Measurement and Model Correlation of Specific Heat
Capacity of Water-Based Nanofluids With Silica, Alumina
and Copper Oxide Nanoparticles
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O’Hanley, Harry, Jacopo Buongiorno, Thomas McKrell, and Linwen Hu. “Measurement and Model Correlation of Specific Heat
Capacity of Water-Based Nanofluids With Silica, Alumina and
Copper Oxide Nanoparticles.” ASME 2011 International
Mechanical Engineering Congress and Exposition (IMECE
2011). In Volume 10: Heat and Mass Transport Processes, Parts
A and B, 1209-1214.
As Published
http://dx.doi.org/10.1115/IMECE2011-62054
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ASME International
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Proceedings of the ASME 2011 International Mechanical Engineering Congress & Exposition
IMECE2011
November 11-17, 2011, Denver, Colorado, USA
IMECE2011-62054 DRAFT
MEASUREMENT AND MODEL CORRELATION OF SPECIFIC HEAT CAPACITY OF
WATER-BASED NANOFLUIDS WITH SILICA, ALUMINA AND COPPER OXIDE
NANOPARTICLES
Harry O’Hanley
Massachusetts Institute of Technology
Cambridge, MA, USA
Jacopo Buongiorno
Massachusetts Institute of Technology
Cambridge, MA, USA
Thomas McKrell
Massachusetts Institute of Technology
Cambridge, MA, USA
Lin-wen Hu
Massachusetts Institute of Technology
Cambridge, MA, USA
ABSTRACT
Nanofluids are being considered for heat transfer applications.
However, their thermo-physical properties are poorly known.
Here we focus on nanofluid specific heat capacity. Currently,
there exist two models to predict a nanofluid’s specific heat
capacity as a function of nanoparticle concentration and
material. Model I is a straight volume-weighted average;
Model II is based on the assumption of thermal equilibrium
between the particles and the surrounding fluid. These two
models give significantly different predictions for a given
system. Using differential scanning calorimetry, the specific
heat capacities of water based silica, alumina, and copper oxide
nanofluids were measured. Nanoparticle concentrations were
varied between 5wt% and 50wt%. Test results were found to
be in excellent agreement with Model II, while the predictions
of Model I deviate very significantly from the data.
INTRODUCTION
Recent research has indicated that dispersions of nanoparticles
in a base fluid, known as nanofluids, can increase the boiling
critical heat flux and overall performance of thermal systems.
Typical nanoparticle concentrations may range from 0.01wt%
to 50wt% and common particle materials include silica,
alumina, copper oxide, zirconia, carbon nanotubes, etc. Water
often serves as the base fluid, though other liquids such as
ethylene glycol have been used [1].
As nanofluids are considered for thermal applications, it is
necessary to be able to predict their thermo-physical properties.
Because nanofluids were initially considered for thermal
conductivity enhancement, this property has been extensively
studied [2]. However, there have been fewer examinations of
nanofluid specific heat capacity [3] [4] [5] [6]. It is the
objective of this investigation to complement existing research
by (i) measuring the specific heat capacity of water-based
silica, alumina and copper oxide nanofluids, and (ii) comparing
the predictions of two popular nanofluid specific heat capacity
models to data.
NOMENCLATURE
cp,f
Specific heat capacity of base fluid (J/g-K)
cp,nf
Specific heat capacity of nanofluid (J/g-K)
cp,n
Specific heat capacity of nanoparticle (J/g-K)
cp,ref
Specific heat capacity of reference (J/g-K)
cp,sample
Specific heat capacity of sample (J/g-K)
mn
Mass of nanoparticles (g)
mH20
Mass of water (g)
mref
Mass of reference (g)
msample
Mass of sample (g)
Qref
Heat flux into reference (Watts)
Heat flux into sample (Watts)
Qsample
Q0
Heat flux baseline (Watts)
φ
Volume fraction (unitless)
ρf
Density of basefluid (g/cm3)
ρn
Density of nanoparticles (g/cm3)
1
Copyright © 2011 by ASME
ρH20
VN
VH20
Density of water (g/cm3)
Volume of nanoparticles (cm3)
Volume of water (cm3)
SPECIFIC HEAT MODELS
There are two specific heat models widely used in the nanofluid
literature. Model I is similar to mixing theory for ideal gas
mixtures [3]. It is a straight average relating nanofluid specific
heat, cp,nf, to basefluid specific heat, cp,f, nanoparticle specific
heat, cp,n, and volume fraction, φ. Using these parameters,
Model I calculates the nanofluid specific heat as,
,
,
1
The stock nanofluids were obtained from commercial vendors,
and diluted with de-ionized water to vary their concentrations.
Prior to mixing, the nanofluids were manually agitated to
ensure uniform dispersion. Dilution was performed by weight
percent using a Mettler Toledo XS105 balance. Four unique
concentrations were prepared for each nanofluid and are listed
in the table below. For each concentration, two identical
samples were prepared and tested.
