Gandhi, K. S.

English

Publications of the IAS Fellows

RESEARCH NEWS 
 
CURRENT SCIENCE, VOL. 92, NO. 6, 25 MARCH 2007 717 
Thermal properties of nanofluids: Controversy in the making?
 
 
K. S. Gandhi 
 
Science of the very small has become big. 
It raises issues that are interesting and 
important to scientific understanding and 
seems to possess clues to the solution of 
knotty technological problems. The focus 
of the present news item concerns ther-
mal properties of suspensions of nano-
particles in fluids, commonly referred to 
as nanofluids. Investigations of their 
thermal properties have thrown up many 
findings that are interesting and challenging 
to explain. The importance of thermal 
properties is in the context of heat re-
moval from small spaces. It is a techno-
logical challenge arising from the need to 
cool high-speed microelectronic devices.  
 Conventional approaches and designs 
have reached their limit and cooling 
threatens to be the limit to both further 
miniaturization and increased speeds. 
One of the conventional approaches is to 
circulate cooling fluids in microchannels 
incorporated in a device. Here, the limi-
tation eventually arises from the ability 
of the fluid to conduct heat away from 
hot surfaces. Thermal conductivity re-
flects the ability of a medium to conduct 
heat. Typically, liquids are better con-
ductors than gases and vapours. For ex-
ample, while air has a conductivity of the 
order of 0.03 W/(m K), water has a con-
ductivity of the order of 0.6 W/(m K). 
Many solids, however, are even better 
conductors than liquids. Thus, even 
common red brick has a conductivity of 
60 W/(m K), while metals like silver and 
copper have a conductivity of 400 W/(m K). 
An exotic material like the carbon nano-
tube (CNT) has a conductivity of 
3000 W/(m K). One obvious solution to 
the cooling problem is to boost the con-
ductivity of a fluid by using a suspension 
of particles of a highly conducting solid 
in it. However, the size of the micro-
channels prevents the use of conven-
tional ‘fine’ particles, which are typically 
micron-sized, since they can clog the 
channels. Nanoparticles are the obvious 
substitute candidates and can make the 
solution feasible. Thus, studying the ther-
mal properties of nanofluids has grabbed 
the attention of scientists and engineers. 
 Three main experimental observations 
have been made during studies on ther-
mal properties of nanofluids, and have 
been summarized by Eastman et al.1. The 
salient features are as follows. 
 First and this is the most enigmatic 
feature, it was found that thermal conducti-
vity of a fluid was enhanced by large fac-
tors when nanoparticles were added up to 
only a small volume fraction. Thus, Lee 
et al.2 found that addition of 4% of Al2O3 
particles increased thermal conductivity 
by a factor of 8%, while according to East-
man et al.1, particles of CuO at the same 
volume fraction enhance the conductivity 
by about 12%. This is interesting since 
conductivity of CuO is less than that of 
Al2O3. Metal particles have been found 
to be much more effective. Patel et al.3 
found that even at as low a volume frac-
tion of about 0.0001, thiol-protected gold 
particles increased thermal conductivity 
by 10%. Other researchers have found 
greater enhancement with metal particles 
than with the lesser conducting oxide parti-
cles, though quantitatively less than that 
reported by Patel et al.3. Thus, ferrofluids 
containing 0.5% of iron particles were 
found4 to increase conductivity by 18%. 
 Secondly, Das et al.5 found that ther-
mal conductivity of nanofluids increased 
with increasing temperature. Clearly, this 
property is very advantageous in cooling 
applications. 
 Lastly, You et al.6 found that nanofluids 
exhibited three-fold increase in critical 
heat flux (CHF) over that of the liquid in 
which the particles were suspended. This 
parameter plays an important role in heat 
transfer where boiling is involved. 
 All these features indicate the potential 
of nanofluids in applications involving 
heat removal. Issues concerning stability 
of nanofluids, since they do aggregate 
with ageing, have to be addressed before 
they can be put to use. Ironically, nano-
fluids of oxide particles are more stable 
but less effective in enhancing thermal 
conductivity in comparison with nanofluids 
of metal particles and CNTs. Though we 
will confine ourselves here to a discus-
sion of enhancement of thermal conduc-
tivity, it is worthwhile to mention that 
enhancement of CHF may prove to be of 
wider utility. 
 Maxwell developed a theory for pre-
dicting the effective conductivity of 
composite dielectric media. It was adop-
ted by Hamilton and Crosser7 to predict 
the thermal conductivity keff of a dilute 
suspension of spherical particles in a 
medium, which could be fluid or a solid, 
and they gave the following equation: 
 
