Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall...
Transcript of Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall...
-
7/28/2019 Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature bou
1/16
Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubeswith imposed wall temperature boundary conditions
Sbastien Ferrouillat a,, Andr Bontemps a, Joo-Paulo Ribeiro b, Jean-Antoine Gruss b, Olivier Soriano b
a Universit Joseph Fourier, LEGI, BP 53X, 38041 Grenoble cedex, Franceb CEA/LITEN/DTS/LETH, 17, Avenue des martyrs, 38052 Grenoble cedex, France
a r t i c l e i n f o
Article history:
Received 6 October 2009
Received in revised form 25 August 2010
Accepted 18 January 2011
Available online 18 February 2011
Keywords:
Nanofluid
Convective heat transfer
Imposed wall temperature
a b s t r a c t
The convective heat transfer of SiO2/water colloidal suspensions (534 wt.%) is investigated experimen-
tally in a flow loop with a horizontal tube test section whose wall temperature is imposed. Experiments
were performed at different inlet temperatures (20, 50, 70 C) in cooling and/or heating conditions at var-
ious flow rates (200 < Re < 10,000). The Reynolds and Nusselt numbers were deduced by using thermal
conductivity and viscosity values measured with the same temperature conditions as those in the tests.
Results indicate that the heat transfer coefficient values are increased from 10% to 60% compared to those
of pure water. They also show that the general trend of standard correlations is respected. The problem of
suspension stability at the highest temperatures is discussed. In order to evaluate the benefits provided
by the enhanced properties of the nanofluids studied, an energetic performance evaluation criterion (PEC)
is defined. This PEC decreases as the nanoparticle concentration is increased. This process is also dis-
cussed in this paper.
2011 Elsevier Inc. All rights reserved.
1. Introduction
The development of high-performance thermal systems has
been stimulated in many fields of new technologies. Conventional
heat transfer devices have to be substantially improved to answer
the needs of systems from the microscale to large power plants. In
this perspective, convective heat transfer can be enhanced in sev-
eral ways, by using either active or passive techniques. In the latter
case, it is made possible by changing the structure of the heat ex-
changer or the properties of the heat exchange surface. However
another possibility is to modify the fluid itself by enhancing its
thermal conductivity. Various techniques have been used to in-
crease the thermal conductivity of base fluids by introducing solid
particles whose conductivity is generally higher than that of liq-
uids. A new class of fluids called nanofluids have recently beendeveloped and tested. As a result, we are seeing an increasing
amount of published work on the subject. Nanofluids are colloids
made of a base fluid and nanoparticles (1100 nm). A substantial
increase in the thermal conductivities of nanofluids containing a
small amount of metallic or non-metallic nanoparticles has been
reported. In addition, some authors have measured an increase of
heat transfer coefficients compared to pure liquids beyond the
mere thermal-conductivity effect. However, many results found
in published literature are not consistent with others or with stan-
dard correlations. Several reasons have been put forward to explainthese discrepancies. In an attempt to explain this type of
behaviour, a range of experiments has been defined: measure-
ments of thermophysical properties of nanofluids, measurements
of pressure drop in channels, measurements of heat transfer coef-
ficients with different boundary conditions, stability of colloidal
suspensions.
2. Selected bibliography
To characterise heat transfer in forced-convection, the heat
transfer coefficient is one of the parameters to be determined. It
takes into account the fluid thermal conductivity either directly
or indirectly using the Nusselt number. Thus, a first assessment
of the heat transfer potential of a nanofluid involves considering
its thermal conductivity. Up to now, most of research has been
published in this area because thermal conductivity is probably
easier to measure than heat transfer coefficients. Consequently,
thermal conductivity results have been used extensively to esti-
mate nanofluid heat transfer enhancement rates. Nevertheless,
while increases in effective thermal conductivity as well as
changes in density, specific heat, and viscosity are important indi-
cations of improved heat transfer behaviour of nanofluids, the net
benefit of nanofluids as heat transfer fluids is determined through
the heat transfer coefficient. Thus, it is essential to directly mea-
sure this coefficient under flow conditions typical of specific appli-
cations and, until now, there has been limited experimental work
0142-727X/$ - see front matter 2011 Elsevier Inc. All rights reserved.doi:10.1016/j.ijheatfluidflow.2011.01.003
Corresponding author.
