26
CHAPTER 4
CHARACTERIZATION OF NANOPARTICLES AND Al2O3 /
WATER NANOFLUIDS
It is important to understand the behavior of nanoparticles and
nanofluids prepared from fundamental point of view in order to apply
nanofluids in practical situations. Therefore, the purchased Al2O3 dry
nanopowder and the prepared nanofluids have been characterized by using the
following methods. X- Ray Diffraction (XRD) to determine the particle
grain size, Scanning Electron Microscope (SEM) to determine the particle
shape, suspension uniformity, and Particle agglomeration, KD2 Pro thermal
property meter to measure the thermal conductivity of nanofluid, Brookfield
cone and plate viscometer to measure the
viscosity of nanofluid
and
pH(Hydrogen potential) meter to determine the pH value of nanofluids.
4.1
DETERMINATION OF NANOPARTICLE GRAIN SIZE
USING XRD
The simplest and most widely used method is (X Ray Diffraction)
XRD for estimating the average nanoparticle grain size. The Al2O3
nanopowder was characterized by (X Ray Diffraction) XRD with a Rigaku Xray Differatometer and Cu-ka1 radiation in the range of 20–80o. All the
reflections in the XRD pattern (Figure 4.1) can be indexed to the tetragonal
phase of Al2O3 using JCPDS (Joint Committee on Powder Diffraction
Standards). The X-ray diffraction test was carried out with a scan speed of
3o/minute. The average grain size is estimated by using Debye-Scherrer
27
formula (Equation 4.1). The full width at half maximum (FWHM) is taken
from the XRD pattern (Figure 4.1).
d
0.9
(FWHM)Cos
(4.1)
where ‘d’, ‘ , and ‘ ’ are the average particle grain size, wavelength of the
Cu-ka1 X rays (1.5418Ao) and Braggs angle respectively. The average grain
size is found to be between 45 to 50nm by using the Scherrer formula (the
error is within the limit of ±5 nm).
Figure 4.1 XRD pattern of Al2O3 nanoparticles
4.2
DETERMINATION OF PARTICLE SHAPE, SUSPENSION
UNIFORMITY OF NANOPARTICLES USING SEM
It is essential to study the particles shape and suspension uniformity
as spherical shape particles give higher thermal conductivity enhancement
than cylindrical particles Xie et al (2002). Wu et al (2009) suggested the
Scanning Electron Microscope (SEM) is the powerful tool to study the shape,
and suspension uniformity.
28
Figure 4.2 SEM image of dry Al2O3 nanoparticles
The purchased Al2O3 dry nanoparticles and prepared nanofluids
have been studied with SEM (Jeol JSM 6360 SEM). Figure 4.2 shows the
SEM image of dry nanoparticles. It is seen that the highly agglomerated
particles in the size ralge of micrometer under atmospheric condition and
most of the nanoparticles are spherical in shape. Apart from studying dry
nanoparticles, the suspended nanoparticles in basefluid have been studied
with SEM. The sample nanofluid under consideration has been prepared to
place in SEM sample holder. The SEM image of suspended particles in base
fluid was obtained by sonicating, placing the sample on sample holder, by
rapid drying for getting solid particles and making them conductive as
suggested by Ghadimi et al (2011). Accordingly, the nanofluid sample is
solidified into a gel (gelified). The nanofluid is sonicated, heated to 40oC and
mixed with gelatin- deionised H2O solution to create the jellified nanofluid. A
thin layer of the mixture is poured into a clean dish and placed in a
refrigerator for 20 minutes to allow the mixture to become gel and then it is
transferred into a vacuum chamber to solidify for 5 hours to remove any
excess liquid from the nanofluid film and prevent out gassing in the SEM. A
1 cm square section is cut from the film and attached to a pin stub specimen
holder.
The sample is sputtered with a thin layer of gold to create a
29
conducting surface. Then the image of suspended and aggregated
nanoparticles was obtained.
Figure 4.3 SEM image of dispersed Al2O3 nanoparticles in water
It is clear from the SEM image (Figure 4.3) that the dispersed
nanoparticles appear to be uniformly dispersed in base fluid and most of the
nanoparticles nearly spherical in shape. It is found that there is no
considerable agglomeration. Lee et al (2009)
revealed that the more
agglomeration reduces electric repulsive force which makes particles
unstable. Karthikeyan et al (2008) found in their experiments with Copper
oxide/water nanofluid that the agglomeration is time-dependent. They have
proposed that the agglomeration increases when time is elapsed and more
agglomeration decreases the thermal conductivity of nanofluid. Therefore,
less agglomeration leaves the nanofluid stable.
4.3
MEASUREMENT
OF
NANOFLUID
THERMAL
CONDUCTIVITY
Nanofluids attracted a vast attention due to increment in thermal
conductivity compared to basefluid. Measuring thermal conductivity
is a
challenge for a long time since different methods and techniques presented
30
different results. On comparing the effect of nanofluid density and specific
heat capacity, thermal conductivity and viscosity on heat transfer play key
role in enhancing heat transfer. Therefore, it is important to understand the
theoretical studies and experimental studies carried out on nanofluid thermal
conductivity and viscosity.
4.3.1
Theoretical Studies on Nanofluid Thermal Conductivity
More than a century ago, Maxwell (1873) derived an equation for
calculating the effective thermal conductivity of solid-liquid mixtures
consisting of spherical particles. Further, the thermal conductivity models
have been developed based on
the idea of Maxwell (1873). These models
are named as Classical models. Many researchers have modified the classical
models
by
incorporating
the
mechanism
for
thermal
conductivity
enhancement such as Brownian motion, clustering, and shape and size of
nanoparticles. These models are named as models derived from classical
models. Therefore, the nanofluid thermal conductivity models are classified
into two main types: Classical models and Models derived from classical
models. The gist of classical thermal conductivity models have been
discussed here.
The models developed to predict the thermal conductivity of a
continuum medium with well-dispersed solid-liquid mixtures by Maxwell
(1873), Hamilton-Crosser (HC) (1962), Bruggeman (Hui et al 1999) and
Wasp (Xuan and Li (2000) are the Classical models. Classical models have
been developed by assuming the nanoparticles do not have bulk movement in
base fluids and the solid particles in the base fluids are composite. The
classical models considered the conduction is the mode for enhanced thermal
conductivity. Therefore, classical models are named as static models or
structural models. Table 4.1 lists out the classical models developed for
determining the nanofluid thermal conductivity.