eff
p mm
p m
31 ,2
k
k kk
k k
φ
φ
= +
+
−
−
 (1) 
where kp and km are the thermal conduc-
tivity of the particles and the medium re-
spectively, and φ is the volume fraction 
of the particles. It is interesting to note 
that particle size does not appear here 
and eq. (1) has been verified for large 
particles. In the limit of particle thermal 
conductivity being much larger than that 
of the medium, and low volume frac-
tions, eq. (1) predicts that enhancement 
in thermal conductivity should be three 
times the volume fraction. Obviously, in 
this limit, the nature of the particles 
should also have no effect. Both these 
are not true in the case of nanofluids. 
Thus, as mentioned earlier, suspensions of 
CuO show lesser enhancement than those 
of metal particles, which are better con-
ductors and show greater enhancement 
than suspensions of nanoparticles of Al2O3, 
which also are good conductors. Kumar et 
al.8 refer to earlier measurements of their 
own as well as others, where enhance-
ment was found to decrease with increas-
ing size of the nanoparticles. What could 
be the possible explanations for all this? 
Effect of material and size 
Maxwell’s theory assumes that tempera-
ture is continuous across the interface be-
tween the medium or that the interface 
offers no resistance to heat transfer. 
However, such resistance can arise due 
to various factors such as scattering of 
phonons and layers of fluid molecules 
adsorbed on the particle surface. As in-
terfacial resistance can be material-
dependent, it is possible that this could be 
the reason for different materials show-
ing different enhancements. The interfacial 
resistance is represented by a coefficient 
Rb, and γ = Rbkm/R, where R is the parti-
cle size, is an estimate of the ratio of  
interfacial resistance to resistance to 
RESEARCH NEWS 
 
CURRENT SCIENCE, VOL. 92, NO. 6, 25 MARCH 2007 718 
conduction in the medium. Nan et al.9 
modified Maxwell’s theory to predict the 
effect of interfacial resistance on keff, and 
in the limit of km/kp << 1 and small vol-
ume fractions, they predict 
 
 
eff
m
11 3 .
1 2
k
k
γφ
γ
−
= +
+
 (2) 
 
It should be noted that existence of inter-
facial resistance can in effect reduce the 
estimated maximum enhancement of 
thermal conductivity. In fact, if γ > 1, the 
effective thermal conductivity is less 
than that of the medium. Thus, the pres-
ence of interfacial resistance is unable to 
provide an understanding of data. 
Effect of Brownian movement 
Measurements on effective thermal con-
ductivity of a polymer matrix embedded 
with alumina nanoparticles10 showed that 
they followed the mixture theory. Thus, 
enhancements were attributed to some 
kind of movement, and Brownian motion 
of nanoparticles was hypothesized to be 
the cause. It turns out that the heat carried by 
diffusion of the centre of mass is negligi-
ble. An alternative is the mixing caused by 
random Brownian movement. At present 
no theory exists to predict the effect of 
such convection, though there are some 
semi-empirical theories8,11,12 which seem 
partially successful. It may be mentioned 
that this effect is dependent on particle 
size, and the theories seem to predict the 
correct trend. However, molecular simu-
lations13 seem to indicate that Brownian 
motion does not have any effect. 
Effect of adsorbed layers and cluster 
formation 
If the layers of molecules of fluid adsor-
bed on the solid have different properties,
this could be a possible explanation. An-
other hypothesis depends upon formation 
of loose clusters of nanoparticles due to 
the attractive forces between them. The 
size of the structure is larger than the in-
dividual particles, and hence, the volume 
fraction of the clusters is larger than that 
of the collection of particles. The effective 
thermal conductivity based on the volume 
fraction of the clusters would be more 
than that predicted based on particle vol-
ume fraction. While this proposal has the 
correct trend, it implicitly assumes that 
conductivity of the trapped fluid mole-
cules is higher than that of the fluid. 
Eastman et al.1 discuss this in detail. 
However, in both the hypotheses it is not 
clear that there exists a basis for the as-
sumed properties. 
 It is apparent that no clear explanation 
of enhanced thermal conductivity has 
been offered so far. It is but natural under 
such circumstances that the experiments 
are repeated using a different technique. 
Conductivity of nanofluids has been 
measured mostly using hot-wire method, 
but a few measurements have been made 
using the standard parallel-plate method. 
Putnam et al.14 used a technique that is 
based on measurement of the extent of 
bending of a laser beam due to a gradient 
in refractive index caused by the tempera-
ture gradient, to measure thermal conduc-
tivity of nanofluids of thiol-protected 
gold particles. They report that the en-
hancements are in accordance with the 
theory of Maxwell! They have thrown 
down the gauntlet at fellow experimen-
talists and theoreticians by stating that 
‘investigations of the properties of nan-
ofluids have reached the awkward situa-
tion of having a greater number of 
competing theoretical models than sys-
tematic experimental results’. Thus it is 
clear that nanofluids will offer a lot more 
excitement, and perhaps controversy in 
the times to come. 
 