E-mail address: [email protected] (S. Ferrouillat).
International Journal of Heat and Fluid Flow 32 (2011) 424439
Contents lists available at ScienceDirect
International Journal of Heat and Fluid Flow
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j h f f
http://dx.doi.org/10.1016/j.ijheatfluidflow.2011.01.003mailto:[email protected]://dx.doi.org/10.1016/j.ijheatfluidflow.2011.01.003http://www.sciencedirect.com/science/journal/0142727Xhttp://www.elsevier.com/locate/ijhffhttp://www.elsevier.com/locate/ijhffhttp://www.sciencedirect.com/science/journal/0142727Xhttp://dx.doi.org/10.1016/j.ijheatfluidflow.2011.01.003mailto:[email protected]://dx.doi.org/10.1016/j.ijheatfluidflow.2011.01.003 -
7/28/2019 Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature bou
2/16
reported in published literature, as shown in Table 1. The nanofluid
types, testing parameters and a summary of results are listed in
this table. Many research groups have found that heat transfer
enhancement exceeds thermal conductivity enhancement in lami-
nar flow (Chen et al., 2008; Faulkner et al., 2004; Hwang et al.,
2009; Jung et al., 2009; Lai et al., 2008; Lee and Choi, 1996; Lee
et al., 2005; Li and Xuan, 2002; Rea et al., 2009; Wen and Ding,
2004; Xuan and Li, 2003; Zeinali Heris et al., 2006a,b, 2007). This
finding indicates that the presence of nanoparticles in the flow
influences the heat transfer beyond what would be expected from
increased thermal conductivity alone. Some authors have attrib-
uted this added effect to particle-fluid interactions.
First, it must be remarked that due to the particle size, it has
generally been considered that the two-phase solidliquid flow
does not lead to specific flow patterns.
The effect of particle volume concentrations have been studied
by several research groups. In laminar flow, at particle volume con-
centrations below 2%, there is a limited Reynolds effect on heat
transfer enhancement. For particle volume concentrations above
2%, the heat transfer enhancement augments with the Reynolds
number. This trend is consistent with the increase of thermal con-
ductivity with increased particle volume concentration. However,
it has been noticed that heat transfer enhancement is more sub-
stantial than thermal conductivity enhancement.
Nevertheless, two groups found that the heat transfer enhance-
ment either is much lower than the effective thermal conductivity
enhancement (graphite nanofluids, Yang et al., 2005) or is not sig-
nificant (nano-diamond nanofluid or ethylene based titanium
nanofluid, Ding et al. (2007)).
Amongst all nanofluids tested, Carbon Nano Tube (CNT) solu-
tions seem to provide the highest heat transfer enhancement
(Faulkner et al., 2004; Ding et al., 2006) compared to other nano-
particles (Al2O3, CuO, TiO2, graphite, etc.). This enhancement can
be related to several potential reasons: improved thermal conduc-
tivity, shear-induced enhancement in flow, reduced boundary
layer, particle re-arrangement, and high aspect ratio of CNTs.
Indeed, particle shape or aspect ratio should be an important fac-
tor. Studies with nearly spherical nanoparticles (aspect ratio
around 1) (Li and Xuan, 2002; Wen and Ding, 2004; Xuan and Li,
2003) show an increase of the convective heat transfer coefficient
up to 60%. Results cited previously on CNT nanofluids, which are
characterised by an aspect ratio above 100, show a heat transfer
enhancement of up to 350% at Re = 800 for 0.5 wt.% nanoparticle
concentration. However, graphite nanofluids results cited previ-
ously (Yang et al., 2005), with an aspect ratio lower than 0.02,
showed a much lower increase of the convective heat transfer coef-
ficient with respect to the effective thermal conductivity. Thus, the
available experimental data seem to show that the particle shape
and the aspect ratio are significant parameters which affect the
thermal performance of nanofluids. However, is yet to be examined
in-depth.
Heat transfer results in turbulent flow are available from few
groups (He et al., 2007; Kulkarni et al., 2008; Li and Xuan, 2002;
Nguyen et al., 2007; Pak and Cho, 1998; Sommers and Yerkes,
2009; Williams et al., 2008; Xuan and Li, 2003; Yu et al., 2009).
