aggregation states. Figure 34 shows that almost 90% of the
experimental results were predicted within 10% of the measured value at lower aggregation states while
at higher aggregation states the thermal conductivity was over predicted.
The comparison of results of the INPBE exercise with different theoretical models was done to
understand the underlying phenomenon responsible for thermal conductivity enhancement. To summarize
following trends were observed:
" Maxwell's static model reproduces the thermal conductivity data obtained during INPBE exercise
very well. Almost 90% results are within 10% accuracy.
" Prasher's aggregate model predictions bound the measured data with a maximum and minimum
value for thermal conductivity obtained by assuming minimum and maximum possible aggregation.
" Dynamic models tend to overestimate enhancement, particularly at high concentration and in nonaqueous nanofluids (Prasher's Model)
e No nanofluid sample seems to have abnormally high thermal conductivity (defined as a very
significant deviation from Maxwell's static model)
" Sensitivity analysis suggests that the uncertainties in assumed parameters produces no significant
change in the obtained results from theoretical models
3. Analysis of Anomalous
Nanofluids
3.1.
Convective Heat Transfer Enhancement in
Methodology
As discussed in Section 1, nanofluids have different heat transfer coefficients than the corresponding
basefluids because their thermo-physical properties such as thermal conductivity, specific heat, viscosity
and density are different as compared to the basefluid. The difference in their properties arises primarily
due to the addition of nanoparticles to the baselfluids. These nanoparticles have higher thermal
conductivity and hence tend to enhance the heat transfer characteristics of the nanofluid as compared to the
corresponding basefluid.
a)
Collection of Data
There have been several experimental studies which suggest that enhancement in heat transfer coefficient
for nanofluids is more than what can be predicted by the classical theoretical correlations for laminar and
turbulent flows. The aim of the research was to investigate if such claims were correct by evaluating the
heat transfer coefficients using equation 6 for laminar flow and equation 5 for turbulent flow regimes.
First, research was conducted to compile the published data on nanofluid heat transfer. The scope was
determined by narrowing the focus of the investigation to one type or a class of nanofluids for which there
is published data about convective heat transfer coefficients, as well as information about particle size,
particle concentration, and experimentation method.
More than 40 published experimental studies on
nanofluid heat transfer coefficients [54-103] were found during this research exercise. Out of these, based
on availability of data and claims of anomalous enhancement 12 studies [93-103] were shortlisted for
analysis of claims of anomalous enhancement. 8 studies [93-100] on laminar flow report enhancement
beyond theoretical prediction by equation 6 while 4 studies [100-103] on turbulent flow report
enhancement beyond theoretical estimation by equation 5. Experimental measurement data and reported
data such as Reynolds number, volumetric flow rate, heat transfer coefficient, viscosity, thermal
conductivity, density, specific heat and other useful datum if provided was extracted and used if necessary
for the comparison and estimation of theoretical value of heat transfer correlation. If necessary the data
was extracted from the figures reported in the published studies using a ruler.
b)
Calculation of theoretical heat transfer coefficient
For heat transfer coefficient, the database on nanofluid convective heat transfer was critically evaluated
with respect to the possibility of abnormal enhancement above the values predicted by existing heat
transfer correlations, when all properties are included in the calculations.
To complete this thesis
objective, the relevant experimental data was used from [93-103].
The Dittus-Boelter correlation for convective heat transfer in fully-developed turbulent flow given by
equation 5 was used to evaluate the HTC for turbulent flow experimental studies [100, 103]:
Nu = 0.023 Re0 8 Pr 0
4
h = 0.023 Re0 8
= 0.023
D
04 06 08
k
0
V0'8
p0. D 02
(12)
where, h, p, u and k are the convective heat transfer coefficient, density, viscosity and thermal conductivity
of the nanofluid respectively. D and V are the diameter of the pipe and the velocity of the nanofluid
respectively. Equation 12 is valid for 0.7 < Pr < 120, Re > 10,000 and L/D > 10.
Some turbulent flow studies [101, 102] compared their data to the Gnielinski correlation for turbulent flow
as given by equation 13
f/8(ReD
NuD
-
1000)Pr
1/2
2
(13)
1 + 12.7 ()'(Pr - 1)
where
f
= (0.79 In ReD )
-
1.64)~-2
Equation 13 is valid for 5000 < Re < 5x10 6 and 0.5< Pr < 2000.
(14)
The correlation given by equation 15 for laminar flow reproduces the complex analytical solution for local
Nusselt number to within 1%. Equation 15 was used to estimate local heat transfer coefficient for the
laminar flow studies
Nux = 1.302(x+)-1/
3
-
x+
1,
Nu = 1.302(x+)-1/ 3 - 0.5,
0.0005
Nux = 4.364 + 8.68(103x+)-0.506e-(41x+)
h(x)D
where, Nu x=
k
0.0005
x+ - 0.0015
(15)
x+ > 0.0015
and the dimensionless distance, x+ = (xD). Equation 15 is valid for Re < 2300
Re Pr
Some of the laminar flow studies reported average heat transfer coefficient over the entire heat transfer
region. This was predicted using equation 16 given by Shah [107] for average Nusselt number.
for x* 5 0.03
for x* > 0.03
=1.953 x* -1/3 - 1
Num = 4.364+ 0.0722
(16)
(L/D) L and D are the length and diameter of the test section. Equation 16 is valid for Re <
where x* = Re.Pr
2300.
Heris et al [93] measured laminar heat transfer coefficient at constant wall temperature boundary condition
and reported the average heat transfer coefficient. Equations 17 and 18 given by the Graetz and Nusselt
were used for the theoretical prediction of heat transfer coefficient.
Om-
NumT
Tw -Tm
Tw -Tc
=
=8gn=
4x"
0 1exp(-24x*)
n
(17)
(18)
and A represents the eigenvalues of the eigenfunctions of the analytical solution.
where x* =LID
Ve*Pr
Values of An~ and Gn can be found from Table 5.3 on page 5. 10 of the heat transfer handbook [ 106].
Because of the contradictory claims put forth by different studies of nanofluids [93-103] about the
prediction of heat transfer in nanofluids by conventional heat transfer correlations, published results
reporting anomalous heat transfer enhancement were re-evaluated with updated nanofluid properties to
correctly include the effect of addition of nanoparticles on 4 main nanofluid properties: thermal
conductivity (k), viscosity (p), specific heat (C,), density (p).
Nusselt number was predicted by the
correlations using the Reynolds and Prandtl numbers which were either reported or calculated with the
measured temperature- and loading-dependent properties. Finally heat transfer coefficient was calculated
using the loading and temperature dependent thermal conductivity which was either reported in the
published results or recalculated using the Nan et al [105] model which was found to be predicting the
thermal conductivity within 10% for the INPBE study.
Shortlisted set of publications [93-103], were investigated. The data that were used to conduct the study
included nanoparticle and base fluid composition, particle size, particle concentration in the nanofluid, any
other pertinent properties of the fluid and its constituents, such as surfactants or additives uses, and the
results of the experiments performed to determine the convective heat transfer coefficient. Data were
extracted from published figures if the data was not presented in a tabular form.
Appropriate correlation for heat transfer coefficient was evaluated using the Reynolds and Prandtl number,
which were either reported or calculated from measured temperature- and loading-dependent thermal
conductivities. These calculations were performed using an excel spreadsheet with extracted data,
nanoparticle properties and basefluid properties as inputs. Once the expected theoretical heat transfer
coefficient was evaluated using the corrected properties of nanofluids, it was compared to the
experimentally measured heat transfer coefficient to determine whether there is any enhancement of heat
transfer in the nanofluids beyond what can be predicted by the established correlations.
Definition of Anomalous Enhancement
c)
The data was plotted with heat transfer coefficient on the y axis and either Re or x/D on the x axis. The
choice of x-axis was based on the availability of data and experimental measurement technique used by the
researchers. Error bars associated with the uncertainty in the experimental measurement were plotted
along the y axis. Similar error bars associated with uncertainty in the theoretical estimation of the heat
transfer coefficient were also plotted along the y axis. Hence each experimental measurement had a
corresponding theoretical estimation both with their error bars. If the error bars of experimental values
were clearly separated from the error bars of the corresponding theoretical estimation with the
experimental value being higher, the enhancement was called as anomalous since it was beyond
experimental measurement error and theoretical estimation error even after accounting for the properties of
nanofluids in the theoretical correlations.
3.2.
Error Analysis
Error estimation is a vital part of any analytical study as it gives an idea about the confidence in the results
of the analysis. Error analysis was performed for each of the studies analyzed in this work. Error could be
present either in the experimental results reported in the papers or in the theoretical estimation of the heat
transfer coefficient due to uncertainty in the prediction by the theoretical model or models/experimental
techniques used to measure nanofluid properties.
3.2.1. Evaluation of Uncertainty in Theoretical Prediction
* Uncertainty in the nanoparticle properties namely C,, k, and p, were conservatively assumed to be 10%
in each of the studies analyzed. Although the nanoparticle properties are easily available through online
databases and materials safety datasheets but there is an uncertainty associated with the change in
physical properties of nanoparticles once they are dispersed in basefluid. Interactions of nanoparticles
with basefluid molecules such as hydroxylation [109,110] and interaction with surfactants [111] could
affect their physical properties.
"
Nanofluid properties were either calculated using theoretical models or were taken from the studies if
they were measured experimentally with reported experimental error. In case the nanofluid properties
were predicted using theoretical models, uncertainties in the nanofluid properties were calculated by
standard propagation of uncertainties in physical properties of nanoparticle through the theoretical
models and model uncertainty was also taken into account. The model uncertainty (aleatory
uncertainty) and input uncertainty (epistemic uncertainty) were treated independent of each other. If the
nanofluid properties were reported as experimentally measured, the reported uncertainty in the
experimental method or the best error estimate for the experimental technique used from the available
literature was used.
* Finally the heat transfer coefficient was estimated using the nanofluid properties uncertainty and the
heat transfer coefficient was calculated by propagating the uncertainties in the nanofluid properties
through the theoretical model used for HTC prediction. Theoretical error is estimated by the simple
error propagation as discussed in Appendix B to obtain the HTC within ±a of the actual value.
3.2.2. Uncertainty in Experimentally Measured Values
Uncertainties in the experimental values were generally reported in the studies analyzed. If the
experimental uncertainty was not reported, a generic uncertainty of 5% was attached to the experimental
heat transfer coefficient. Typical uncertainty in heat transfer coefficient measurement experiments was
found to be 3-5%. Table V listed below shows what uncertainties were imposed on different properties,
experimental techniques and theoretical models for each of the experimental studies analyzed in this work.
Table VII Experimental studies analyzed for laminar flow convective heat transfer coefficient
Paper
Authors
Nanofluid
Characterization
Composition
Particle
Size and
Nanoparticle
Concentration
Reynolds
Number/
Flowrate
Range
Boundary
Condition
750-2200
Constant
heat flux
k
(W/
A12 0 3/water
Nanofluid
45 nm
and 150
nm
Spherical
p
(Pa-s)
p
(kg/m 3)
Cp
(J/kg-K)
Ubbelohde
viscometer
Mixture
formula
Mixture
formula
Result/Conclus
ion
m-K)
Shape
Anoop
et al
[95]
Properties Calculation/Measurement
0.26
0.52
1.06
1.61
2 18
vol %,
vol %,
vol%,
vol %,
vol %
THW
DC Power
Supply
Anomalous
enhancement
observed with
an increasing
trend at higher
concentration
and higher
Reynolds
number
Ding et
al [96]
CNT/water
nanofluid
Aspect
ratio
>100
0.10 wt%,
0.25 wt%,
0.50 wt%
800-1200
Flowrate
measured
by
weighting
(±4.6%)
Constant
heat flux
DC Power
Supply
KD-2
Bohlin
CVO
Rheometer
Mixture
formula
Mixture
formula
Very high
enhancement
observed in the
developing
region of the
laminar flow
regime. It is
surely
anomalous.