1. Eastman, J. A., Phillpot, S. R., Choi,  
S. U. S. and Leblinski, P., Annu. Rev.  
Mater. Res., 2004, 34, 219–246. 
2. Lee, S., Li, S. U. S. C. S. and Eastman,  
J. A., Trans. ASME: J. Heat Transfer, 
1999, 121, 280. 
3. Patel, H. E., Das, S. K., Soundararajan, 
T., Nair, A. S., George, B. and Pradeep, 
T., Appl. Phys. Lett., 2003, 83, 2931– 
2933. 
4. Hong, T-K., Yang, H-S. and Choi, C. J., 
J. Appl. Phys., 2005, 97, 064311. 
5. Das, S. K., Putra, N., Thiesen, P. and 
Roetzel, W., Trans ASME: J. Heat 
Transfer, 2003, 125, 567–574. 
6. You, S. M., Kim, J. H. and Kim, K. H., 
Appl. Phys. Lett., 2003, 83, 3374– 
3376. 
7. Hamilton, R. L. and Crosser, O. K., Ind. 
Eng. Chem.: Fundamentals, 1962, 1, 187–
191. 
8. Kumar, D. H., Patel, H. E., Kumar, V. R. 
R., Sundararajan, T., Pradeep, T. and 
Das, S. R., Phys. Rev. Lett., 2004, 93, 
144301. 
9. Nan, C-W., Birringer, R., Clarke, D. R. 
and Gleiter, H., J. Appl. Phys., 1997, 81, 
6692–6699. 
10. Putnam, S. A., Cahill, D. G., Ash, B. J. 
and Schadler, L. S., J. Appl. Phys., 2003, 
94, 6785–6788. 
11. Jang, S. P. and Choi, S. U. S., Appl. 
Phys. Lett., 2004, 84, 4316–4318. 
12. Patel, H. E., Soundararajan, T., Pradeep, 
T., Dasgupta, A., Dasgupta, N. and Das, 
S. K., Pramana – J. Phys., 2005, 65, 
863–869. 
13. Evans, W., Fish, J. and Keblinski, P., 
Appl. Phys. Lett., 2006, 88, 093116. 
14. Putnam, S. A., Cahill, D. G., Braun, P. 
V., Ge, Z. and Shimmin, R. G., J. Appl. 
Phys., 2006, 99, 084308. 
 
 
 
K. S. Gandhi, a CSIR Emeritus Scientist, 
is in the Department of Chemical Engi-
neering, Indian Institute of Science, 
Bangalore 560 012, India 
e-mail: gandhi@chemeng.iisc.ernet.in 
 
 
 
 


Thermal properties of nanofluids: controversy in the making?

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Thermal properties of nanofluids: controversy in the making?

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