31
Table 4.1 List of Classical models for nanofluid thermal conductivity
Researchers
Thermal conductivity models
Maxwell
k eff
kf
(1873)
kp
2k f
kp
2k f
2 (k p
kf )
(k p
kf )
Factors considered
Based
on
effective
medium theory[EMT],
randomly dispersed, and
uniform sized spherical
particles.
Hamilton –
Crosser (HC k eff
kf
model)
Applicable for spherical
k p ( n 1) k f (n 1) (k f k p ) and cylindrical particles.
k p ( n 1)k f
(k f k p )
Developed by
using
(1962)
shape factor, n.
Bruggeman
model (Hui
For a binary mixture of
homogeneous spherical
and randomly dispersed
nanoparticles. Particles
interaction
taken into
account. No limitations
et al 1999).
k eff
kf
1
(3
4
2
[3
1]
kp
1)
kp
kf
(2
3 )
2
(2 3 ) 2 2(2 9
kf
kf
4
kp
9 2)
kf
for
particle
volume
concentration.
Wasp model
(Xuan and
Li 2000).
k eff
kf
kp
kp
2kf
2 (k f k p )
2k f
(kf k p )
Considered shape factor
as unity. Not valid for
spherical particles.
where,’keff’ - indicates effective thermal conductivity, ‘p’ indicates solid
particle, and ‘f’ indicates water (base fluid) and ‘ ’ indicates particle volume
concentration.
Based on the literature survey, the classical models were found to
be unable to predict the nanofluid thermal conductivity. This is because the
classical models did not include the effect of temperature, effects of particle
32
size,
interfacial
layer
between
particle/fluids,
particle
distribution,
nanoparticles cluster, aggregate and Brownian motion of particles.
Consecutively, the thermal conductivity models have been developed by
considering the factors which were not considered by Classical models. Few
of the thermal conductivity models developed by the researchers have been
given in the forthcoming section. Table 4.2 lists out few of the widely used
models proposed by modifying the classical models for determining the
nanofluid thermal conductivity.
Table 4.2 List of nanofluid thermal conductivity models derived from
Classical models
Researchers
Pak and Cho
(1998)
Yu and Choi
(2003)
Thermal conductivity models
k eff
kf
k eff
1 7.47
k pe
kf
2k f
k pe
Xuan and Li
(2003)
k eff
kp
2k f
kf
kp
2k f
Bhattacharya
et al (2004)
k eff
Jang and Choi
(2004)
k eff
kf
Factors considered
2k f
k p (1
1 C
df
dp
2 (k pe
(k p
2 (k p k f )
(k p k f )
)k f
k f Re 2 d p Pr
k f )(1
k f )(1
cp
2k f
)
K BT
3 rc
Under the assumption
that the dispersion of
suspended
nanoparticles cause the
enhancement of
thermal conductivity.
Inclusion of interfacial
) 3 layer and modified
Maxwell model
3
Developed by the
random motion of
nanoparticles,
interfacial interactions.
Inclusion of combined
base fluids and
nanoparticle thermal
conductivities.
Considered the
convection and
conduction heat
transport and dynamic
motion of
nanoparticles.
33
Table 4.2( Continued)
Researchers
Shukla and
Dhir (2005)
Li and
Peterson
(2006)
Avsec and
Oblak (2007)
Timofeeva et
al (2007)
Chandrasekar
et al (2009a)
Chandrasekar
et al (2010)
Abbaspoursan
i et al (2011)
Shames et al
(2012)
Factors considered
keff
k p 2k f 2 ( k p k f )
C (T ToBased on macroscopic
model, Brownian
kf
k p 2k f
(k p k f )
ka 4
motion and set the
lower limit for brown
motion.
k eff
Temperature dependent
1 0.764481 0.01868867T 0.46214175
model and valid for
kf
27oC -36oC and valid
k eff
1 3.76108
0.017924T 0.30734
for Al2 O3/water,
kf
CuO/water and
nanofluids
k eff
k p (n 1) k f ( n 1) e ( k f k p )
Consideration of liquid
kf
k p ( n 1)k f
(
k
k
)
layer thickness.
e f
p
Based on effective
k eff
1 3
medium theory for
kf
Al2O3 nanofluids with
the effect of
agglomeration.
3
Developed by
keff
k p (n 1)k f ( n 1)(1
) (k p k f )
3
macroscopic model of
kf
k p (n 1) k f (1
) (k p k f )
HC and inclusion of
C (T To)
Brownian motion with
ka4
respect to temperature.
0.023
0.126
1.358
Based on the prediction
keff
c p , nf
M
nf
of thermal conductivity
kf
cp
M nf
of water and the
molecular weight of
nanoparticle and base
fluids.
Accounts for the
k eff
T
1 m
R ' R '' ....
interfacial shell,
kf
Te
(d p )
Brownian motion, and
aggregation of
particles.
By assuming the
k eff
k staic k dynamic
nanoparticles are st
kf
different sizes.
Considered the effect
of nanolayer.
Thermal conductivity models
where, a- particles size, b-base fluid, C-constant, cp -specific heat, effeffective, f-base fluid, KB -Boltzmann constant, k-thermal conductivity, M-
34
Molecular weight, n-shape factor, nf- nanofluid, p-Particle, R' and R'' are the
parameters which depends on the nanofluid properties, T -temperature, Toinitial temperate,
-density, Re-Reynolds number, Pr Prandtl number,
particle volume concentration, , - intrinsic and dynamic viscosity,
-
-ratio
of nanolayer thickness to the original particle radius=h/r, -ratio of nanolayer
thermal conductivity to particle thermal conductivity ‘k’, m- factor that
depends on the properties of the solid particle, base fluid and interfacial shell,
-and
4.3.2
-empirical constants determined from experimental data.
Experimental Studies on Nanofluid Thermal Conductivity
Many experimental work have been carried out to measure the
thermal conductivity. This is because the predicted thermal conductivity
results are not consistent at a particular nanofluid. Most of the investigators
used Transient Hot Wire (THW) technique to measure the thermal
conductivity of nanofluids. Table 4.3 lists out few of the widely referred
experimental results of nanofluid thermal conductivity.