Heris et
al [93]
Choi et
al [98]
Kurows
ka et al
[98]
A12 0 3/water
Nanofluid
A12 0 3/water
Nanofluid
151 nm (0.15
vol %)
350 nm (0.25
vol %)
20 nm
Spherical
30±5 nm
Spherical
Spherical
0.1 vol%,
1.0 vol%,
2.0 vol%,
2.5 vol%,
3.0 vol%
N/A
0.01 vol%,
0.02 vol%,
0.03 vol%,
0.1 vol%,
0.2 vol%,
0.3 vol%
400-750
0.15 vol%,
0.25 vol%
30-60
Flowrate
determine
d by flow
meter
(+0.01
1/hr)
Cu/Ethylene
Glycol
Nanofluid
Prasher
et al
[97]
20 nm (SEM)
Aggregate
size (100-300
Flowrate
controlled
by
HV77921
-40 pump
Spherical
0.50 vol%,
0.75 vol%,
1.00 vol%
Constant
Wall
Temperatu
re
Max
well'
Constant
Heat flux
THW
Einstein
formula
Mixture
formula
Mixture
formula
Anomalous
enhancement in
the HTC was
observed and
the
enhancement
increased with
increasing
Peclet number
and increasing
concentration
of nanoparticles
VM 10-A
Viscometer
BX 300
DSC
204 F1
Anomalous
enhancement
was confirmed
only at 0.3
Vol%
s
equat
ion
AC Power
Supply
concentration
Constant
heat flux
N/A
Brookfield
DV II+
Viscometer
Mixture
Formula
Only
vol
fraction
weighed
Anomalous
enhancement
seen only at the
entrance point
of the flow
regime
N/A
N/A
Mixture
formula
Mixture
formula
Higher
enhancement at
higher
DC Power
Supply
1 -9
(ml/min)
Constant
heat flux
(Micro
DC Power
concentration
pump Inc)
Supply
0.3 vol %,
0.5 vol%,
0.8 vol%,
1.0 vol%,
1.2 vol%,
1.5 vol%,
2.0 vol%
850-2200
Constant
heat flux
0.6 vol%,
1.00 vol%,
1.60 vol%
1050,
1600
Constant
heat flux
Flowrate
measured
by
weighting
(±4.6%)
DC Power
Supply
nm)
and
enhancement
decreases along
the flow
direction but
the anomalous
nature couldn't
A12 0 3/water
Nanofluid
be confirmed
Li et al
[100]
<100 nm
Spherical
Cu/water
nanofluid
Ding et
al [94]
27-56 nm
A12 0 3/water
Nanofluid
Spherical
THW
NXE-1
viscometer
Mixture
formula
Mixture
formula
Anomalous
enhancement
was confirmed
with higher
deviation at
higher
concentration
and the
divergence
from the
theoretical
estimation was
seen at higher
Reynolds
number
KD-2
Einstein
Equation
Mixture
formula
Mixture
formula
Anomalous
enhancement
observed in the
developing
region of the
laminar flow
regime. The
enhancement
decreased with
increasing
distance along
DC Power
Supply
the
flow
direction.
Enhancement
increased at
higher
concentration
of nanoparticles
Table VIII Experimental studies analyzed for turbulent flow convective heat transfer coefficient
Paper
Authors
Nanofluid
Characterization
Particle
Particle
Shape
Size
Xuan
and Li
[100]
< 100 nm
Result/Conclusion
Volumetric
Concentration
Reynolds
Number
Range
Boundary
Condition
Properties
Calculation/Measurement
k
p
p
C,
(W/
(Pa-s) (kg/m 3 ) (J/kg-K)
0.3%, 0.5%,
0.8%, 1.0%,
1.2%, 1.5%
2.0%
10,00025,000
Constant
heat flux
THW
Mixture
formula
Mixture
formula
Flowrate
measured
by
weighing
fluid (1%)
DC Power
Supply
NXE1
visco
meter
Anomalous
enhancement* in
HTC was observed
at concentration
beyond 1 vol%.
The enhancement
increases with
increasing vol
conc. and
increasing
Reynolds number
0.2%
400018000
N/A
Yu
and
Choi'
s
Mod
e15
Einste
in
formu
la
Mixture
formula
Mixture
formula
Experimental
results show a
consistently higher
enhancement as
compared to
theory. The
enhancement is
m-K)
Duangth
ongsuk
and
Wongwi
ses [101]
N/A
Cu/water
nanofluid
21 nm
TiO 2/water
nanofluid
N/A
Flowrate
determined
by
electronic
balance
beyond
the
theoretical and
experimental errors
and hence is
anomalous*
Pak and
Cho
[103]
27 nm (TiO 2)
13 nm
(A12 0 3)
TiO 2/water
A12 0 3/water
Yu et al
[102]
-170 nm
(DLS and
Small angle
X-ray
scattering)
Aspect
Ratio ~ 1
A120 3 (1.34%,
2.78%)
Grain
like
shape
TiO 2 (0.99%,
2.04%,3.16%)
Disks or
platelets
3.7%
Aspect
Ratio 4:1
1400060000
Constant
heat flux
Masu
da et
al 6
Brook
field
cone
and
plate
visco
meter
Mixture
formula
Mixture
formula
Anomalous
enhancement* was
seen both for titania
and alumina
nanofluid beyond 1
vol% conc. The
enhancement
increased at higher
nanoparticle
concentration and
also at higher
Reynolds number
3,00012,000
Constant
heat flux
THW
DVII+Pro
visco
meter
Mixture
formula
Mixture
formula
Anomalous
enhancement*
observed which
increases with
higher Reynolds
number
SiC/water
nanofluid
*Anomalous enhancement is observed only under conditions of viscosity of nanofluid estimated at room temperature. As discussed in Section 3.4,
temperature variation of viscosity can have a significant effect on the analysis and the experimental and theoretical curves shift closer to each other
if viscosity is estimated at higher temperature which can be the source of error in the analysis due to unknown experimental temperatures.
Table IX Nanofluid Property Estimation and experimental HTC uncertainty
Nanofluid Property Estimation Uncertainty
Paper Authors
Viscosity
pt
pt (Pa.s)
Thermal
Conductivity
k (W/m-K)
Densityc
Specific Heat'
p
(kg/m 3)
Cp (J/kg-K)
Mass Flowrate
Uncertainty
Experimental HTC
uncertainty
(kg/s)
Anoop et al [95]
THW (±2%)
a
Mixture
Formula
Mixture
Formula
±5% (assumed)
±5% (assumed)
Ding et al [96]
KD2 (±3%)
a
Mixture
Formula
Mixture
Formula
±4.6%(reported)
±5% (assumed)
Heris et al [93]
Maxwell's model
a
Mixture
Formula
Mixture
Formula
±5% (assumed)
±5% (assumed)
a
Mixture
Formula
Mixture
Formula
±5% (assumed)
±3%
a
Mixture
Formula
Mixture
Formula
±5% (assumed)
±5% (assumed)
a
Mixture
Formula
Mixture
Formula
±5% (assumed)
±5% (assumed)
(±10% assumed
from INPBE)
Choi et al [98]
THW
(±5%, assumed
from INPBE)
Kurowska et al [99]
Maxwell's model
(±10% assumed
from INPBE)
Prasher et al [97]
Maxwell's model
(±10% assumed
from INPBE)
Li et al [100]
THW
a
Mixture
Formula
Mixture
Formula
1% (reported)
±4%
(±5%, assumed
from INPBE)
Ding et al [94]
KD2 (±3%)
a
Mixture
Formula
Mixture
Formula
±4.6%(reported)
±5% (assumed)
Li et al [100]
THW
NXE-1
viscometer
Mixture
Formula
Mixture
Formula
±1% (reported)
±4%
Mixture
Formula
Mixture
Formula
±5% (assumed)
±5% (assumed)
(±5%, assumed
from INPBE)
Duangthongsuk and Maxwell's model
Wongwises [101]
(±10% assumed
from INPBE)
(±5%
measurement
uncertainty
due to volume
fraction.
±10%
uncertainty
assumed due
to
temperature)
Mean of MIT
data and
Einstein's
model b
(±4.32%
model
uncertainty,
calculated by
using the
bounds as
MIT data and
Einstein's
model.
±10.00%
temperature
uncertainty)
Pak and Cho [103]
Maxwell's model
(±10% assumed
from INPBE)
Yu et al [102]
THW
(±5%, assumed
from INPBE)
Brookfield
viscometer
Mixture
Formula
Mixture
Formula
±5% (assumed)
Mixture
Formula
Mixture
Formula
1% (reported)
±5% (assumed)
(±2%,
measurement
uncertainty.
±10%
temperature
uncertainty)
DV 11+
Viscometer
±5%
(±5%)
ny
k C only. Since Pe number does not account for viscosity, we do
=pvDC~
a. Laminar flow correlations require the calculation of Peclet number, Pe =
not need to estimate the viscosity of the medium to calculate the heat transfer coefficient using correlations
b. Turbulent flow convective heat transfer studies did not report viscosity measurement procedure/technique. In such cases the viscosity bounds
had to be estimated. Williams et al [55] at MIT performed experiments to measure viscosity of nanofluids. They devised a formula using their
experimental data and found the viscosity to be considerably higher than reported by classical Einstein formula, (y = p,(l + 2. 5 p)). The
bounds for viscosity were calculated with maximum estimated by the formulae reported in [55] and the minimum by the Einstein's formula.
0
Williams et al [55] viscosity
measurement (upper limit)
4.910
For alumina nanofluid: y(0, T) = pw(T)e(o.zo92-o)
m
For zirconia nanofluid: p (0, T) = p
(11-190
(T)e .196 -0)
Hence the viscosity was estimated to be the mean of the maxima and the minima. The uncertainty was estimated by the deviation of the mean
from the maxima and minima.
c.
Uncertainties in density and specific heat of nanofluid were calculated using error propagation through the mixture formula assuming standard
10% uncertainties in nanoparticle properties (Although nanoparticle properties can be determined with a good accuracy there is still an
uncertainty as their physical properties might be affected by the interaction with basefluid molecules. Phenomenon like hydration are very
common and are reported to effect the physical properties of nanofluids)
3.3.
Experimental Studies Analyzed
The studies analyzed basically included published experimental work on laminar and turbulent flow
regimes. Table VII and Table VIII list the various published experimental works which had reported an
anomalous enhancement of heat transfer coefficient when compared to the prediction by the theoretical
correlations.
3.3.1.
Laminar Flow
Table VII lists the published studies which report anomalous enhancement of convective heat transfer
coefficient during laminar flow. Heat transfer coefficient data was extracted from the papers and was
compared to the theoretical correlation relevant to the experimental conditions used in the measurement.
Anoop et al [95] did an experimental investigation on the convective heat transfer characteristics in the
developing region of tube flow with constant heat flux with alumina-water nanofluids. Two particle sizes
were used, one with average particle size of 45 nm and the other with 150 nm. It was observed that in the
developing region, the nanofluid heat transfer coefficients show higher enhancement with respect to the
HTC of water than in the developed region. A new correlation was proposed by Anoop et al to predict the
heat transfer coefficient for the range of nanofluids used in their experiments. Experimental data on
measured heat transfer coefficient and Reynolds number was extracted only for 150 nm nanoparticles.
The theoretical value of heat transfer coefficient was predicted using equation 15. Uncertainties and
methods of estimation of nanofluid properties for predicting theoretical HTC have been listed in Table
IX.
Viscosity was measured using Ubbelohde viscometer. Since equation 15 uses the Peclet Number (Pe)
which is the product of Reynolds number (Re =
pvD
'
) and Prandtl number(Pr = '),
effect of error in
viscosity measurement is cancelled. Since the Reynolds number was directly extracted from the paper,
precision was taken to use the same value of viscosity for the prediction of Prandtl number as was used by
the authors in the estimation of Reynolds number so that the effect of viscosity measurement was
cancelled. Error in estimation of thermal conductivity using THW was reported to be 2%. Error in density
and specific heat was estimated by propagation of uncertainties through formulae. Figure 35 to Figure 38
show the variation of both experimental and theoretical HTC with Reynolds number at x/D=147
(-halfway in the tube). An error bar is associated with each experimental measurement as well as
theoretical estimation. It can be clearly seen that the HTC there is a clear anomalous enhancement which
is not predicted by the regular theoretical correlation given by equation 15. This anomalous enhancement
becomes more prominent (>15%) at higher Reynolds number and increases with higher concentration of
nanoparticles.