Table 1: Nanofluid sample concentrations
Nanofluid
Conc. 1
(stock)
(1)
,
Conc. 2
While it is simple and thus widespread in the literature, Model I
has little theoretical justification in the context of nanofluids.
Model II [3] [7] is based on the assumption of thermal
equilibrium between the particles and the surrounding fluid. It
is straightforward to show that also the particle and fluid
densities (ρn, and ρf, respectively) must affect the specific heat
of the nanofluid,
,
(2)
Conc. 3
Conc. 4
NANOFLUIDS
The specific heat capacities of three nanofluids were analyzed:
alumina-water (Nyacol AL20DW), silica-water (Ludox TMA
420859), and copper oxide-water (Alfa Aesar 45407). The
nanofluid properties, as cited by the manufacturers, are
presented in the table below.
Nanofluid
NYACOL
AL20DW
Ludox TMA
420859
Alfa Aesar
45407
Particle Size (nm) or
Surface Area (m2/g)
pH
Specific
Gravity
50 nm
4.0
1.19
140 m2/g
4.07.0
1.227-1.244
30 nm
Silica-water
34wt%
(19.0vol%)
25.5wt%
(13.5vol%)
15wt%
(8.5vol%)
8.5wt%
(4.1vol%)
Copper
Oxide-water
50wt%
(13.7vol%)
37.5wt%
(8.7vol%)
25wt%
(5.0vol%)
12.5wt%
(2.2vol%)
While nanofluids were diluted and prepared according to their
weight fraction, calculations were performed using volume
fraction. Using the nanoparticle volume, Vn, and the water
volume, VH20, the volume fraction can be calculated as,
A rigorous derivation of Equation (2) is presented in [8].
Predictions of nanofluid specific heat capacity were made using
both models and compared to experimental measurements.
Water was the base fluid of all nanofluids used in this
investigation. Therefore, handbook values of temperaturedependent water specific heat and density were used in
calculating theoretical nanofluid specific heat [9]. Additionally,
the specific heat and density of the nanoparticles were assumed
to be equal to the respective thermo-physical properties of
particle material in bulk form.
Aluminawater
20wt%
(6.4vol%)
15wt%
(4.6vol%)
10wt%
(2.9vol%)
5wt%
(1.4vol%)
(3)
Substituting in nanoparticle mass, mn, and density ρn, and water
mass, mH20, and density, ρH20, Equation (3) can be rewritten as,
(4)
Equation (4) can be used to determine the nanoparticle volume
fraction of nanofluid concentrations created by dilution with
de-ionized water.
MEASUREMENT METHOD
A heat-flux type differential scanning calorimeter (TA
Instruments Q2000) was used to measure the nanofluid specific
heat capacities. The differential scanning calorimeter (DSC)
measures the heat flux into a sample as a function of
temperature during a user prescribed heating regime. It
accomplishes this by comparing the heat flux into a pan
containing the sample with the heat flux into an empty pan.
Hermetically sealed aluminum pans (TA Instruments) were
used.
The classical three-step DSC procedure was followed to
measure specific heat capacity [10] [11]. Additionally, testing
procedures adhered to protocols set forth in the ASTM Standard
Test Method for Determining Specific Heat Capacity by
Differential Scanning Calorimetry (E 1269-05).
2
Copyright © 2011 by ASME
The tthree-step DSC
C procedure beegins with desiigning a heatin
ng
regim
me, which shou
uld contain the temperature raange of interesst.
Next,, a measuremeent is taken with
w
two emptty sample pan
ns
loadeed into the DS
SC. During this measuremen
nt, the baselin
ne
heat flux, Q0, is obtained.
o
The results of thiis measuremen
nt
indicaate the bias in the machine, allowing
a
for it to be accounteed
for duuring data redu
uction.
The second measu
urement is of a reference sample,
s
with a
know
wn specific heat, cp,ref. A pan
p containing
g the referencce
sample and an emp
pty pan are loaaded into the DSC.
D
The heaat
flux iinto the referen
nce sample, Qref, is recorded
d throughout th
he
identiical heating reg
gime.
The thhird measurem
ment is made on
n the actual sam
mple of interesst.
A pann containing th
he sample and an empty pan are loaded intto
the D
DSC. The heatt flux into thee sample, Qsammple, is recordeed
durinng an identicaal heating reegime as the previous tw
wo
measuurements. Th
he heat flux
x curves fro
om the threee
measuurements are used
u
to comparratively determ
mine the specifi
fic
heat oof the sample, cp,sample, where,
,
,
In thhese tests, de--ionized waterr was used ass the referencce
sample, with specifi
fic heat values obtained
o
from a handbook [9
9].
The D
DSC heating prrocedure consisted of three seegments:
22.
33.
ULTS AND DISCUSSION
RESU
DSC m
measurements of pure ethyleene glycol andd glycerin were
in goood agreementt with literatuure values off specific heaat
capaciity. The resultss of these testss, presented in Tables 2 and 3
below
w, validate the D
DSC methodology and machiine calibration..