Table 4.3 List of experimental studies on nanofluid thermal conductivity
Maximum
Particle
thermal
Nanoparticles/Base
Volume
Investigators
conductivity Consideration
fluids
Concentration
enhancement
(%)
(%)
Al2O3 / Water
1.30–4.30
32.4
Masuda et al
31.85ºC –
(1993)
86.85ºC
TiO2/Water
3.10–4.30
10.8
Al2O3/Water/Ethylene
3.00–5.50 /
Glycol (EG)
16 / 41
5.00–8.00
Wang et al
Room
(1999)
temperature
4.50–9.70 /
CuO/Water/ EG
34 / 54
6.20–14.80
35
Table 4.3(continued)
Maximum
Particle
thermal
Nanoparticles/Base
Volume
Investigators
conductivity Consideration
fluids
Concentration
enhancement
(%)
(%)
Al2O3/Water/ EG
1.00–4.30 /
10 / 18
1.00–5.00
Lee et al
Room
1.00–3.41 /
(1999)
CuO/Water
12 / 23
temperature
1.00–4.00
TiO2/Water
0.50–5.00
33
Eastman et al
Room
Cu/ EG
0.01–0.56
41
(2001)
temperature
Al2O3/Water/ EG
5.00
23 / 29
Xie et al
(2002)
Das et al
(2003)
Li and
Peterson
(2006)
Hong et al
(2006)
Chopkar et al
(2006)
Beck et al
(2009)
Mintsa et al
(2009)
Al2O3/ Pongamia oil
/Glycerol
Room
temperature
5.00
38 / 27
CuO/Water
Al2O3/Water
1.00–4.00
36
1.00–4.00
38.4
CuO/Water
Al2O3/Water
1.00–4.00
28.6
2.00–10.00
29
27.5ºC – 34.7ºC
CuO/Water
2.00–6.00
51
Fe/ EG
0.10–0.55
18
Al2Cu/Water/ EG
1.00–2.00
96/76
SiC/Water/ EG
1.00–4.00
24 / 23
28.9ºC – 33.4ºC
Effect of
clustering
Effect of
particle shape
and size
Al2O3/Water
1.86–4.00
20
2.00–3.01
19
0–18
31/31
Al2O3/ EG
Al2O3/Water
24 ºC36 ºC
Effect of
particle size
20ºC – 48ºC
CuO/Water
0–16
24
Turgut et al
(2009)
TiO2/Water
0.2–3.0
7.4
13ºC – 55ºC
Chandrasekar
et al (2010)
Al2O3/Water
0.33-5
24
Effect of
particle volume
fraction
Longo
and
Zilio (2011)
Al2O3/Water
1–4%
2-16
1 to 40oC
36
However, the authors have noted that there is significant
discrepancy in the thermal conductivity data when measurements are
conducted at higher temperatures. The authors explained that this discrepancy
is due to natural convection effect in the transient hot-wires method. Ju et al
(2008) showed that the transient hot-wire method can give erroneous results
if the measurements are carried out just after the sonication. This is because
the sonication increases temperature of the nanofluid sample. Li et al (2008)
found nearly the same thermal conductivity values in their measurements,
there might still be some erroneous results in the literature due to the above
mentioned factors Ju et al (2008).Another important reason for discrepancy in
experimental data is the clustering of nanoparticles Hong et al (2006).The
level of clustering depends on many parameters. It was shown that adding
some surfactants and adjusting the pH value of the nanofluid provide better
dispersion, stability and prevent clustering to some extent Wang et al (2009).
Therefore, when performing experiments, researchers should also consider the
type and amount of additives used in the samples and pH value of the
samples.
Many researchers have revealed the factors which increase or
decrease the thermal conductivity of nanofluids. Some of the investigations
and suggested factors have been given in this section. The major factors
which affect the nanofluid thermal conductivity are a) Particle volume
concentration, b) Particle materials, c) Brownian Motion, d) Nanoparticle
size, e) Particle shape/surface area, f) Temperature, g) Basefluid materials,
and
h ) pH value. The summary of important conclusions on nanofluid
thermal conductivity proposed by the researchers are: a) the thermal
conductivity increases with increasing particle volume concentration, b) the
thermal conductivity enhancement of metal nanoparticles is higher than the
oxide nanoparticles, c) higher the Brownian motion
the higher thermal
conductivity enhancement, d) smaller nanoparticles are better for stability and
37
enhancement of thermal conductivity, e) the rod-shaped particles thermal
conductivity is higher than the spherical nanoparticles, f) the thermal
conductivity increases with increasing temperature g) the nanofluid with
water and ethylene glycol mixture have good potential applications in cooling
applications, and h) pH value affects the thermal conductivity.
The thermal conductivity of nanofluids can be measured with
different techniques, such as the transient hot-wire method, temperature
oscillation technique, steady-state parallel plate method, optical beamdeflection technique, and thermal lensing method. Among them, the transient
hot-wire method is widely used by many researchers Wu et al (2009). Paul et
al (2010)
proposed the Transient Hot-Wire (THW) method is the most
popular method for measuring thermal conductivity of nanofluid used by
scientists and researchers and it gives lower experimental error. This is
because of simplicity, and eliminating convective contribution to the heat
transfer from the measurements.
In this investigation, Transient hot-wire method is used to measure
the nanofluid thermal conductivity. The thermal conductivity of nanofluid
was measured by using a KD2 Pro thermal property meter, Figure 4.4
(Decagon Device, Inc., USA), which is based on Transient hot-wire technique
with the ±5% accuracy of measurements. Fourier’s law for conduction heat
transfer can be utilized to measure thermal conductivity of a material.
Temperature difference can cause heat transfer through materials which is
known as conduction heat transfer. This method is based on applying a
constant current to a platinum wire and measuring the time evolution of its
electrical resistance due to temperature increase. It consists of a handheld
microcontroller and sensor needles. The KD2’s sensor needle contains both a
heating element and a thermistor.
38
The
controller
module
contains
a
battery,
a
16-bit
microcontroller/AD converter, and power control circuitry (Figure 4.5). The
thermal conductivity measurement assumes several things like: (i) The
heating source is infinitely long (ii) The medium is both homogeneous and
isotropic, and at uniform initial temperature To. Although these assumptions
are not true in the strict sense, they are adequate for accurate thermal
properties measurements. The sensor needle used was KS-1 which is made of
stainless steel having a length of 60 mm and a diameter of 1.3 mm, and
closely approximates the infinite line heat source which gives least
disturbance to the sample during measurements. The sensor needle can be
used for measuring thermal conductivity of fluids in the range of 0.2–2
W/mK.