Figure 38 shows the HTC variation along the tube during the developing flow regime at a Reynolds
number 1550. It can be seen that there is a higher deviation of experimental value from the theoretical
estimation and the enhancement is anomalous as the error bars do not overlap
1 wt% Alumina
4 wt% Alumina
950
950
900
--
850
850-
--
800---
750
-
700
-
650
-
750
----
--
600
1400 Re
1900
700
-1---
650
--
2400
-
900
--
Experimental HTC
---
-
-
600 +
900
Figure 35 Local HTC vs Re for 1 wt% alumina
(x/D=147; 150 nm particles) Anoop et al
1400
Re1900
Experimental HTC -0-Theoretical HTC
Figure 36 Local HTC vs Re for 4wt% alumina
(x/D=147; 150 nm) particles) Anoop et al
6 wt% Alumina
1000
-
-
-
950
900
------
-
850
800
-
750
-
-
700650
--
600
--
-
600
--
1100
-
Re
1600
2100
Experimental HTC -1-Theoretical
--
HTC
Figure 37 Local HTC vs Re for 6 wt% alumina (x/D=147;
150 nm particles) Anoop et al
1100
-_-_-_-_-
4 wt% alumina, Re=1550
-
-
1050
1050L
950
-
--
---
850
-1
800750
600 700
650----
-
---
-
900
-
800
-- -
-
-
-
_
_
600--50
100
-+-
x/D
Experimental HTC
150
200
-U- Theoretical HTC
Figure 38 HTC vs (x/D) for 4 wt% alumina (150 nm nanoparticles)
Anoop et al
250
2400
---
Theoretical(0.6%) -e-Experimental(0.6%)
-+-Experimental(1%)
3000
3000
2500
2500
2000
-
-
-
-
--
2000
1500
-U-Theoretical(1%)
--
1500
1000
----
-
500
25
63
500
116
x/D
146
172
25
63
116
146
172
x/D
Figure 39 Local HTC in the developing region for
0.6 vol% alumina (Re 1600)
Ding et al
-+-
-
1000
Experimental(1.6%) -- W-Theoretical(1. 6%)
Figure 40 Local HTC in the developing region for 1 vol%
alumina (Re1600)
Ding et al
-+o-Experimental(0.6%)
-U-Theoretical(0.6%)
2500
35003000-
---
2000
L
25002000
-
----
-
1500-
1000
-
1000
-
-
500
500
0
1500
25
0
-
--
63
11/j
146
25
172
63
116
146
172
x/D
Figure 41 Local HTC in the developing region for 1.6 vol%
alumina (Re 1600) Ding et al
-Experimental(1%) --2500--
Theoretical(1%)
Figure 42 Local HTC in the developing region for
0.6 vol% alumina (Re 1050) Ding et al
-o-Experimental(1.6%)
2500 ,
2000
2000-
1500
1500
1000
- ----
1000
-
500
-U-Theoretical(1.6%)
- -
--
500
-~
__
-
_
-
----
-
0
25
63
116
146
172
Figure 43 Local HTC in the developing region for 1.0
vol% alumina (Re 1050) Ding et al
25
63
x/D 1 1 6
146
Figure 44 Local HTC in the developing region
for 1.6 vol% alumina (Re 1050) Ding et al
172
-
Ding et al [93] did an experimental work on the convective heat transfer of nanofluids, made of y-A1203
nanoparticles and de-ionized water, flowing through a copper tube in the laminar flow regime. The results
showed considerable enhancement of convective heat transfer using the nanofluids. The enhancement was
particularly significant in the entrance region, and was much higher than that solely due to the
enhancement on thermal conductivity. It was also shown that the classical Shah [107] equation failed to
predict the heat transfer behavior of nanofluids. Experimental data on heat transfer coefficient was
extracted for the 0.6 vol%, 1.0 vol% and 1.6 vol% alumina nanofluids for Reynolds number of 1050 and
1600. Viscosity was estimated using Einstein model given by equation 19
y = If (1 + 2.50)
(19)
where pf is the viscosity of the basefluid and 0 is the volume fraction of nanoparticles in the nanofluid
The calculated viscosity was used to estimate the Prandtl number which was used for estimation of
theoretical HTC. Thermal conductivity was measured using KD2 instrument and was extracted from the
paper. The uncertainty in the measured thermal conductivity was reported to be 3%. Other uncertainties
were propagated using simple error propagation. Figure 39 to Figure 44 represent the comparison of
theoretical predictions obtained from equation 15 with the experimental data extracted. It can be clearly
observed that the heat transfer coefficient measured during experiments is considerably higher than the
theoretical estimation
after accounting
for errors in theoretical
estimation and experimental
measurements. There is a clear anomalous enhancement and the deviation is more prevalent in the
entrance region. Uncertainties and methods of estimation of nanofluid properties for predicting theoretical
HTC have been listed in Table IX.
0.2 vol%_alumina
1000
9
1- vd1
alumna-
1000
900
900
800
800
-
---
-
700
600
500
400-
400
1!500
3500 Pe
-4-Experimental HTC --
1500
5500
Theoretical HTC
Pe
-4-Experimental HTC --
Figure 45 Average experimental HTC and average
theoretical HTC plotted as a function of Peclet number
for 0.2 vol% alumina nanofluid (Heris et al)
5500
Theoretical HTC
Figure 46 Average experimental HTC and average
theoretical HTC plotted as a function of Peclet number
for 1.0 vol% alumina nanofluid (Heris et al)
2 voIalumina
1000
3500
1000
900
800
800
700
-
--
600
-
-
500
700
600
t---_-_
-
-
-
--
500
400
400
1500
3500
Pe 5500
1500
3500
Pe
-4-Experimental HTC --
-4-Experimental HTC -U-Theoretical HTC
Figure 47 Average experimental HTC and average
theoretical HTC plotted as a function of Peclet number
for 2.0 vol% alumina nanofluid (Heris et al)
900
800
700
600
500
400
1500
3500
Theoretical HTC
Figure 49 Average experimental HTC and average
theoretical HTC plotted as a function of Peclet
number for 3.0 vol% alumina nanofluid (Heris et al)
3~v~~W/G-a{umina--
1000
5500
Pe
-+-Experimental HTC --
5500
Theoretical HTC
Figure 48 Average experimental HTC and average theoretical HTC
plotted as a function of Peclet number for 2.5 vol% alumina nanofluid
Heris et al
Heris et al [97] investigated nanofluids containing CuO and A120 3 oxide nanoparticles in water as base
fluid. The laminar flow convective heat transfer through circular tube with constant wall temperature
boundary condition was examined. The experimental results emphasize that the single phase correlation
with nanofluids properties (Homogeneous Model) is not able to predict heat transfer coefficient
enhancement of nanofluids. Experimental data was extracted for 0.2 vol%, 1.0 vol%, 2.0 vol%, 2.5 vol%
and 3.0 vol% A120 3 nanofluid. Since constant wall temperature boundary condition was used during the
experiments, equation 17 was used to predict the theoretical heat transfer coefficient. Peclet number was
reported and hence there was no issue of viscosity measurement uncertainty. Thermal conductivity was
estimated using equation 1 for effective medium theory. An uncertainty of 10% was attached to the model
for prediction of thermal conductivity as was found during the INPBE exercise. The comparison of the
theoretical HTC result with experimental values for different concentration has been shown in Figure 45
to Figure 49. HTC is plotted as a function of Peclet number. It can be clearly observed that there is a
higher deviation of experimental values from the theoretical prediction at higher Peclet number. High
Peclet number is equivalent to higher Reynolds number for a given concentration and hence the trend of
higher deviation might be attributed to a more chaotic movement of nanoparticles at higher Reynolds
number enhancing the heat transfer rate. A more detailed analysis needs to be done to understand the
mechanism of this enhancement.
Choi et al [99] measured convective heat transfer coefficient of water-based A120 3 nanofluids flowing
through a uniformly heated circular tube in the fully developed laminar flow regime. The paper reports
that the convective heat transfer coefficient of the nanofluids increases by up to 8% at a concentration of
0.3 vol% compared with that of pure water and this enhancement cannot be predicted by the Shah
equation. Experimental HTC data was extracted for 0.1 vol%, 0.2 vol% and 0.3 vol% alumina nanofluid.
Equation 15 was used to predict the experimental HTC after the estimation of nanofluid properties as per
the methods listed in Table IX. Viscosity was measured using VM-1OA viscometer while the thermal
conductivity was measured using transient hot wire method. Measured viscosity was used to estimate the
Prandtl number. Error propagation was done to get the uncertainty in the value of
1700
1650OLoIAunn
2 VO4%-A
1650
1600 t
1600
-
-
-
1550
1550
--
-
1500
1500
11450
-
1400
1350
220
1450
-
-
-
--
1400
-
460 x/D 6 8 0
-- *-Experimental
900
1350
-U-Theoretical
1350
--
x/D
0
500
-*-Theoretical HTC --
Figure 50 Local theoretical HTC and experimental HTC
plotted as a function of x/D in the developing flow
region (Re =700, 0.1 vol% alumina) (Choi et al)
1000
1500'
Experimental HTC
Figure 51 Local theoretical HTC and experimental HTC
plotted as a function of x/D in the developing flow region
(Re =700,0.2 vol% alumina)
(Choi et al)
vol% Alumina
17000.3
1700--16501600
---
1550
-----
15001450-1400
-
--
220
460/D 680
900
1350
Experimental
-Theoretical
Figure 52 Local theoretical HTC and experimental HTC
plotted as a function of x/D in the developing flow region
(Re =700, 0.3 vol% alumina) (Choi et al)
the HTC predicted by the theory. Uncertainty associated with each parameter is listed in Figure 50 to
Figure52 show the data for experimental and theoretical HTC after analysis. Although the experimentally
measured HTC is consistently higher than the theoretically predicted HTC, the value is within the bounds
of experimental error and theoretical estimation error except for 0.3 vol% concentration nanofluid. In
other words, the enhancement cannot be really confirmed to be anomalous at concentrations lower than
0.3 vol% because of the uncertainty in the values of experimental and the theoretical HTC.
Kurowska et al [98] investigated convective heat transfer in nanofluid based on Cu (approx. 0.15 vol %
and 0.25 vol %) nanoparticles at constant heat flux conditions. A 30% increase in average heat transfer
coefficient was reported against the results obtained for a pure host liquid (ethylene glycol). Even more
significant increase was reported in the entrance region. Experimental HTC data was extracted for 0.15
vol% Cu- nanofluid. Temperature dependent nanofluid viscosity was estimated using empirical formula
of type r7 = aT2 + bT +c as given by Eastman et al [108]. The constants a, b and c were determined for
both the nanofluids using the Brookfield DV 11+ viscometer. The temperature for the estimation of
nanofluid properties was 298 K. Viscosity thus estimated was used in the estimation of Pr number to
avoid viscosity measurement errors. Effective medium theory was used to estimate the thermal
conductivity of nanofluid with 10% accuracy as reported in the INPBE study. Figure 53 and Figure 54
show the comparison of experimental measurements reported with the theoretical estimation. Figure 53
shows that there is an anomalous enhancement at the beginning of the entrance region but the
enhancement is very nearly predicted by the theory once the flow starts to develop. Figure 54 shows that
average HTC generally increases with increasing Reynolds number but anomalous enhancement could
not be confirmed. The wavy behavior of the experimental curve is reported to experimental errors.