Table 22: Propylene G
Glycol
Tempeerature (°C)
35
45
55
Equilibratee and remain isothermal att 25°C for on
ne
minute
Ramp to 75
5°C at 10°C/m
min Remain iso
othermal at 75°°C for one min
nute
Theoretical cp (J/gK)
2.56
2.62
2.65
Meeasured cp (J/gK)
22.54  0.191
22.64  0.185
22.65  0.185
Theoretical cp (J/gK)
2.39
2.41
2.42
Meeasured cp (J/gK)
22.41  0.008
22.42  0.002
22.44  0.001
Table 33: Glycerin
Tempeerature (°C)
35
45
55
(5
5)
m
of the reference
r
and
and mref and msample represent the masses
sample, respectively
y. Sample masses were measu
ured using a
Perkin Elmer AD6 autobalance.
a
11.
were uused to calculaate the specificc heat capacityy and error barrs
indicaate standard devviation.
Figurees 1-9 show thhe nanofluids ddata and the cuurves predicted
d
by Moodels I and II. As expected, as nanoparticle concentration
n
increaases, the speciffic heat capacitty decreases. H
However, Modeel
I largeely underestim
mates the decreease, while Moodel II offers a
much more accuraate prediction of nanofluidd specific heaat
capaciity. These coonclusions are consistent wiith the alumina
nanofl
fluid results reeported in [3],, and expand the validity of
o
Modell II to silica annd copper oxidee nanofluids.
Heat flux measurem
ment was con
ntinuous from 25°C to 75°C
C.
Howeever, for analy
ysis, specific heat capacities were calculateed
at 355°C, 45°C an
nd 55°C. An
A uncertainty
y analysis waas
performed via the propagation of
o error. Unccertainty in th
he
measuurement of speecific heat cap
pacity was fou
und to be on th
he
orderr of 10-4 (J//g-K).
For each samplee of nanofluiid
conceentration, threee measuremen
nts were taken.. These valuees
were then averaged to yield the daata points and related
r
standarrd
deviaations presented
d below.
Prior to nanofluid measurement, this DSC meethodology waas
validaated by analyzing two puree fluids, ethyllene glycol an
nd
glyceerin. The results obtained fro
om these measurements werre
comppared against handbook
h
valu
ues of specificc heat for thesse
liquidds [12]. Nextt, three measu
urements weree performed on
o
each nanofluid sam
mple. The averrages of thesee measurementts
Figu
ure 1: Alumina--water at 35°C
3
Copyright © 2011 by ASME
E
Figu
ure 2: Alumina-water at 45°C
Figgure 5: Silica-w
water at 45°C
Figu
ure 3: Alumina-water at 55°C
Figgure 6: Silica-w
water at 55°C
Fiigure 4: Silica-w
water at 35°C
Figure 7: Copper Oxid
de-water at 35°°C
4
Copyright © 2011 by ASME
E
and gllycerin, whichh were confirm
med against haandbook valuess.
The nnanofluid data were used too test the preddictions of two
populaar mixture moodels for speciific heat. Thee results clearly
y
sugge st that the model basedd on particlee/fluid thermaal
n
equilibbrium (Model II) yields moore accurate ppredictions than
the moodel based on a straight voluume-weightedd average of the
particlle and fluid sppecific heats (M
Model I).
G
Given its sound
theoreetical basis, wee believe Moddel II is generaally applicablee,
while Model I shouuld be abandonned. To furthher improve the
accuraacy of Modell II, future innvestigations ccould focus on
n
measuuring the acttual density and specific heat of the
nanopparticles in disspersion and coompare them to those of the
bulk m
materials.
Figuree 8: Copper Oxiide-water at 45°°C
ACKN
NOWLEDGM
MENTS
The M
Materials Reseearch Science and Engineeering Center at
a
Harvaard Universityy offered theeir DSC forr use in thiis
investtigation. Withinn this facility, Dr. Philseok K
Kim, Dr. Kosta
Ladavvac, and Roxannne Kimo offerred invaluable instruction and
d
advicee on the machinne’s operation..
REFE
ERENCES
Figuree 9: Copper Oxiide-water at 55°°C
Even for Model II, there appeaar to be smalll discrepanciees
betweeen the data an
nd predictions. These could co
ome from errorrs
in thhe listed stocck nanofluid concentrationss, experimentaal
uncerrtainties in dillution or incon
nsistencies in using the bullk
materrial propertiess in the mo
odel, instead of the actuaal
nanopparticle properrties. Recent research sugg
gests that thesse
propeerties may diff
ffer if the matterial is in nan
noparticle form
m
versuus bulk form [8]. Agglom
meration/sedimeentation of th
he
nanopparticles could
d also affect thee results [8]. Investigation of
o
these effects is left for
f future work
k.
NCLUSIONS
CON
Usingg a heat flux differential
d
scaanning calorim
meter (DSC), th
he
speciffic heat capacities of wateer-based silicaa, alumina an
nd
coppeer oxide nanofl
fluids at variou
us nanoparticlee concentration
ns
were measured. The
T
DSC prrocedure was validated by
b
measuuring the speccific heat capaccities of pure ethylene glyco
ol
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