The Al2O3/water nanofluids up to 3% volume concentrations have
been used for thermal conductivity measurement. The 45ml sample was taken
just after the preparation of nanofluid. This is because the minimum amount
of nanofluid required for thermal conductivity measurement is 45 ml. At the
beginning of a measurement, a period of time, 30 s, was needed for the
system to become steady at 20°C. Then, a heating power ‘q’ was applied
abruptly and briefly for 30 s through a needle. Finally, the solution
temperature was cooled naturally. During the cooling period, the fluid
temperature T1 at time t1 and temperature T2 at time t2 were recorded. Then,
the thermal conductivity is calculated using Equation 4.2. For each run, the
total experimental time, including the steady period, the heating period, and
the cooling period, was about 90 s, and there was more than 5 min between
measurements to avoid the effects of natural convection of the fluid caused by
heating in the previous measurement.
At the end of the reading, the controller computes the thermal
conductivity using the change in temperature ( T) – time data .The thermal
39
conductivity of nanofluid was calculated according to the following
Equation (4.2).
k
q
4 ( T2
T1 )
In
t2
t1
(4.2)
where ‘k’ is thermal conductivity of nanofluid, ‘q’ is constant heat rate
applied to an infinitely long and small ‘line’ source,
T1 and
T2 are the
changes in the temperature at times ‘t1’ and ‘t2’ respectively. At least five
measurements were taken for each concentration and their average values
were reported.
Figure 4.4 Photograph of KD2 Pro thermal properties analyzer
40
Figure 4.5 Schematic sketch of KD2 Pro thermal properties analyzer
The ASTM D5334 (2000) and IEEE 442-1981 standards suggest
collecting temperature (T)–time (t) data over a 1000 s heat time, plotting the
data on semi log graph paper, selecting a segment of the data by eye that
appears to fit a straight line, selecting two points on that line and computing
‘k’ from Equation 4.2. The same method and procedure was followed for
measuring the thermal conductivity of
nanofluid at different temperatures.
The calibration of the sensor needle was carried out first by measuring
thermal conductivity of distilled water, glycerin and ethylene glycol. The
measured values for distilled water, glycerin and ethylene glycol were 0.611,
0.292 and 0.263 W/mK respectively, which are in agreement with the
literature values of 0.613, 0.285 and 0.252 W/mK respectively within ± 5%
accuracy.
The measured thermal conductivity values have been given in
Appendix 4.1 and 4.2 and the same have been plotted in Figure 4.6 and 4.7
41
0.636
Experimental data
Chandrasekar et al (2010)
0.634
0.632
0.630
0.628
0.626
0.624
0.622
0.620
0.618
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Particle volume concentration (%)
Figure 4.6
Variation of thermal conductivity of
Al2O3 / water
nanofluid with particle volume concentration
0.675
0.670
0.1% Nanofluid
0.4% Nanofluid
0.8% Nanofluid
0.665
0.660
0.655
0.650
0.645
0.640
0.635
0.630
0.625
0.620
0.615
34
36
38
40
42
44
46
48
50
52
o
Nanofluid temperature, C
Figure 4.7 Effect of temperature on nanofluid thermal conductivity
42
It is studied from Figure 4.6 that the thermal conductivity of
nanofluid is higher than water. The thermal conductivity of 0.1%, 0.4% and
0.8% nanofluid is 1.2%,2% and 3.2% respectively higher than water at 35oC.
It is also found that the thermal conductivity of nanofluid increases with
increasing particle volume concentration. This is because of more particles
loading has higher particle surface to volume ratio. The mechanism for this
enhancement may be because of particle to particle interactions, nanoparticle
cluster and Brownian motion. The deviation between the experimental data
and predicted value are in the range of 0.2% - 0.4%. This is because the
nanofluid sample was taken for measurement just after preparation using
sonication. The sonication may increase the temperature of the sample Ju et al
(2008).
Therefore, it is expected that the measured thermal conductivity
values may deviate from the predicted values.
Form Figure 4.7, it is observed that the thermal conductivity
increases with increasing temperature. The measured thermal conductivity of
0.1%,0.4% and 0,8% nanofluid at 50oC is 5.5%, 6% and 6.5% respectively
higher than the nanofluid at 35oC.This is because at elevated temperature the
viscosity decreases which leads to intensify the
enhance the
Brownian motion and
nanoconvection effect. These results agree well with the
measured thermal conductivity data suggested by Masuda (1993), Choi et al
(2001), Xie et al (2002), Das et al (2003), and Chandrasekar et al (2010) for
Al2O3 water nanofluid at low particle volume concentration. The thermal
conductivity enhancement is a better indicator for the assessment of
enhancement of heat transfer coefficient when nanofluid is used in the design
of heat exchange equipment Kakaç et al (2009).
Therefore, it is expected that thermal conductivity enhancement
may increase the convective
exchanger.
heat transfer in a helically coiled tube heat
43
4.4
MEASUREMENT OF NANOFLUID VISCOSITY
Nanofluid viscosity is an important parameter like thermal
conductivity for practical applications since it directly affects the pressure
drop and pumping power in forced convection. Thus from application point of
view, ideal nanofluid should not only posses high thermal conductivity but
also should have low viscosity. It is suggested that the nanofluid viscosity
depends on many parameters such as; particle volume concentration, particle
size, temperature, and extent of clustering. Increasing particle volume fraction
increases viscosity and this was validated by many studies like Wang et
al(1999), Murshed et al (2008), Chen et al (2009) and Chandrasekar et al
(2010). They have revealed the nanofluid viscosity is a function of particle
volume concentration and increases with increasing particle volume
concentration. They have also reported that the heat transfer increase may be
when particle volume concentration is more and increases the pressure drop.
4.4.1
Theoretical Studies on Nanofluid Viscosity
The nanofluid viscosity analytical models are classified into two
main types : Classical models, Models derived from Classical models.
Einstein (1906), Krieger,(1959), Niesen (1970) and Bachelor (1977) are the
first who developed the nanofluid viscosity model. These models are based on
the assumption of dilute, suspended, spherical particles and no interaction
between the nanoparticles. These are valid only for relatively low particle
volume concentration. This is the motivation for developing nanofluid
viscosity model for higher particles volume concentration. Table 4.4 lists out
the classical viscosity models proposed by different researchers.
44
Table 4.4 List of Classical models for nanofluid viscosity
Researchers
Nanofluid viscosity models
Factors considered
Valid
Einstein
nf
(1906)
1 2.5
for
spherical
particles of low particle
f
volume fraction
Based
Krieger and
Dougherty
[K-D]model
on
0.02.
randomly
mono-dispersed spheres.
m
nf
f
1
p
Valid
m
for
maximum
close packed particles of
(1959)
0.64.