5000
1500
-
4500
--
-
4000
1400
1300
3500
-
12
3000
2500-2000
-
0 0
-
1000
1500
-
1000
500
900
800
0.00
100.00 600.00 300.00 400.00
-
Experimental HTC
Figure 53 Local experimental and theoretical HTC in
the developing flow region (Re=60, q=1900 W/m2K)
Kurowska et al
700
-
0
-Experimental
20
-
40 Re 60
80
100
HTC -U-Theoretical HTC
Figure 54 Average experimental and theoretical HTC vs
Reynolds number (Kurowska et al)
Prasher et al [98] report the heat transfer coefficient in both developing and fully-developed regions by
using water based alumina nanofluids. Experimental test section consists of a single 1.02-mm-diameter
stainless steel tube which is electrically heated to provide a constant wall heat flux. Experiments were
performed with 0.5 vol%, 0.75 vol% and 1.0 vol% A120 3 nanofluids for 3 different flow-rates 1 ml/min, 5
ml/min and 9 ml/min. Data was extracted from the paper and the theoretical estimation was done using
equation 15. Thermal conductivity was predicted the effective medium theory with an uncertainty of 10%
which was taken into account duding error analysis. Viscosity was estimated using Einstein's model. This
viscosity was used for estimation of both Reynolds and Prandtl number. Hence error in viscosity doesn't
matter since it cancels out in the Peclet number (Pe=Re.Pr).After analysis of error, the results obtained
are shown in Figure 55 to Figure 63. Concentration of nanoparticles in these nanofluids is very low and
no anomalous enhancement seems obvious. A trend of higher deviation from theoretical values at higher
concentration and higher flowrate (Reynolds number) is seen. Although results of the experimental
measurements are consistently above the theoretically estimated value, they are within the bounds of
theoretical and experimental uncertainty and hence any anomalous enhancement couldn't be confirmed.
5500
4300
5000
4500
3800
4000
-
3300
3500
30002800 4
2500
2000
2300
0
50
100x/D 150
200
250
-- *Experimental HTC (0.5 vol%, 9ml/min)
-Theoretical HTC (0.5 vol%, 9ml/min)
Figure 55 Local experimental and theoretical HTC
(0.5 vol% alumina, 9ml/min)
Prasher et al
0
50
10
9/D 150
200
250
-+-Experimental HTC (0.5 vol%, 5ml/min)
Figure 56 Local experimental and theoretical HTC
(0.5 vol% alumina, Smi/min)
Prasher et al
3400
-
5200
32003000
4700
4200
2800--
3700
-
3200
2600
2400
-
2200
--
-
--
-
2700
2200
-4-Experimental HTC (0.5 vol%, 1 ml/min)
-4-Theoretical HTC (0.5 vol%, 1 ml/min)
0
50
100
150
200
250
x/D
-4--Experimental HTC (0.75 vol%, 9ml/min)
-4-Theoretical HTC(0.75 vol%, 9ml/min)
Figure 57 Local experimental and theoretical HTC
(0.5 vol% alumina, 1ml/min)
Prasher et al
Figure 58 Local experimental and theoretical HTC
(0.75 vol% alumina, 9ml/min)
Prasher et al
0
100
x/D
300
200
3400--
4200
3200
3700
3000
2800
3200-
4-
2700
2200
2600
2400
2200
0
50
200
250
10 0 x/D 150
-+-Experimental HTC (0.75 vol%, 1 ml/min)
-U-Theoretical HTC (0.75 vol%, 1 ml/min)
0
50
200
250
10 0 x/D 1 5 0
-+- Experimental HTC (0.75 vol%, Sml/min)
-4-Theoretical HTC (0.75 vol%, 5ml/min)
Figure 59 Local experimental and theoretical
Figure 60 Local experimental and theoretical
HTC (0.75 vol% alumina, 1 ml/min)
Prasher et al
HTC (0.75 vol% alumina, 5 ml/min)
Prasher et al
4700
-
-
5200
4200
4700
4200
3700--
3700
3200
-
3200
2700
2700
-
2200
2200
0
--
.
---
50
100 x/D 1 5 0
200
250
-4--Experimental HTC (1.00 vol%, 9ml/min)
L-1-Theoretical HTC (1.00 vol%, 9 ml/min)
Figure 61 Local experimental and theoretical
HTC (1.0 vol% alumina, 9 ml/min)
Prasher et al
-
-
-
0
50
150
200
-4--Experimental HTC (1.00 vol%,...
-U-Theoretical HTC (1.00 vol%,...
Figure 62 Local experimental and theoretical
HTC (1.0 vol% alumina, 5 ml/min)
Prasher et al
250
3400
3200
3000
----
-
2800
2600
2400
-
2200
-
---
x/D
0
50
100
150
200
250
-4--Experimental HTC (1.00 vol%, 1 ml/min)
-U--Theoretical HTC (1.00 vol%, 1 ml/min)
Figure 63 Local experimental and theoretical
HTC (1.0 vol% alumina, 1 mI/min)
Prasher et al
1000
1000
0.3 vol % Cu
900
900
800
800
700
J
-- -
-------
-
Cui
-1-----
700
600
600
500
-.-
90 0vo
-
500
-
400
400
-
500
1000 Re 1500
2000
2500
-4-Experimental HTC -U-Theoretical HTC
Figure 64 Average theoretical and experimental HTC
vs Reynolds number (0.3 vol% Cu) (Li et al)
500
1C00 Re 1500
Experime ital HTC --
2500
2000
Theoretical HTC
Figure 65 Average theoretical and experimental HTC
vs Reynolds number (0.5 vol% Cu) (Li et al)
1000
O.8 vot% Cu
900
-+-
-
-
900--
800
-
-
800
-
-
700
-
600
-
500
600
-
400
1000
1500Re 2000
-
500
400
500
-
-
--
--4-Experimental HTC -M-Theoretical HTC
500
1000 Re 1500
2000
2500
--- Experimental HTC -U-Theoretical HTC
Figure 66 Average theoretical and experimental
HTC vs Reynolds number (0.8 vol% Cu) (Li et al)
Figure 67 Average theoretical and experimental HTC
vs Reynolds number (1.0 vol% Cu) (Li et al)
2500
81
1000
-
-v--%-
-
1100
.2volCu
1.5
900
1000-
---
-
-
8004-
700
-- - --------
700
--
CU
-
900
800
Vol%
----
700-
-
600
600
500--
-
500
400
--
-
400
500
1000 Re
1500
2000
500
1000
1500 Re 2000
2500
Experimental HTC -Theoretical HTC
Figure 69 Average theoretical and experimental HTC vs
Reynolds number (1.5 vol% Cu) (Li et al)
-+-
-Experimental HTC -Theoretical HTC
Figure 68 Average theoretical and experimental HTC vs
Reynolds number (1.2 vol% Cu) (Li et al)
1200
-
1100
0vol% Cu
- -
-
1000
900
800 ------
700
600
-
------
500
400
-4-
-
-
g~o
10P0
xperimenta HTC
15 Oh
ZOOP
2500
eoretica HTC
Figure 70 Average theoretical and experimental HTC vs
Reynolds number (2.0 vol% Cu) (Li et al)
Li et al [94] investigated convective heat transfer and flow characteristics of Cu-water nanofluid in a tube
for the laminar and turbulent flow. They discussed the effects of such factors as the volume fraction of
suspended nanoparticles and the Reynolds number on the heat transfer and flow characteristics in detail.
They report that their experimental results show the suspended nanoparticles remarkably increase the
convective heat transfer coefficient of the base fluid and showed that the friction factor of the sample
nanofluid with the low volume fraction of nanoparticles is almost not changed. Compared with the base
fluid, for example, they reported that the convective heat transfer coefficient increased about 60% for the
nanofluid with 2.0 vol% Cu nanoparticles at the same Reynolds number. The different concentrations of
82
Cu-water nanofluid used for this study were 0.2 vol%, 0.5 vol%, 0.8 vol%, 1 vol%, 1.2 vol%, 1.5 vol%
and 2.0 vol%. The experimental data was extracted from the paper and theoretical estimation of HTC was
made using equation 13 using nanofluid properties estimated as per methods given in Table IX. Thermal
conductivity was measured using transient hot wire method. Viscosity was measured using a NXE-1
viscometer. Thermal conductivity and viscosity were both measured with 5% accuracy. Error analysis
was performed and the results are shown in. Figures 64 to 70. It can be clearly seen that the
experimentally measured values for the HTC are way higher than the theoretically estimated HTC. The
enhancement seen in these cases is certainly anomalous as it is way beyond the experimental and
theoretical estimation uncertainty. Moreover the enhancement is higher at a higher concentration and a
higher Reynolds number, a trend which has been consistently observed across most of the data analyzed.
Ding et al [96] investigated the heat transfer behavior of aqueous suspensions of multi-walled carbon
nanotubes (CNT nanofluids) flowing through a horizontal tube. They reported that significant
enhancement of the convective heat transfer is observed and the enhancement depends on the flow
conditions (Reynolds number, Re), CNT concentration and the pH. Two nanofluids with 0.1 wt% and 0.5
wt% concentration were tested. Thermal conductivity was measured with KD2 property meter with 3%
2400
2200
5000
0.1 wt% CNT
4500
4
2000
4000
1800-
3500
3000
1600
1400
-
----
1200
2000
1000
1500 41000
800
600
500
-
0
50 x/D
-- Experimental HTC
10 0
150
200
-Um-Theoretical HTC
Figure 71 Local experimental and theoretical HTC (0.1 wt%
CNT, Re=800) Ding et al
0
---
50
/
1 00
Experimental HTC ---
150
200
Theoretical HTIC
Figure 72 Local experimental and theoretical HTC (0.5 wt%
CNT, Re=800) Ding et al
accuracy while viscosity was measured using CVO rheometer. Measured viscosity and thermal
conductivity was used for prediction of Prandtl number. After HTC data extraction and comparison with
theoretically predicted HTC the plots have been shown in Figure 71 and Figure 72.
3.3.2.
Turbulent Flow
Four experimental studies were analyzed for turbulent flow to check if the claims of the anomalous
enhancement in HTC were valid under the experimental and theoretical uncertainty limits.
Xuan and Li [94] investigated convective heat transfer and flow features of Cu-water nanofluid in a tube.
Both the convective heat transfer coefficient and friction factor of the sample alumina nanofluids for the
turbulent flow were measured, respectively and new type of convective heat transfer correlation was
proposed to correlate experimental data of heat transfer for nanofluids. The alumina nanofluids having
concentrations 0.3 vol%, 0.5 vol%, 0.8 vol%, 1.0 vol%, 1.2 vol%, 1.5 vol%, and 2.0 vol% were used
during this study. Thermal conductivity was measured using transient hot wire method. Viscosity was
measured using a NXE-1 viscometer. Thermal conductivity and viscosity were both measured with 5%
accuracy. The experimental data was extracted and compared to theoretical values with uncertainty
attached to each value. The uncertainty in theoretical estimation was determined by error propagation and
the uncertainties in the different parameters have been listed in Table IX. The results are shown in Figure
73 to Figure 79. At lower concentration the experimentally measured values are very close to the ones
predicted by theory, The plots suggest that the experimental enhancement is always above the
theoretically predicted value but it can be clearly distinguished only at a higher concentration of
nanoparticles (>1 vol%) and also the enhancement deviates from the theoretical value at higher Reynolds
number.
0.3 vol% Cu nanofluid
0.5 vol% Cu nanofluid
10000
10000
9000
9000
8000
HTC
8000
HTC
00
i
(W/m2(?
(W/m2fPOO
6000
6000
5000
5000
4000
4000
8000
Re 18000
-+-Experimental HTC
Figure 73 Average theoretical and experimental HTC vs
Reynolds number (Li et al)
10000
Re 20000
-4-Experimental HTC
Figure 74 Average theoretical and experimental HTC
vs Reynolds number (Li et al)
0.8 vol% Cu nanofluid
10000 T!
11000
1.0 vol% Cu nanofluid
t
--
--
9000
HTC
-
---
8000
HTC
(W/m2K
(W/m2K000
6000
5000 A...
5000
-
---
10000
-----
1500(e
-
20000
25000
Figure 75 Average theoretical and experimental HTC vs
Reynolds number (Li et al)
---
4000
=
Experimental HTC -U-Theoretical HTC
---
00
6000 T
4000
--
10000
9000
8000
-
--
-4-
10000
1500(Re 20000
25000
Experimental HTC -U-Theoretical HTC
Figure 76 Average theoretical and experimental HTC vs
Reynolds number (Li et al)
1.2 vol% Cu nanoflul
12000
9500
1.5 vol% Cu Nanofluid
11000
8500
10000
HTC7500
9000
-
8000
(W/m2K)
(W/m2K)
6500
7000
--
-
6000-
5500 +4500
-
IHTC
5000
-
-
4000
10000
15 0 00 Re
-4-Experimental HTC
20000
Figure 77 Average theoretical and experimental HTC vs
Revnolds number (Li et al)
-
10000
--
--
1500ORe
20000
Experimental HTC
Figure 78 Average theoretical and experimental HTC vs
Reynolds number (Li et al)
13000
2.0 vol %Cu nanofluid
-
12000
--
-
11000
10000
HTC 9000
(W/m2K)8000
-
7000-t6000
-
-
--
5000
--
4000
13 0 0 0
8000
Re
18000
23000
-+-Experimental HTC
Figure 79 Average theoretical and experimental HTC vs
Reynolds number (Li et al)
0.2 vol% Titania (TiO2
11000
--
10000
-
-
9000
7000
-
E 6000
-
-
-
---
8000
-
-
--
-
-
5000
--
-
U40003000
2000
1000
-
3000
8000
-
13000
18000
Reynolds Number
-9--Experimental HTC
Theoretical HTC
Figure 80 Average theoretical and experimental HTC vs Reynolds number
(Duangthongsuk et al)
Duangthongsuk and Wongwises [101] studied the forced convective heat transfer and flow characteristics
of a nanofluid consisting of water and 0.2 vol% TiO2 nanoparticles. The heat transfer coefficient and
friction factor of the TiO 2-water nanofluid flowing in a horizontal tube-in-tube counter flow heat
exchanger under turbulent flow conditions were investigated. The results reported in this study show that
the convective heat transfer coefficient of nanofluid is slightly higher than that of the base liquid by about
86
6-11%. The heat transfer coefficient of the nanofluid increases with an increase in the mass flow rate of
the hot water and nanofluid, and increases with a decrease in the nanofluid temperature, and the
temperature of the heating fluid has no significant effect on the heat transfer coefficient of the nanofluid.
They also reported that the Gnielinski equation failed to predict the heat transfer coefficient of the
nanofluid. Figure 80 shows the experimental data and theoretically predicted data on the HTC vs Re plot.
It is clear from the plot that the enhancement is really anomalous as it is not predicted by the theory
within the bounds of experimental/theoretical error.
30000
30000
1.34 vol% alumina
20000
2.78 vol% Alumina
25000
HTC
15000-
20000
(W/m2N00
HTC
10 0 0 0
5000
5000
10000
2 0 00
30000
40000
-+--Experimental
50000
10000 20000 30000 40000 50000
Re
-+-Experimental HTC
HTC
Figure 81 Experimental and theoretical HTC vs Reynolds
number (Pak and Cho)
-
Figure 82 Experimental and theoretical HTC vs Reynolds
number (Pak and Cho)
19000 -O.g9v%-Titania-
2.04 vol% Titania
18000
17000
-
16000
15000
14000
HTq 30 00
HTC
(W/m2K
11000
(W/g0
JL0000
9000-7000
--
8000
-
6000
----
4000
5000
10500
30509
-+-Experimental HTC --
e
Figure 83 Experimental and theoretical HTC vs Reynolds
number (Pak and Cho)
--
-
,
10000
50500
Theoretical HTC
-
--
30000
50000
Re
Experimental HTC -U-Theoretical HTC
Figure 84 Experimental and theoretical HTC vs Reynolds
number (Pak and Cho)
3.16 vol% Titania
24000
-
19000
H15OO
(W/m2K)
9000
10000
30000
50000
Re
-4--Experimental HTC
-U-Theoretical HTC
Figure 85 Experimental and theoretical HTC vs Reynolds
number (Pak and Cho)
Pak and Cho [103] investigated turbulent heat transfer behaviors of dispersed fluids (ultrafine metallic
oxide particles suspended in water) in a circular pipe. Two different metallic oxide particles, y-alumina
(A120 3) and titanium dioxide (TiO 2) with mean diameters of 13 and 27 nm, respectively, were used as
suspended particles. The Reynolds and Prandtl numbers varied in the ranges 104-10 5 and 6.5-12.3,
respectively. Nanofluids investigated included 0.99 vol%, 2.04 vol%, 3.16 vol% titania nanofluids and
1.34 vol%, 2.78 vol% alumina nanofluids. Relevant experimental data was extracted from the paper and
theoretical estimation of HTC was made using the Dittus Boelter correlation as given by equation 5. The
data has been plotted in Figure 81 to Figure 85. It can be seen from the plots that there is definitely an
anomalous enhancement observed in case of 2.78 vol% alumina and 3.16 vol% titania. At lower
concentrations, however the enhancement couldn't be confirmed under the limits of experimental
measurement uncertainty and theoretical estimation error. However it is again noted that the
experimentally measured value has a higher deviation at higher Reynolds number.
Yu et al [102] performed experiments with a water-based nanofluid containing 170-nm silicon carbide
particles at a 3.7% volume concentration and having potential commercial viability. Heat transfer
coefficients for the nanofluid were presented for Reynolds numbers ranging from 3300 to 13,000 and are
compared to the base fluid water. Relevant experimental data was extracted. Final plot of HTC vs Re is
shown in Figure 86. There appears to be a significant deviation of experimental HTC from theoretical
beyond the uncertainties in the experimental measurement and theoretical estimation. The enhancement
shows higher deviation at higher Reynolds number, a trend observed in most of the studies analyzed.
However this enhancement is observed when we have evaluated the viscosity at room temperature. As
explained in Section 3.4 temperature variation of viscosity could significantly affect the analysis. As we
see in the following section the experimental and theoretical curve for HTC move closer at higher
temperature.
4000040000
-
3.7 vol% SIC nanofluid
3500
3000025000
HTC
(W/m219 0 0 0 0
15000
-
10000
-
-
5000-
3000
5000 Re
7000
9000
11000
-4-Experimental HTC -U-Theoretical HTC
13000
Figure 86 Experimental and theoretical HTC vs Reynolds number (Yu et al)
89
3.4.
Interpretation of Results
3.4.1.
Turbulent Flow
During this research exercise, 4 turbulent flow experimental studies [100-103] claiming an anomalous
enhancement in the heat transfer coefficient beyond the prediction by theoretical models were analyzed.
On analysis it was observed that the experimental heat transfer coefficient measured at the reported
Reynolds number was higher than the theoretical prediction by Dittus Boelter correlation or Gnielinski
correlation. Although this seems anomalous even after accounting for theoretical and experimental errors,
one of the things which still remain unknown is the fluid temperature during the experiments. Due to lack
of information on temperature of the experiments the properties of nanofluids were evaluated at room
temperature. However, the correlations require the properties of the nanofluid at an average temperature
of the heated section. This could affect the estimation of the heat transfer coefficient from the correlation.
It was shown in INPBE that the temperature effect on the thermal conductivity of nanofluid is not very
significant in the temperature range 25 C-35 C and density and specific heat are also not strong functions
of temperature. Hence the most dominant effect of temperature is on the viscosity of nanofluid. The
Viscosity of water
1.4
--
1.2
-
1A
E
0.8
0.4
0.2
-
--
0
0
20
40
60
80
100
T (C)
Figure 87 Variation of viscosity of water with temperature
120
temperature effect of viscosity on nanofluid is captured by the change in viscosity of the basefluid with
temperature as shown by Williams et al [55] for alumina and zirconia nanofluids. The general variation of
Table X Water Viscosity Data
Temperature p (mPa.s)
% of Room T
Dittus-Boelter
% change in Nu Re a 1/p
Nu a 1/p"
10
1.308
145%
0.86
-14%
0.687997
15
1.155
128%
0.90
-10%
0.779134
20
1.002
111%
0.96
-4%
0.898104
25
0.8999
100%
1.00
0%
1
30
0.7978
89%
1.05
5%
1.127977
35
0.72545
81%
1.09
9%
1.240471
40
0.6531
73%
1.14
14%
1.37789
45
0.6001
67%
1.18
18%
1.499583
50
0.5471
61%
1.22
22%
1.644855
55
0.50695
56%
1.26
26%
1.775126
60
0.4668
52%
1.30
30%
1.927806
65
0.4356
48%
1.34
34%
2.065886
70
0.4044
45%
1.38
38%
2.225272
75
0.3797
42%
1.41
41%
2.370029
80
0.355
39%
1.45
45%
2.53493
85
0.335
37%
1.48
48%
2.686269
90
0.315
35%
1.52
52%
2.856825
95
0.2986
33%
1.55
55%
3.013731
100
0.2822
31%
1.59
59%
3.188873
nanofluid viscosity pyf is given by equation (10)
Inf (P, T) = ybf (T)f(#)
(10)
where pbf (T) is the temperature dependent viscosity of basefluid and f(q) is an arbitrary functional
dependence on volumetric fraction,
#
of nanoparticles which is determined by experiments.
Effect of temperature on the analysis
(1.5 vol% Cu Nanofluid (Li et al))
12000
11000
10000
-
9000
HTC
Experimental HTC
(T=25CQ
-4s-
-
8000
-U-Theoretical
(T=25 C)
4-
7000
..
HTC
-Experimental HTC
(T=45 C)
6000
-Theoretical
45 C)
5000
4000
18000
8000
HTC (T=
28000
Reynolds Number
Figure 88 Effect of nanofluid temperature on theoretical and experimental HTC
Effect of temperature on analysis
(2.0 vol% Cu Nanofluid (Li et al))
13000
12000
--
11000
10000
1000
*
-
9000
HTC
8000
--HTC
Experimental HTC
(T=25 C)
Theoretical HTC
(T=25C)
ExperimentalHTC(T
HTC
-4o- -i-Theoretical
(T=45 C)
6000
--
5000
-
-
I
U-Theoretical HTC (T=
45 C)
4000
8000
18000
28000
Reynolds Number
Figure 89 Effect of nanofluid temperature on theoretical and experimental HTC
92
The studies analyzed during this research exercise for turbulent flow heat transfer coefficient had used
water based nanofluids. Hence it was worthwhile to look at the temperature variation of viscosity of
water. The temperature variation of viscosity of water has been shown in Figure 87.
As shown in Table X, at 55 C the viscosity of water drops almost to 56% of the room temperature value.
Hence temperature variation of viscosity can significantly affect the value of the heat transfer coefficient
prediction by the correlations. Table X indicates that the value of Nusselt number for turbulent flow
estimated by Dittus Boelter correlation increases by almost 26% as compared to room temperature value,
if the fluid temperature of experiment would be 55 C. Hence the theoretical prediction of heat transfer
coefficient will be 26% higher for a given Reynolds number at 55 C. Hence there is a considerable
amount of error induced in the prediction of heat transfer coefficient due to estimation of viscosity at
room temperature (25 C). In general a temperature higher than room temperature (which is obvious for
experiments) would cause the theoretical prediction to move upward because of higher Reynolds number.
Another uncertainty that comes due to unknown temperature while plotting the data is in the Reynolds
number. Since the viscosity changes very rapidly with temperature, Reynolds number is actually affected
inversely. Since the temperature of estimation of reported Reynolds number is unknown there could be a
horizontal shift induced due to the Reynolds number. Hence if the viscosity would be estimated at higher
temperature, the Reynolds number will be higher leading to a right side shift the experimental curve as
well as theoretical curve.
Hence the experimental temperature seems to be an important factor in the estimation of HTC and
comparison to experimental data. As discussed above a higher temperature leads to an upward shift of the
theoretical estimation curve and right side shift of the experimental and theoretical HTC curve.
To illustrate the effect of viscosity variation with temperature on HTC, the data for viscosity obtained by
Li et al [100] was modified to obtain viscosity at 45 C. This viscosity which was 67% of its room
temperature value was then used to evaluate the Reynolds number and Prandtl number at 45 C and then
these were used in the Dittus Boelter correlation to predict the heat transfer coefficient. The new HTC
obtained was plotted as a function of the new Reynolds number and compared to the results at 25 C.
Figure 88 and Figure 89 show the comparison of results obtained. The dotted lines show the results
obtained by assuming average experimental temperature of 45 C while the solid lines represent the results
obtained by assuming 25 C as the temperature for calculation of nanofluid properties. As discussed above
the experimental and theoretical curve shift towards right due to higher value of Reynolds number
because of lower viscosity at higher temperature. And as shown in Table I, Nusselt number is higher
which means a higher estimation of nanofluid HTC. Hence, it is clear from the above example that if the
coolant temperature of 45 C would have been account for in viscosity, no anomalous enhancement should
have been observed. Hence it could be possible to mistake the temperature effect on viscosity as
anomalous heat transfer coefficient enhancement during turbulent flow. Similar trend was confirmed in
all the 4 experimental studies analyzed for turbulent flows. Figures 90-93 confirm that trend.