Power law model and
Nielson
p
nf
(1970 )
(1 1.5
p
)e
(1
m)
more
appropriate
for
particle volume fraction
f
more than 0.02.
Bachelor
(1977)
nf
1 2.5
6.5
2
f
Considered the effect of
Brownian motion
Many nanofluid viscosity models have been developed by
modifying the classical models by different investigators. Few of the widely
used models have been given in Table 4.5.
45
Table 4.5 List of nanofluid viscosity models derived from classical models
Researchers
Brinkman
(1952)
Kitano et al
(1981)
Effective viscosity models
2
nf
Wang et al
1999)
eff
Drew and
Passman
(1999)
eff
Tseng and
Li(2003)
nf
Maiga et al.
(2004)
nf
Namburu
et al (2008)
Chandraseka
r et al.
(2010)
Karimi et al
(2011)
Shanker
et al (2012)
1
f
nf
Nguyen
(2007)
)2.5
(1
f
Pak and Cho
(1998 )
Kulkarni et
al. (2006)
1
eff
m
533.9 2 )
(1 39.11
f
1 7.3
123
2
f
1 2.5
f
Developed for
TiO2/water nanofluids
13.47e 35.98
f
123
2
7.3
Factors considered
Formulated by two
corrections of Einstein’s
model.
Based on maximum
concentration of two
phase mixture.
Developed by taking the
room temperature as
reference.
Particle volume fraction
is the key factor for
improved viscosity.
Formulated for dilute
suspension of small
spherical particles of two
phase mixtures.
Derived for Al2O3 /water
nanofluids.
1
f
107.12 2 )
Temperature dependent
model and valid for 5 oC2
(1078.3 15857 20587 )(1 / T )
50oC.
Temperature dependent
nf
(2.1275 0.0215T 0.00027T 2 )
nanofluids viscosity
f
model and valid for 1%4%.
Temperature dependent
Log nf Ae BT
model. Valid for 1-10%
of Al2O3 nanofluids and
-35oC to 50oC.
n
Contribution of
nf
electromagnetic aspects
1 b
1
and mechanical –
f
geometrical aspects
taken into account.
Considered the fluid
Formulated
by
using
GA-NN
temperature ,size,
(Genetic Algorithm-Neural Network.
particle volume
concentration, and base
fluid
2
Correlation developed
Log nf (1.75 16.85 23.5 2 )
by taking particle size,
dp
concentration,
temperature. Valid for
exp 0.015 0.15 31.39 2 5.65
..
dp
0.0< <0.01 only
In(
nf
)
(2.8751 53.548
46
where
-volume fraction, dp – particle diameter,
temperature, h-inter particle spacing,
- dynamic viscosity, T –
p-particle, f, b, -base fluid, eff-
effective, nf- nanofluids, A,C, a, b, c, n –constants.
Based on the literature review, it is understood that the nanofluid
viscosity increases when particle volume fraction is increased and nanofluid
viscosity decreases when temperature is increased. The mechanisms proposed
are subject to the conditions such as lower/higher particle volume fraction,
lower/higher temperature, spherical/non spherical shape, below/above critical
size, pH value, and type of base fluids etc. Moreover, the exact mechanism
cannot be conceived until the optimum level of particle volume concentration,
optimum size for achieving the stability and low agglomeration of
nanoparticles. Because higher the particle loading results the more
agglomeration and higher the particle size results erosion and easy settling.
Therefore, exact nanofluid analytical viscosity model is to be
derived based on the desirable conditions like less agglomeration, low
viscosity, without eroding tube wall surfaces, and without lowering thermal
conductivity.
4.4.2
Experimental Studies on Nanofluid Viscosity
The research groups Pak and Cho (1998), Das et al (2003), Heries
et al (2006) , Kulkarni et al (2006), Liu et al (2006), and Chandrasekar et al
(2010) experimentally measured the viscosity of different nanofluids. They
have suggested the experimental viscosity data is higher than the predicted
viscosity. Nevertheless, the general trend is that the viscosity increases with
increasing particle volume concentration. Nguyen et al (2007) hobserved
increasing viscosity with increasing particle size. Nguyen et al (2007), and
Longo and Zilio (2011). Analyzed the effect of temperature on viscosity and
observed a decrease in viscosity with increasing temperature.
47
The researchers have presented that the measured viscosity values slightly
deviates from the calculated values.
However, at present, it is difficult to
obtain a consistent set of experimental data for nanofluids that covers a wide
range of particle size and particle volume concentration.
In this investigation, the viscosity of nanofluid was measured by
using Brookfield cone and plate viscometer (LVDV-I PRIME C/P) equipped
with a 2.4 cm 0.8ocone (Figure 4.8.and 4.9) supplied by Brookfield
engineering laboratories of USA. The cone is connected to the spindle drive
while the plate is mounted in the sample cup. Spindle used was CPE-40 which
can be used for samples in the viscosity range of 0.3 – 1028 cP. Using
electronic gap adjusting feature provided with the viscometer, a gap of 0.013
mm between the cone and the plate is maintained within which the test fluid is
placed. The 2ml sample was used for viscosity measurement.
As the spindle is rotated, the viscous drag of the fluid against the
spindle is measured by the deflection of the calibrated spring. Cone and plate
geometry requires a sample volume of only 0.5–2 ml and hence the
temperature equilibrium is achieved rapidly within a minute. The spindle type
and speed combination will produce satisfactory results when the applied
torque is between 10% and 100% of the maximum permissible torque. Hence
during measurements, the readings were discarded if the applied torque does
not fall within this prescribed range. The spindle speeds available with this
viscometer falls in the range of 0–100 rpm and the shear rate range is 0–750
1/s. The viscometer was benchmarked with distilled water, glycerin and
ethylene glycol at room temperature. The measured values of viscosity for
distilled water, glycerin and ethylene glycol were 0.82, 10.9 and 360.5 cP,
respectively, which agree well with the literature values of 0.79, 10.7 and 352
cP, respectively, with ±5% accuracy. The measured viscosity values have
48
been given in Appendix A4.3 and A4.4 .The results have been given in the
form of graphs Figures 4.10 and 4.11.