Effect of Temperature (2.78 vol% alumin a)
30000
25000
20000
HTC
xperimental HTC (T=25 C)
15000
-T
10000
_
heoretical HTC (T=25 C)
-
xperimental HTC (T= 45 C)
heoretical HTC (T= 45 C)
Reynolds Number
Figure 90 Pak et al
Effect of Temperature (3.16 vol% Titania)
24000
19000
HTC
---
Experimental HTC (T=25 C)
0---Theoretical HTC (T=25 C)
Experimental HTC (T=45 C)
9000
-
-0-
Theoretical HTC (T=45 C)
-. ---.
4000
5000
55000
Reynolds Number
Figure 91 Pak et al
Temperature Sensitivity of Data (0.2 vol% Titania)
10000
-
9000
8000
2
7000
E
z
I-
6000-4--
Experimental HTC (T=25 C)
5000
Theoretical HTC (T=25 C
-QQ
-00-
-
-
---A4- Theoretical
(T=25
ExperimentalHTC
HTC
(T=45C)C)
-04-
2000
4000
9000
14000
19000
Reynolds Number
Figure 92 Duangthongsuk et al
Theoretical HTC (T=45 C)
Effect of Temperature (3.7 vol% SIC nanofluid)
38000
33000
28000
HT3000
---
Experimental HTC (T=25 C)
----
Theoretical HTC (T=25 C)
18000
13000
Experimental HTC (T= 45 C)
-
8000
3000
8000
13000
@-
Theoretical HTC (T= 45 C)
18000
Reynolds Number
Figure 93 Yu et al
3.4.2.
Laminar Flow
During this exercise, 8 laminar flow studies [93-100] were analyzed and most of the studies did display
anomalous enhancement in the developing flow region. Another noticeable trend among most of the
studies was that the enhancement was large at the entrance and decreased as the flow developed matching
the theoretical prediction once the flow was fully developed. Interestingly, viscosity does not affect the
prediction of HTC in the laminar flow regime as in case of turbulent flow. This is because of the fact that
the laminar flow equations 16 and 17 account for Peclet number (Pe = Re.Pr) hence viscosity is not a part
of the prediction of HTC. The trend in the HTC in the developing regime is still remains unexplained and
can be a good topic for future work.
4. Conclusion
An international nanofluid property benchmark exercise, or INPBE, was conducted by 34 organizations
participating from around the world. The objective was to compare thermal conductivity data obtained by
different experimental approaches for identical samples of various nanofluids. The main findings of the
study were as follows:
- The thermal conductivity enhancement afforded by the tested nanofluids increased with increasing
particle loading, particle aspect ratio and decreasing basefluid thermal conductivity.
- For all water-based samples tested, the data from most organizations deviated from the sample
average by ±5% or less. For all PAO-based samples tested, the data from most organizations
deviated from the sample average by ± 10% or less.
- The classic effective medium theory for well-dispersed particles accurately reproduced the INPBE
experimental data, thus suggesting that no anomalous enhancement of thermal conductivity was
observed in the limited set of nanofluids tested in this exercise.
- Some systematic differences in thermal conductivity measurements were seen for different
measurement techniques.
However, as long as the same measurement technique at the same
temperature conditions was used to measure the thermal conductivity of the basefluid, the thermal
conductivity enhancement was consistent between measurement techniques.
Studies claiming an anomalous enhancement in HTC were analyzed and comparison was made with the
theoretical estimation with proper calculation of nanofluid properties to be used in the prediction of
nanofluid heat transfer coefficient. Uncertainties in the theoretical prediction/ experimental measurement
of nanofluid properties were also accounted for while predicting HTC from theory. Also experimental
uncertainties were estimated to the experimental HTC measurement. An enhancement beyond the
experimental/ theoretical uncertainties was confirmed as anomalous. The main trends observed in the
analysis were
1) Experimentally measured HTC deviates from the theoretical prediction for nanofluids from about
10%-100%. Uncertainties in measurement of HTC were generally of the order of 5% and the
theoretical estimation uncertainty was about 10%. Although enhancement during turbulent flow
seems anomalous, it could be a case of mistaken temperature effect on viscosity as explained in
Section 3.4. Anomalous enhancement could only be concluded for laminar flow.
2)
A trend of higher deviation from the theoretical prediction at higher Reynolds number was seen.
Although in case of turbulent flow this deviation could be solely due to temperature affect on
viscosity, for laminar flow in developing regime this needs to be further investigated
3) A trend of higher deviation from the theoretical prediction at higher concentration was observed
suggesting an increasing HTC from factors other than just change in properties.
4) Analysis of temperature sensitivity of viscosity on the HTC prediction for turbulent flow shows
that unknown fluid temperatures in experiments could lead to a significant shift in the theoretical
prediction and experimental measurement curves as discussed in Section 3.4. Hence use of
viscosity corresponding to the correct fluid temperature is very important during turbulent flow
and could be a possible reason for the observed anomalous enhancement in the turbulent flow
studies. However the temperatures of experiments need to be confirmed from the researchers.
5) Interestingly estimation of viscosity doesn't affect the prediction of laminar flow HTC because
theoretical correlations always account for Peclet number (Pe=Re.Pr)which eliminates viscosity.
6) An anomalous enhancement was systematically observed during laminar flow in the entrance
regime. This enhancement in the laminar flow during developing flow regime couldn't be
explained.
Possible sources of such an enhancement still need to be explored and can be
extended as future work.
REFERENCES
1. Buongiorno, J. , Lin-Wen Hu, Sung Joong Kim, Ryan Hannink, Bao Truong, and Eric Forrest,
2008, "Nanofluids for Enhanced Economics and Safety of Nuclear Reactors: An Evaluation of
the Potential Features, Issues, and Research Gaps," Nuclear Technology, 162, pp. 80-91
2. Choi, S. U. S., 1995, "Enhancing Thermal Conductivity of Fluids With Nanoparticles,"
Developments and Applications of Non-Newtonian Flows, D. A. Siginer and H. P. Wang,
American Society of Mechanical Engineers, New York.
3. J. C. Maxwell, A Treatise on Electricity and Magnetism, II Edition, Clarendon, Oxford (1881).
4.
Q. Li,
and Xuan, Y.M., in Heat Transfer Science and Technology, edited by Buxan Wang,
Higher Education Press, pp. 757-762 (2000).
5. J. A. Eastman, S. U. S. Choi, S. Li, W. Yu, L. J. Thompson, "Anomalously increased effective
thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles"
Appl. Phys. Lett., 78(6), 718-720 (2001).
6. H. U. Kang, S.H. Kim, and J.M. Oh, "Estimation of Thermal conductivity of nanofluid using
experimental effective particle volume fraction", Experimental Heat Transfer, 19(3), 181-191
(2006).
7. T.-K. Hong, Yang H., Choi C. J., "Study of the enhanced thermal conductivity of Fe
nanofluids", J. Appl. Phys., 97, 064311 (2005).
8. S. Jana, A. Salehi-Khojin, W. H. Zhong, "Enhancement of Fluid Thermal Conductivity by the
Addition of Single and Hybrid Nano-additives" ,Thermochimica Acta, 462, 45-5 5 (2007).
9. M. Chopkar, Das P.K., Manna I., "Synthesis and Characterization of Nanofluid for Advanced
Heat-Transfer Applications", Scripta Materialia 55, 549-552 (2006).
10. S. Shaikh, K. Lafdi, R. Ponnappan, "Thermal conductivity enhancement in carbon nanoparticle
doped PAO oil: An experimental study",J. Appl. Phys., 101, 064302 (2007).
11. H. Xie, Wang J., Xi T., and Ai F.,"Thermal conductivity enhancement of suspensions containing
nanosized alumina particles", J. Appl. Phys., 91, 4568-4572 (2002).
12. H. Xie, Wang J., Xi T., and Liu Y., "Thermal conductivity of suspensions containing nanosized
SiC particles", Int. J. Thermophysics, 23, 571-580 (2002).
13. S. M. S. Murshed, Leong K. C., and Yang C., "Enhanced thermal conductivity of TiO2 - water
based nanofluids", Int. J. Thermal Sciences, 44, 367-373 (2005).
14. C. H. Chon, K.D. Kihm, S.P. Lee, S.U.S. Choi, "Empirical correlation finding the role of
temperature and particle size for nanofluid (A120 3 ) thermal conductivity enhancement", Appl.
Phys. Lett. 87, 153107 (2005).
15. K. S. Hong, T.-K. Hong, H.-S. Yang, "Thermal conductivity of Fe nanofluids depending on the
cluster size of nanoparticles", Appl. Phys. Lett. 88, 031901 (2006).
16. S. H. Kim, S. R. Choi, D. Kim, "Thermal conductivity of metal oxide nanofluids: Particle size
effect and laser irradiation", J. Heat Transfer 129 298-307 (2007).
17. C. H. Li and G.P. Peterson, "The effect of particle size on the effective thermal conductivity of
A12 0 3-water nanofluids", J. Appl. Phys. 101 044312 (2007).
18. G. Chen, Yu W.H., Singh D., Cookson D., Routbort J., "Application of SANX to the study of
particle-size-dependent thermal conductivity in silica nanofluids", J. Nanoparticle Research,
10(7), 1109-1114 (2008).
19. P. D. Shima, J. Philip, B. Raj, "Role of microconvection induced by Brownian motion of
nanoparticles in the enhanced thermal conductivity of stable nanofluids", Appl. Phys. Letter., 94,
1 (2009).
20. S. K. Das, Nandy Putra, Peter Thiesen and Wilfried Roetzel., "Temperature Dependence of
Thermal Conductivity Enhancement for Nanofluids", J. Heat Transfer, 125, p. 567 - 574 (2003).
101
21. D. Wen, and Ding Y., "Effective thermal conductivity of aqueous suspensions of carbon
nanotubes (carbon nanotube nanofluids)", J. Thermophysics and Heat Transfer, 18, 481-485
(2004).
22. C. H. Li and G. P. Peterson, "Experimental investigation of temperature and volume fraction
variations on the effective thermal conductivity of nanoparticle suspensions (nanofluids)", J.
Appl. Phys., 99, 084314 (2006).
23. H. D. Kumar, Patel H. E., Rajeev K. V. R., Sundararajan T., Pradeep T. and Das S. K., "Model
for heat conduction in nanofluids", Phys. Rev. Letter., 93 (14), 144301 (2004).
24. S. P. Jang and Choi, S. U. S., "Role of Brownian motion in the enhanced thermal conductivity of
nanofluids", Appl. Phys. Lett., 84, 4316 (2004).
25. R. Prasher, Bhattacharya P., and Phelan P. E., "Thermal Conductivity of Nanoscale Colloidal
Solutions (Nanofluids)", Phys. Rev. Lett. 94, 025901 (2005).
26. H. E. Patel, Sundararajan T., Pradeep T., Dasgupta A., Dasgupta N. and Das S. K., Pramana, A
micro-convection model for thermal conductivity of nanofluids, J. Physics, 65 (5), 863 - 869
(2005).
27. H. E. Patel, T. Sundararajan and S. K. Das, "A cell model approach for thermal conductivity of
nanofluids", J. Nanoparticle Research, Vol 10(1), 87-97 (2008).
28. P. Keblinski, S. R. Phillpot, S. U. S. Choi, J. A. Eastman,"Mechanism of Heat flow in
Suspensions Containing Nano-sized Particles (Nanofluids)", Int. J. Heat Mass Transfer, 45, 855863 (2002).
29. B. X. Wang, Zhou, L. P, and Peng X. F., "The Effective Thermal Conductivity of Liquid with
Suspension of Nanoparticles", Int. J. Heat Mass Transfer, 46, 2665-2672 (2003).
30. M. Foygel, Morris R. D., Anez D., French S., and Sobolev V. L., "Theoretical and computational
studies of carbon nanotube composites and suspensions: Electrical and thermal conductivity",
Phys. Rev. B, 71, 104201 (2005).