Figure 4.8 Photograph of
Brook field viscosity analyzer
Figure 4.9 Cone and plate assembly of Brook field viscometer
49
0.850
Experimental data
Chandrasekar et al (2010)
0.845
0.840
0.835
0.830
0.825
0.820
0.815
0.10%
0.40%
0.80%
Particle volume concentration, %
Figure 4.10 Variation of viscosity with particle volume concentration.
0.90
0.85
0.1% Nanofluid
0.4% Nanofluid
0.8% Nanofluid
0.80
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.35
0.30
30
40
50
60
70
80
o
Nanofluid temperature, C
Figure 4.11 Effect of temperature on nanofluid viscosity
50
It is studied from Figure 4.10 that the viscosity of nanofluid is
higher than water. It is also found that the viscosity of nanofluid increases
with increasing particle volume concentration. The measured viscosity of
0.1%,0.4% and 0,8% nanofluid at 35oC are 3%, 3.7% and 6% respectively
higher than water at the same temperature. The maximum viscosity increase is
6% at 0.8% nanofluid. The deviation between the experimental data and
predicted value are in the range of 1%-2%. This may be because of slight
increase of temperature while preparing nanofluid by using
ultrasonication
Ju et al (2008).
From Figure 4.11, it is observed that the nanofluid viscosity
decreases with increasing temperature. The 0.1% nanofluid at 50oC is 30%
lower than 0.1% nanofluid at 35oC. The 0.4% nanofluid at 50oC is 35% lower
than 0.4% nanofluid at 35oC. The 0.8% nanofluid at 50oC is 38% lower
than0.8% nanofluid at 35oC.This is because at elevated temperature the shear
stress decreases which leads to intense the particle to particle interaction and
Brownian motion. The present viscosity results hold good agreement with the
experimental data presented by Choi (1999), Wang et al(1999) Murshed et al
(2008), Kulkarni et al (2002), Das et al(2003),Maiga et al (2004), Chen et al
(2009), Nguyen et al (2007), and Chandrasekar et al (2010). Therefore, it is
expected that the higher the particle concentration may increase the pressure
drop and pumping power.
4.5
INSPECTION OF NANOFLUID STABILITY
Stability of the nanofluid suspension is a crucial issue for both
scientific research and practical applications to provide better cooling. To
consider and evaluate stability of nanoparticles inside the base fluid,
sedimentation velocity calculation of small spherical particles is found by
using Stokes law. Stokes law (Equation 4.3) includes the effective parameters
for stability of nanofluids.
51
v
2r 2
9
p
f
g
(4.3)
where, ‘v’ is the sedimentation velocity, ‘r’ the radius of particles, ‘ ’ is
viscosity of liquid; ‘ ’ is the density while ‘p’ and ‘f’ subscripts are the
particles and liquid, respectively. Finally, ‘g’ is the gravity acceleration,
which is the main reason of sedimentation. There are three forces acting on
suspended particle such as buoyancy force, drag force and body force. Their
balance makes the nanoparticle stable. Buoyancy and drag forces are acting
upward and resisting against body force acting downwards resulting from
gravitational attraction
Hiemenz and Dekker (1986). Therefore, lower
particle size, lower viscosity, lower temperature difference are the stability
parameters. Addition of surfactant, pH control and Ultrasonic agitation
(vibration) are the three common techniques for making stable nanofluids.
Addition of surfactant and pH control is the two techniques to
prevent clustering and agglomeration while ultrasonic vibration is applied to
break down agglomeration. Zhu et al (2009), Wang et al (2009) and Pantzali
et al (2009) used all three techniques to improve the stability of nanofluid.
Surfactants can be defined as chemical compounds added to
nanoparticles in order to lower surface tension of liquids and increase
immersion of particles. Several literatures talk about adding surfactant to
nanoparticles to avoid fast sedimentation; however, enough surfactant should
be added to particle at any particular case. In researches, several types of
surfactant had been utilized for different kinds of nanofluids. The most
significant ones could be listed as a) Sodium dodecylsulfate (SDS)
Chandrasekar et al (2010), b) Salt and oleic acid Hwang et al (2007), c)
Cetyltrimethylammoniumbromide (CTAB),
Jiang (2003), d) Dodecyl
trimethylammonium bromide (DTAB) and sodium octanoate (SOCT),Li et al
52
(2008) e)Hexadecyltrimethylammoniumbromide (HCTAB),Yu et al (2010), f)
Polyvinylpyrrolidone (PVP), Pantzali et al(2009), and g) Gum Arabic, Madni
et al (2010).
Xie et al (2002) showed the stability of carbon nanotubes / water
nanofluids by taking simple acid treatment. This was caused by a
hydrophobic-to-hydrophilic conversion of the surface nature due to the
generation of a hydroxyl group. As the pH value of the solution departs from
the Iso Electric Point (IEP) of particles the colloidal particles get more stable
and ultimately modify the thermal conductivity of the fluid. The disadvantage
of adding surfactant at the high temperatures as above than 60oC leads to
damage the bonding between surfactant and nanoparticles. Ghadimi (2011)
reviewed the stability of nanofluids, instruments and methods that can rank
the relative stability of nanosuspension. The list includes UV–Vis
spectrophotometer, zeta potential, sediment photograph capturing, TEM
(Transmission
Electron
Microscopy)
and
SEM
(Scanning
Electron
Microscopy),light scattering, three omega and sedimentation balance method.
In this investigation, UV –Vis spectrometer, zeta potential analysis
with pH values, and sediment photograph methods have been carried out to
ensure the stability.
4.5.1
Stability Inspection with UV –Vis Spectrophotometer
Ultra Violet–Visible spectrophotometer (UV–Vis) measurements
have been used to quantitatively characterize the stability of nanoparticles
dispersed in base fluids. The UV–Vis spectrophotometer exploits the fact that
the intensity of the light becomes different by absorption and scattering of
light passing through a fluid. Jiang et al (2003) were the first who proposed
nanofluid sedimentation estimation by using UV–Vis spectrophotometer.
53
Further, this method was used by Hwang et al (2007), and Lee et al
(2009) have used the same method.
In this investigation, the UV-Vis. spectrophotometer, Lambda 35
model, Perkin Elemer make, absorption range of 190 nm to 1100nm was used
to study the stability of nanofluid. The inspection range is from 230nm to
600nm. The U-V vis. spectrometer works under the principal of Beer –
Lamberts law. Beer –Lamberts law relates that an absorbance of light and
proportion of material through is passing. The lesser the suspended particles
in the solution makes the light absorption lesser.
In this method, the first step is to find the peak absorbance of the
dispersed nanoparticles at very dilute suspension by scanning. The relative
stability measurement is followed by preparing the desired concentration of
nanofluid and put aside for a couple of days. Whenever it is needed to check
the relative stability, the supernatant concentration is measured by UV–Vis
spectrophotometer and the absorbance is plotted against wavelength.
3.2
3.0
Peak 224nm
0.1% vol.Nanofluid
0.4% vol.Nanofluid
0.8% vol.Nanofluid
2.8
2.6
2.4
Peak 224nm
2.2
2.0
1.8
1.6
1.4
1.2
Peak 210nm
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
200
400
600
800
1000
1200
Wavelength (nm)
Figure 4.12 UV-Vis. spectrum obtained for Al2O3/ water nanofluid just
after preparation
54
Figure 4.12 shows the stability of 0.1%, 0.4% and 0.8% nanofluid
just after preparation by using ultrasonic agitation. It is shown that all three
nanofluids light absorption strength (broadband of Full Width at Half
Maximum (FWHM)) is wider in range of 210nm to 230nm. The range of
suspended nanoparticles absorption is 1.1-3.1.It is seen that the absorption
strength of 0.1% nanofluid is lower. This is because the 0.1% nanofluid
leaves more ‘particle free region’ in base fluids. The 0.4% and 0.8%
nanofluids absorption strength are relatively higher than 0.1% nanofluid. The
0.1%, 0.4% and 0.8% nanofluids are stable just after preparation.
Figure 4.13 UV-vis. spectrum obtained for 0.1%Al2O3/water nanofluid
From Figure 4.13, it is observed that the light absorption strength of
0.1% nanofluid just after preparation is wider than the 0.1% nanofluid after 30
days. Therefore, the 0.1% nanofluid just after preparation possesses good
stability and the 0.1% nanofluid after 30 days of preparation is fairly stable.
This is because the light absorption strength is significantly reduced after 30
days.
55
Figure 4.14 UV-vis. spectrum obtained for 0.4% Al2O3 / water nanofluid
From Figure 4.14, it is observed that the light absorption strength of
0.4% nanofluid just after preparation is wider than the 0.4% nanofluid after 30
days The peak is maintained in the range same range of wavelength.
Therefore, the nanofluid just after preparation and
after 30 days possesses
good stability.
From figure 4.15, it is observed that the light absorption strength of
0.8% nanofluid just after preparation is wider than the 0.8% nanofluid after 30
days. The peak is maintained in the same range of wavelength. Therefore, the
nanofluid just after preparation and after 30 days possesses good stability.
56
Figure 4.15 UV-Vis. spectrum obtained for 0.8% Al2O3 / water nanofluid
On the comparing the results of UV spectra of 0.1%,0.4% and 0.8%
Al2O3 /water nanofluid, the 0.1% nanofluid possesses poor stability and 0.4%
and 0.8% nanofluid have good stability even after 30 day of preparation.
4.5.2
Stability Inspection by Measuring pH value
When dispersing Al2O3 nanoparticles into any base fluid, the
particle surface can acquire an electric charge by absorbing or desorbing at
the particle/liquid interface, especially when the base fluid is a polar medium
like distilled water Hunter (2004). This absorbing and desorbing mechanism
form two layers that surround the particle surface. The inner region is the
Stern layer, where the ions are strongly attached to the particle surface. The
diffuse layer, which is the outer layer, contains ions that are not firmly bound.
The potential at this electrical double layer (EDL) boundary is known as the
zeta potential ( ). The magnitude of
represents the strength of the
electrostatic energy barrier between particles. A greater
increases the inter
particle repulsion in a nanofluid of similar nanoparticles. Hence, less
57
aggregation will occur and the nanofluids will be more stable. The
and the
thickness of the EDL are strongly dependent on the pH value. Once the pH
value exceeds a certain limit, the ions cause significant shrinkage of the EDL,
and the nanofluid is no longer be stable Hunter (1989,2004).
Xie et al (2002, 2002a), and Lee et al (2006) measured the thermal
conductivity of nanofluids with water, ethylene glycol, and pump oil as base
fluid. They have reported significant decrease in thermal conductivity
enhancement with increasing pH values. They have related the Iso-Electric
Point (IEP) of Al2O3 nanoparticles and pH value which causes mobility of
nanoparticles. The (IEP) is the point at which there is no either positive or
negative electrical charge of particles at certain pH value. Wang et al (2009)
suggested the pH value affects the thermal conductivity and stability of
nanofluids. Zeta potential and associated suspension stability are: 0 mV little or no stability, 15Mv- some stability but settling lightly, 30mV-moderate
stability, 45mV-good stability, and 60mV- very good stability. Generally, a
suspension with a measured zeta-potential above 30 mV (absolute value) is
considered to have good stability Vandsburger (2009).Therefore, measuring
the pH value corresponding to the IEP is one of the most common methods
among the researchers to determine the stability.
Therefore, it is essential to measure the pH value of nanofluid to
ensure the optimum value for attaining the maximum thermal conductivity
and stability before applying nanofluid in any thermal systems.
In this investigation, the pH(Hydrogen potential) meter (Deep
vision,0.01 accuracy, in the range of 1-14, working temperature range 0 –
100o C was used to measure the pH value of Al2O3/water nanofluid. The pH
meter was calibrated by using a single point calibration technique, with a
standard buffer solution of pH 7.00. The measured pH values have been given
in Appendix A.4.5. The same are plotted in Figure 4.16.
58
8.0
7.5
7.0
6.5
6.0
5.5
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Particle volume concentration, %
Figure 4.16 Variation of pH value with particles volume concentration
Figure 4.16 shows that the pH value decreases with increasing
particle volume concentration. Xie et al (2008)
proposed the pH value
corresponding to isoelectric point of Al2O3/water nanofluid is 9.2. If the
measured pH value is away from the optimum pH value then the nanofluid is
stable Wang (2009). In this investigation, the prepared nanofluid at
0.4%,0.8% volume concentration were found to be away from the pH value
9.2. Therefore, very large repulsive forces among the nanoparticles when pH
is far from isoelectric point. And make the particle stable in base fluid. In case
of 0.1% nanofluid, the pH value is not far away from 9.2.Therefore, 0.1%
nanofluid is fairly not stable while comparing with 0.4% and 0.8% nanofluid
concentration just after preparation. This ensures that the nanofluids prepared
are stable because of very large repulsive forces among the nanoparticles
when pH is far from isoelectric point. Therefore, the dispersed nanoparticles
are expected to be stable and give maximum thermal conductivity.