102
31. R. Prasher, W. Evans, P. Meakin, J. Fish, P. Phelan, P. Keblinski, "Effect of aggregation on
thermal conduction in colloidal nanofluids", App. Phys. Lett., 89, 143119, (2006).
32. J. Eapen, J. Li and S. Yip, "Beyond the Maxwell limit: Thermal conduction in nanofluids with
percolating fluid structures", Phys. Rev. E 76, 062501 (2007).
33. J. Philip, P. D. Shima and R. Baldev, " Evidence of enhanced thermal conduction through
percolating structures in nanofluids", Nanotechnology, 19, 305706 (7pp) (2008).
34. W. Yu and S. U. S. Choi, "The Role of Interfacial Layers in the Enhanced Thermal Conductivity
of Nanofluids: A Renovated Maxwell Model", J. Nanoparticle Res., 5, 167 (2003).
35. J. Eapen, J. Li, and S. Yip, "Mechanism of Thermal Transport in Dilute Nanocolloids", Phys.
Rev. Lett. 98, 028302 (2007).
36. J. Eapen, W. C. Williams, J. Buongiorno, L. W. Hu, S. Yip, R. Rusconi, R. Piazza, "Mean-Field
Versus Micro-Convection Effects in Nanofluid Thermal Conduction", Phys. Rev. Lett., 99,
095901, (2007).
37. R. K. Iler, The Chemistry of Silica, Ch. 4, J. Wiley and Sons (1979).
38. J. G. Gutierrez and M. Riccetti, IMECE2008-67283, Proc. 2008 ASME Int. Mech. Eng.
Congress and Expo, Oct 31 - Nov 6, Boston, Massachusetts, USA (2008).
39. J. J. Healy, J. J. de Groot and J. Kestin, The Theory of the Transient Hot-Wire Method for
Measuring Thermal Conductivity, Physica, 82C, 392-408 (1976).
40. T. Boumaza and J. Redgrove, Use of the Transient Plane Source Technique for Rapid Multiple
Thermal Property Measurements, Int. J. Thermophysics, 24, 2, 501-512 (2003).
41. R. G. Miller and L. S. Fletcher, A Facility for the Measurement of Thermal Contact
Conductance, Proc. of the 10th Southeastern Seminar on Thermal Sciences, New Orleans, LA,
263-285 (1974).
42. H. Ziebland, Thermal Conductivity, Vol. 2, edited by R. P. Tye, Academic Press, London, 96 110 (1969).
103
43. R. W. Powell, Thermal Conductivity, Vol. 2, edited by R. P. Tye, Academic Press, London, 288
- 295 (1969).
44. H. Eicher, G. Salje, and H. Stahl, "Thermal diffusion measurements using spatially periodic
temperature distributions induced by laser light", J. Appl. Physics, 44, 5383 (1973).
45. C. W. Nan, R. Birringer, David R. Clarke, H. Gleiter, "Effective thermal conductivity of
particulate composites with interfacial thermal resistance", J. Appl. Phys. 81 (10), 15 May
(1997).
46. P. Keblinski, R. Prasher, J. Eapen, "Thermal conductance of nanofluids: is the controversy over
?"
,J. Nanoparticle Research, 10, 1089 (2008).
47. 0. M. Wilson, Hu X., Cahill D. G., Braun P. V., "Colloidal metal particles as probes of
nanoscale thermal transport in fluids", Phys. Rev. B, 66, 224301 (2002).
48. S. Huxtable, Cahill D. G., Shenogin S., Xue L., Ozisik R., Barone P., Usrey M., Strano M. S.,
Siddons G., Shim M., Keblinski P., , "Interfacial heat flow in carbon nanotube suspensions",
Nat. Mater., 2, 731 (2003).
49. E. V. Timofeeva, A. N. Gavrilov, J. M. McCloskey, Y. V. Tolmachev, S. Sprunt, L. M. Lopatina
and J. V. Selinger, "Thermal conductivity and particle agglomeration in alumina nanofluids:
Experiment and theory", Phys. Rev. E., 76, 061203 (2007).
50. R. G. Miller, Beyond ANOVA, Basics of Applied Statistics, CRC Press, pp. 69 - 111 (1997).
51. S. M. Ross, J. Engineering Technology, 20(2), pp. 3 8 - 4 1, Fall (2003).
52. G. W. Snedecore, Cochran, W. G., Statistical Methods, Iowa State University Press (1989).
53. H. Motulsky, Intuitive Biostatistics, Oxford University Press, pp 284-286 (1995).
54. Rea U., McKrell T., Hu LW, and Buongiorno J. 2008, "Laminar Convective Heat Transfer and
Viscous Pressure Loss of Alumina-Water and Zirconia-Water Nanofluids," Int. J. Heat Mass
Transfer.
104
55. Williams, W. C., Buongiorno, J., and Hu, L. W., 2008, "Experimental Investigation of
and
Turbulent Convective Heat Transfer and Pressure Loss of Alumina/Water
Zirconia/Water Nanoparticle Colloids (Nanofluids) in Horizontal Tubes," ASME J. Heat
Transfer, Vol 130
56. Li Qiang and Xuan Yimin, 2002, "Convective heat transfer and flow characteristics of Cu-water
nanofluid," Science in China (Series E), Vol 45 No.4
57. J.H. Lienhard IV, J.H. Lienhard V, A Heat Transfer Textbook, second ed.,Phlogiston
Press,
2002.
58. Kulkarni, Devdatta P., Namburu, Praveen K., Ed Bargar, H. and Das, DebendraK., 2008
"Convective Heat Transfer and Fluid Dynamic Characteristics of Si02 Ethylene Glycol/Water
Nanofluid",Heat Transfer Engineering,29:12,1027 -
1035
59. Sidi El Be'caye Mai-ga, Samy Joseph Palm, Cong Tam Nguyen, Gilles Roy, Nicolas Galanis,
(2005), "Heat transfer enhancement by using nanofluids in forced convection flows",
International Journal of Heat and Fluid Flow 26, 530-546
60. Ying Yang, Z. George Zhang, Eric A. Grulke, William B. Anderson, Gefei Wu, 2005, "Heat
transfer properties of nanoparticle-in-fluid
dispersions (nanofluids)
in laminar flow",
International Journal of Heat and Mass Transfer 48, 1107-1116
61. Khalil Khanafer, Kambiz Vafai, Marilyn Lightstone, "Buoyancy-driven
heat transfer
enhancement in a two-dimensional enclosure utilizing nanofluids", International Journal of Heat
and Mass Transfer 46 (2003) 3639-3653
62. Weerapun Daungthongsuk, Somchai Wongwises, 2007, "A critical review of convective heat
transfer of nanofluids", Renewable and Sustainable Energy Reviews 11 (2007) 797-817
63. Sidi El B'ecaye Maiga, Cong Tam Nguyen, Nicolas Galanis, Gilles Roy, 2004, "Heat transfer
behaviours of nanofluids in a uniformly heated tube", Superlattices and Microstructures 35
(2004) 543-557
105
64. Jake Kim, Yong Tae Kang, Chang Kyun Choi, 2004, "Analysis of convective instability and
heat transfer characteristics of nanofluids" Physics of fluids, Volume 16, Number 7
65. Weerapun Duangthongsuk, Somchai Wongwises, 2008, "Effect of thermophysical properties
models on the predicting of the convective heat transfer
coefficient
for
low
concentration nanofluid", International Communications in Heat and Mass Transfer 35 (2008)
1320-1326
66. Yurong He, Yi Jin, Haisheng Chen, Yulong Ding, Daqiang Cang, Huilin Lu, 2007, "Heat
transfer and flow behaviour of aqueous suspensions of TiO2 nanoparticles (nanofluids) flowing
upward through a vertical pipe",International Journal of Heat and Mass Transfer 50 (2007)
2272-2281
67. Weerapun
Duangthongsuk, Somchai
andpressure drop
Wongwises
, 2009, "Heat transfer
enhancement
characteristics of TiO2-water nanofluid in a double-tube counter flow
heat exchanger", International Journal of Heat and Mass Transfer, 52 (2009) 2059-2067
68. Gilles Roy, Samy Joseph Palm and Cong Tam Nguyen, 2005, "Heat Transfer and Fluid Flow of
Nanofluids in Laminar Radial Flow Cooling Systems", J. of Thermal Science Vol.14, No.4,
(2005),1003-2169
69. Jie Li, Clement Kleinstreuer, 2008, "Thermal performance of nanofluid flow in microchannels" ,
International Journal of Heat and Fluid Flow 29 (2008) 1221-1232
70. Shung-Wen Kang, Wei-Chiang Wei, 2005, "Experimental investigation of silver nanofluid on
heat pipe thermal performance", Proceedings of Tamkang University 2005 International Nano
and MEMS Workshop
71. Yulong Ding, Haisheng Chen, Yurong He, Alexei Lapkin, Mahboubeh Yeganeh, Lidija Siller
and Yuriy V. 2007, "Forced convective heat transfer of nanofluids", Advanced Powder
Technology, Vol. 18, No. 6, pp. 813-824 (2007)
106
72. Dongsheng Wen , Yulong Ding, 2005, " Formulation of nanofluids for natural convective heat
ttransfer applications ", International Journal of Heat and Fluid Flow 26 (2005) 855-864
73. Yimin Xuan , Wilfried Roetzel, 2000, "Conceptions for heat transfer correlation of nanofluids"
International Journal of Heat and Mass Transfer 43 (2000) 3701-3707
74. Yulong Ding *, Hajar Alias, Dongsheng Wen, Richard A. Williams, 2006, "Heat transfer of
aqueous suspensions of carbon nanotubes (CNT nanofluids)", International Journal of
Heat
and Mass Transfer 49 (2006) 240-250
75. Bock Choon Pak and Young I. Cho, "Hydrodynamic and heat transfer study of dispersed fluids
with submicron metallic oxide", Experimental Heat Transfer, 11:151-170, 1998
76. Tsung-Hsun Tsai, Reiyu Chein, 2007, "Performance analysis of nanofluid-cooled microchannel
heat sinks ", International Journal of Heat and Fluid Flow 28 (2007) 1013-1026
77. W.Y. Lai, B. Duculescu, P.E. Phelan & Ravi Prasher, 2006, "A Review of Convective Heat
Transfer with Nanofluids for Electronics Packaging 0-7803-9524-7/06 IEEE
78. J. Buongiorno, "Convective Transport in Nanofluids ", J. of Heat Transfer Vol. 128, 240-250
79. N Masoumi, N Sohrabi and A Behzadmehr, 2009, "A new model for calculating the effective
viscosity of nanofluids " J. Phys. D: Appl. Phys. 42 (2009) 055501 (6pp)
80. Xiaolei Fan, Haisheng Chen, Yulong Ding, Pawel K. Plucinski and Alexei A. Lapkin, "Potential
of 'nanofluids' to further intensify microreactors ", J. of Royal Society of Chemistry, Green
Chem., 2008, 10, 670-677
81. J.Lee , Roger D Flynn, Kenneth E Goodson, John K Eaton, 2007, "Convective heat transfer of a
nanofluid (DI + A12 0 3) in microchannel", 2007 ASME-JSME Thermal Engineering Summer
Heat Transfer Conference
82. Rashmi W, Ismail A F, Asrar W, Khalid M, and Faridah Y, 2008, Natural Convection Heat
Transfer in nanofluids-a numerical study, Proceedings of the 2008 ASME
Fluids
Engineering Conference
107
83. Dale A., Jamil A. Khan, Andrew M. Hayes and Aly Shaaban, 2008, "Evaluating The Thermal
Characteristics Of Copper-II and Zinc-Oxide Nanofluids Flowing over a Heated Flat Plate
Proceedings of 2008 ASME Summer Heat Transfer Conference
84. Pietro Marco Congedo, Stefano Collura and Paolo Maria Congedo, 2008, "Modeling and
analysis of natural convection heat transfer in nanofluids ", Proceedings of 2008 ASME Summer
Heat Transfer Conference
85. Ahmad Falahatpisheh and Omid Abouali, 2008, "Free Convection of nanofluid in vertical
annuli", Proceedings of the Sixth International ASME Conference on
Nanochannels,
Microchannels and Minichannels, ICNMM2008-62090, 23-25 June 2008
86. S Kabelac and K.B. Anoop, 2008, "Experimental convective heat transfer with nanofluids",
Proceedings of the Sixth International ASME Conference on Nanochannels, Microchannels and
Minichannels, , ICNMM2008-62099, 23-25 June 2008
87. Klaudia Chmiel-Kurowska, Grzegorz Dzido, Andrzej Gierczycki, Andrzej B. Jarzebski, 2008,
"Experimental Investigation of heat transfer to nanofluids ", Proceedings of the Sixth
International ASME
Conference
on Nanochannels,
Microchannels
and Minichannels,
ICNMM2008-62215, 23-25 June 2008
88. Byung-Hee Chun, Hyun Uk Kang, and Sung Hyun Kim, 2008, "Effect of alumina
nanoparticles in the fluid on heat transfer in double-pipe heat exchanger system ", Korean
J. Chem. Eng., 25(5), 966-971 (2008)
89. Hessamoddin
Abbassi,
and Cyrus Aghanajafi,
2006,
"Evaluation
of Heat Transfer
Augmentation in a Nanofluid-Cooled Microchannel Heat Sink ", Journal of Fusion Energy,
Vol. 25, No. 3/4, December 2006
90. Manoj Chopkar, A. K. Das, I. Manna, P. K. Das, 2008, "Pool boiling heat transfer characteristics
of ZrO2-water nanofluids from a flat surface in a pool", Heat Mass Transfer (2008) 44:9991004
108
91. A.K. Nayak, M.R. Gartia, P.K. Vijayan, 2008, "An experimental investigation of single-phase
natural circulation behavior in a rectangular loop with A120 3 nanofluids
Thermal
Experimental
and Fluid Science 33 (2008) 184-189
92. M.N. Pantzali, A.A. Mouza, S.V. Paras, 2009, "Investigating the efficacy of nanofluids as
coolants
in plate heat exchangers
(PHE)",
Chemical
Engineering
Science (2009),
doi:10.1016/j.ces.2009.04. 004
93. Heris S.Z., Esfahany M.N., Etemad S.Gh, 2007. Experimental investigation of convective heat
transfer of A12 0 3/water nanofluid in circular tube, International Journal of Heat and Fluid Flow
28 (2007) 203-210
94. Wen D., Ding Y., 2004. Experimental investigation into convective heat transfer of nanofluid at
the entrance region under laminar flow conditions. International Journal of Heat and Mass
Transfer 47 (24), 5181-5188
95. Anoop K.B., Sundararajan T., Das S.K., 2009. Effect of particle size on the convective heat
transfer in nanofluid in the developing region. International Journal of Heat and Mass Transfer
52 (2009) 2189-2195.