The pH value of nanofluids was measured 15 and 30 days after the
preparation in order to study the stability. The results are plotted in 4.17. It is
seen from Figure 4.18 that the pH value of 0.1% nanofluid considerably
59
increases with respect to days. It reaches 8.9 and this is very nearer to the 9.2
pH at which sedimentation occurs easily. It is found that the pH value of 0.4%
and 0.8% nanofluid are far away from isoelectric point pH value 9.2.
Therefore, 0.4% and 0.8% nanofluids are relatively stable even after 30 days.
9.0
0.1% Nanofluid
0.4% Nanofluid
0.8% Nanofluid
8.5
8.0
7.5
7.0
6.5
6.0
5.5
0
5
10
15
20
25
30
No. of days
Figure 4.17 Variation of pH value with no. of days
4.5.3
Stability Inspection with Photograph Capturing Technique
Figure 4.18 Photograph of Al2O3 / water nanofluids at static condition:
Just after preparation
60
The photographs of test tubes with nanofluid were taken by using
Sony digital camera of 16.1 Mega Pixel ,W Series, 5x Optical Zoom Cybershot (Black).
It is seen from Figure 4.18 the 0.1%, 0.4% and 0.8% nanofluids do
not show the visible sedimentation of nanoparticles. It means that the
prepared nanofluids are stable just after preparation. Whereas, in Figure 4.19,
the 0.1% nanofluid shows much visible sedimentation at the bottom of the test
tube. The 0.4% and 0.8% do not show much sedimentation. Therefore the
0.1% nanofluid has poor stability and 0.4% and 0.8% nanofluid have good
stability when the nanofluids are kept static for 30 days. This is because of
low particle volume concentration 0.1% nanofluid tends to agglomerate
easily. The low particle volume concentration has lack of nanoparticles to
generate adequate repulsive forces for making stable suspension.
Figure 4.19 Photograph of Al2O3 / water nanofluid at static condition:
30 days after preparation
This results holds agree with the results of Wu and Kumar (2004)
and Keblinski et al (2002). Agglomeration of nanoparticles exerts a negative
effect on heat transfer enhancement, particularly at low volume fraction, since
61
the agglomerated particles tend to settle down in the liquid, which creates
large regions of particle-free liquid with high thermal resistance,
Wu and
Kumar (2004) and Keblinski et al (2002).
Figure 4.20 Photograph of Al2O3 / water nanofluid at flowing condition:
30 days after preparation
In order to compare the sedimentation of nanofluid at static and
flow condition, the prepared nanofluid have been made flow in a coiled tube.
The nanofluids were made flow after 15days from the date of preparation.
Figure 4.20 shows the stability of 0.1%, 0.4% and 0.8% nanofluid under flow
condition. It is seen from figure that there is no observable sedimentation
even after 30 days. This is because of re-establishment of nanoparticles when
nanofluids are made flow.
Therefore, under static condition the 0.4% and 0.8% nanofluids
show good stability even after 30 days and 0.1% nanofluid shows
sedimentation. It is found that under flow condition 0.1%,0.4% and 0.8%
nanofluids show good stability.
62
4.6
OTHER THERMOPHYSICAL PROPERTIES OF
Al2O3 / WATER NANOFLUIDS
The other properties of 0.1%, 0.4% and 0.8% Al2O3 / water
nanofluids just after preparation at room temperature are as follows.
Table 4.6 Properties of Al2O3 / water nanofluids
Particle volume concentration,
0.1%
0.4%
0.8%
Density, kg/m3
1263.4
2125.6
3006
Specific heat capacity, J/kg K
3086.6
2125.6
1014.4
Thermal conductivity, W /m K
0.618
0.622
0.630
Dynamic viscosity, cP
0.825
0.83
0.85
pH value
7.67
6.04
5.71
%
The density and specific heat capacity (Table 4.6) are the calculated
values by using analytical models proposed by Pak and Cho (1998) and Xuan
and Roetzel (2000) respectively. The thermo physical properties of interest
are the density, specific heat capacity, thermal conductivity and viscosity.
The density and specific heat capacity are estimated by using the analytical
models proposed by Pak and Cho (1998) and Xuan and Roetzel (2000).
However, thermal conductivity and viscosity have been measured and
compared with the analytical models proposed by Chandrasekar et al(2010) in
this investigation.
4.6.1
Density of Nanofluid
The density of nanofluid contributes to the convective heat transfer.
Density of nanofluid at atmospheric temperature is estimated based on the law
of mixtures. The nanoparticles dispersed into basefluid lead to increase the
63
mass by maintaining volume remains constant. Therefore, the density of
nanofluid increases while adding nanoparticles. The density of nanofluid is
estimated at the average bulk temperature by the Equation 4.4 proposed by
Pak and Cho (1998).
nf
s
(1
)
w.
(4.4)
where‘s’ indicates solid particle, ‘nf’ indicates nanofluid, and ‘w’ indicates
water (base fluid). The calculated density and specific heat values are given in
Figures 4.21 and 4.22 they have given in Appendix A 4.6 and A 4.7.
Figure 4.21 shows the variation of density with particle volume
concentration. It is seen that the density increases with increasing particle
volume concentration.
3200
3000
Pak and Cho ( 1998)
2800
2600
2400
2200
2000
1800
1600
1400
1200
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Particle volume concentration,%
Figure 4.21 Effect of particle volume concentration on nanofluid density
64
4.6.2
Specific Heat Capacity of Nanofluid
The specific heat capacity of Al2O3/water nanofluid is estimated by
using the Equation 4.5 given by Xuan and Roetzel (2000).
( c p ) nf
p c p,p )
w (1
)c p,w
(4.5)
3500
3000
Xuan and Roetzel (2000)
2500
2000
1500
1000
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Particle volume concentration,%
Figure 4.22 Effect of particle volume concentration on nanofluid specific
heat capacity
where‘s’ indicates solid particle, ‘nf’ indicates nanofluid, and ‘w’ indicates
water (base fluid).
It is found from Figure 4.22 that the specific heat capacity of Al2O3
/ water nanofluid decreases with increasing particle volume concentration. It
implies that less heat input is required to increase the temperature of nanofluid
at higher particle volume concentration. Therefore, lower the specific heat of
nanofluid can lead to higher convective heat transfer.