96. Ding Y., Alias H., Wen D., Williams R.A., 2006. Heat transfer of aqueous suspensions of carbon
nanotubes (CNT nanofluids), International Journal of Heat and Mass Transfer 49 (2006) 240250
97. Lai W.Y., Phelan P.E., Vinod S., Prasher R., 2008, Convective Heat Transfer for water-based
alumina nanofluids in a single 1.02-mm, IEEE 978-1-4244-1701-8/08.
98. Hwang K.S., Jang S.P., Choi S.U.S., 2009. Flow and convective heat transfer characteristics of
water-based A1203 nanofluids in fully developed laminar flow regime, International Journal of
Heat and Mass Transfer 52 (2009) 193-199
109
99. Kurowska K.C., Dzido G., Gierczycki A., Jarzebski A.B., 2008. Experimental Investigation of
Heat Transfer to Nanofluids, Proceedings of the Sixth International ASME Conference on
Nanochannels, Microchannels and Minichannels ICNMM2008
100. Xuan Y., Li
Q., 2003.
Investigation on convective heat transfer and flow features of nanofluids.
Journal of Heat Transfer 125, 151-155.
101. Duangthongsuk W., Wongwises S., 2009, Heat transfer enhancement and pressure drop
characteristics of TiO 2-water nanofluid in a double-tube counter flow heat exchanger,
International Journal of Heat and Mass Transfer 52 (2009) 2059-2067
102. Yu W., France D.M., Smith D.S., Singh D., Timofeeva E.V., Routbort J. L., 2009, Heat transfer
to a silicon carbide/water nanofluid, International Journal of Heat and Mass Transfer 52 (2009)
3606-3612
103. Pak, Bock Choon and Cho, Young I.(1998), 'Hydrodynamic and heat transfer study of dispersed
sub-micron metallic oxide particles', Experimental Heat Transfer, 11:2, 151 -
170
104. Buongiorno et al, 2009, A benchmark study on thermal conductivity of nanofluids, Journal of
Applied Physics 106, 094312 (2009)
105. C. W. Nan, R. Birringer, David R. Clarke, H. Gleiter, J. Appl. Phys. 81 (10), 15 May (1997).
106. A. Bejan, A.D. Kraus, Heat Transfer Handbook, John Wiley and Sons, 2003.
107. Shah R.K. (1975) Thermal entry length solutions for the circular tube and parallel plates,
Proceedings of the 3rd National Heat and Mass Transfer Conference, Indian Institute of
Technology, Bombay, I (Paper HMT-1 1-75).
108. J. A. Eastman, S.R. Phillpot, S.U.S. Choi, P. Keblinski, Thermal transport in nanofluids, Annu.
Rev. Mater. Res.,34, (2004), 219
109. Liwei Li, Dmitry Bedrov, and Grant D. Smith, "Water-Induced Interactions between Carbon
Nanoparticles", J. Phys. Chem. B, 2006, 110 (21), pp 10509-10513
110
110. Siao-Wei Yeh, Yao-Te Chang, Chia-Hung Chou, Kung-Hwa Wei, "Effect of SurfaceHydroxylated CdS Nanoparticles on the Morphological Transformation of Polystyrene-blockPoly(ethylene oxide) Thin Films", Correspondence to Kung-Hwa Wei, Department of Materials
Science and Engineering, National Chiao Tung University, Hsinchu, Taiwan 30049
111. S. R. Johnson, S. D. Evans,and R. Brydson, "Influence of a Terminal Functionality on the
Physical Properties of Surfactant-Stabilized Gold Nanoparticles", Langmuir, 1998, 14 (23), pp
6639-6647
111
Appendix A - Statistical treatment of INPBE data
For each fluid sample, the thermal conductivity raw data (x 1 , x 2 .... .,
xiN, ) from
the i-th organization were
processed to estimate the organizational mean (3, ) and standard deviation (s1), respectively, as:
X, =
T) ,-
xij and si=
(A.1)
ni j=1
The values of X,and s, for each organization are shown in Figures 6 through 18 as data points and error
bars, respectively. The normality of the xy datasets was checked using the Shapiro-Francia W' test
was found to be satisfactory. Peirce's criterion
7
6
and
was used to identify outliers which were not included in
the sample average and variance calculations described below, but are shown in Figures 6 - 18 as filled
data points.
The analysis of data among different organizations was carried out using the Random Effects Model 6 . In
the Random Effects Model, an assumption is made that the conclusions from the analysis can be applied
to a wider class of measurements of which the n, populations (or organizations, in this case) are a
representative subset. The model assumes that:
xY =
+a,+e
(A.2)
where p is the estimator of the sample mean, a is the systematic error for each organization (which are
treated as random errors among organizations), and ey is the random or unexplained error for each
measurement. It is helpful to note that
a, = x, eu = x Y - x,
(A.3)
It is assumed that a, and ey are normally distributed with zero means and standard deviations of o-, and q-,
respectively. The normality of the ey datasets was checked using the Shapiro-Francia W' test and was
found to be satisfactory. This analysis assumes that standard deviations within the organizations are equal
(ai = ae). This was checked by performing pair-wise F-tests on ai.
The standard Random Effects Model uses a weighted average as the sample average (taking into account
the number of data points reported by each organization).
p = z= N1
(A.4)
n,,
We believe that this definition overemphasizes the contributions from organizations that reported many
data points. For the purposes of this study, a more appropriate estimator of the sample mean is an
unweighted average of organization averages given in the following equation:
=
I
i
(A.5)
zE
This way, each organization contributes equally to the ensemble average. This estimator has been
analyzed in the literature" and its variance is given by
o-.2
1 I (
=Var()=
- 1(
I ,
0.2
1
|
e +0o-
,
)
(A.6)
where
2
1
'2
L (n.-)2
*(N - I) ,
.2 =
(A.7)
I
N = In
i=1
2 _
a
(MSA no
(A.8)
(A.9)
113
MSA= (n
l
(I~
1
no =
The standard error (-v')
- NA 2
9
=1(A.10)
n_____
N -'
I -1N
(A.11)
of the unweighted average is shown in Figures 6 - 18 as dotted lines plotted
above and below the sample average. The literature shows that the estimator (A.5) is preferred over the
estimator (A.4) if 0-a > a 2
56,58.
The statistical analysis shows that this condition is satisfied for the
INPBE data.
Thermal conductivity ratios were determined from the ratio of the nanofluid thermal conductivity to the
basefluid thermal conductivity and are given as yi. If an organizational mean for a given fluid sample was
identified as an outlier in the thermal conductivity analysis, it was not excluded here in determining
enhancements. A second round of applying the Peirce criterion excluded those enhancements that were
outliers.
The standard deviation (error bars) of the thermal conductivity enhancements (data points) for individual
organizations shown in Figures 19 through 26 were calculated by propagating the standard deviation of
the numerator and denominator 59 . That is, if y = x/xJbf, then:
__
enh
(Sfl(S)
((A.12)
The procedure for calculating the thermal conductivity enhancement sample average and its variance was
based on Eqs. (A.5) through (A. 11), where the thermal conductivity for each organization, X,, is replaced
114
by the thermal conductivity enhancement for each organization,
y , and n
is the harmonic average of the
total number of measurements used to calculate the enhancement.
To compare the different measurement techniques, the Fixed Effects Model was used5 6. For each
technique, the technique average and the variance were determined using Eqs. (A.5) through (A. 11)
above. For an unbalanced data set (one in which there are a different number of data points for each
measurement technique to be compared), the approximate Tukey-Kramer intervals were used, which
depend on the probability statement,
Pi E T- -
7, ± ga
+
2
where q
n,
for all i,i' = 1 - a,
(A.13)
e
is the upper c point of the "studentized" range distribution for k (the number of
measurement techniques compared) and v, the degrees of freedom (N - k). If the interval given in Eq.
(A. 12) does not contain zero for any combination of two measurement techniques, then the difference in
technique mean is statistically significant.
115
APPENDIX B- Error Analysis for Theoretical Heat Transfer Coefficient
The error analysis for the HTC was done using the standard propagation of error. Prediction of HTC using
theory requires the knowledge of following thermal hydraulic variables: thermal conductivity (k),
viscosity (p), density (p), specific heat (C,) , flowrate (v) and temperature (). Hence
h = f(k, p, y, Cp, v, T)
B. 1
Neglecting the temperature effect, the variance in the heat transfer coefficient predicted using the values
of these thermal hydraulic variables was calculated using the standard error propagation given by
equation B.2
o
(
2h
Oh
2
ak) 2 + (-U2 +
h
h
Oh
-2 + (B-Cc,)2 + (
B.2
where x represents the standard deviation in quantity X. The partial derivate w.r.t. variable X is
calculated by differentiating the correlation used for the prediction of HTC w.r.t. variable X. x was
obtained from the experimentally reported values or was estimated assuming standard uncertainties.
The standard deviation in HTC data is obtained from equation B.2 by taking the square root of the
variance. This is value which is plotted on the error bars of theoretical estimated HTC. The error bars in
the figures are 2 uh long spanning ch in both directions. Hence we are 66.66% sure that our estimation is
within these error bounds. Hence, a significant deviation beyond this bound even after accounting for
experimental measurement uncertainty can be safely termed as anomalous.
In case a thermo-physical property of nanofluid was estimated using theoretical models, the uncertainty in
the estimation of that property was estimated in the same way using standard propagation of errors
through the independent variables (which were properties of nanoparticles and basefluid).
116