Some of them (He et al., 2007; Kulkarni et al., 2008; Li and Xuan,
2002; Nguyen et al., 2007; Xuan and Li, 2003) reported heat trans-
fer enhancement for turbulent flow higher than predicted by the
pure fluid correlation (DittusBoelter), even when the measured
nanofluid properties were used in defining the dimensionless
groups in the correlation. However, these same researchers show
that turbulent friction factors in their nanofluids can be predicted
by the traditional friction factor correlations for pure fluids if the
measured nanofluid viscosity is used. Moreover, it has been shown
that the heat transfer enhancement increases with increased parti-
cle volume concentration. The heat transfer enhancement is the
highest for Cu particles, (Table 1), followed by Al2O3 particles
and then TiO2 particles at the same concentration levels. When
taking into account thermal conductivity, it is not surprising that
the Cuwater nanofluid shows the highest heat transfer enhance-
ment. However, the thermal conductivity enhancements of
Al2O3 and TiO2 in water are similar although the heat transfer
enhancement of Al2O3 in water is higher than that of TiO2 in water.
Nevertheless, two groups found that the heat transfer coefficient of
Nomenclature
At thermocouple cross section areaCp specific heat capacityd tube diameterdh hydraulic diameterD thermocouple diameter
f fanning friction factorh heat transfer coefficientht heat transfer coefficient near the thermocouplek thermal conductivityl thermocouple lengthL tube length_m mass flow rate
Nu Nusselt numberP perimeter of the thermocouplePe Peclet numberPr Prandtl number_Q heat flow rate
Rw thermal resistance of the copper tube wallRe Reynolds numberS heat exchange area
Sp cross section areaU overall heat transfer coefficient
Greek symbolsb shape factor
DP pressure dropDTlm log mean temperature differencee absolute roughnessu nanofluid volume fractionuw nanofluid mass fraction
l dynamic viscosityK Darcy coefficientq densityw particle sphericity
Subscriptsb bulke externalexp experimentalf base fluidi internalin inletnf nanofluidout outlets nanoparticlest thermocouplew wall
S. Ferrouillat et al. / International Journal of Heat and Fluid Flow 32 (2011) 424439 425
-
7/28/2019 Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature bou
3/16
nanofluids (Al2O3 and TiO2 in water and SiC in water) was lower
than for pure water for constant average velocity in turbulent flow
(Pak and Cho, 1998; Yu et al., 2009).
Recently, Williams et al. (2008) and Rea et al. (2009) studied
turbulent convective heat transfer behaviour of Al2O3 and ZrO2nanoparticle dispersions in water. They demonstrated that if the
measured temperatures dependent on the thermal conductiv-
ity and viscosity of the nanofluids are used in calculating the
Reynolds, Prandlt, and Nusselt numbers, the existing correlations
(DittusBoelter and Blasius/MacAdams) accurately reproduce the
experimental convective heat transfer and viscous pressure loss
behaviour in tubes. This finding indicates that no abnormal heat
transfer enhancement was observed when nanofluid propertieswere accurately taken into account.
At present, there is too little data to establish the heat transfer
enhancement trend with laminar or turbulent flow as a function of
particle type and/or size. The thermal conductivity enhancement
seems to increase with particle size, but more experiments are re-
quired to establish this type of trend with regard to heat transfer
enhancement. Some authors show a heat transfer coefficient
enhancement with particle size (Kulkarni et al., 2008) and some
others show that for a given flow Reynolds number and particle
concentration, the convective heat transfer coefficient does not
seem to be sensitive to the average particle size (He et al., 2007 ).
Moreover, as nanofluids are usually moderately concentrated
suspensions of anisotropic objects, they can be non-Newtonian
materials with a thermodependent rheology. Therefore, it is funda-mental that a thermo-rheo-structural study of these materials be
conducted. As a conclusion of this scientific work, it seems clear
that there is a general lack of characterisation concerning the ther-
mal properties of nanofluids.
Few studies have been conducted which carefully examine
nanofluid stability (Sommers and Yerkes, 2009; Bontemps et al.,
2008a,b). Discoloration of the nanofluid has been observed after
being cycled at high flow rates and increased temperatures for long
periods of time. This may be the result of nano-abrasion occurring
in the loop. The authors suppose that the optical change was due to
trace contaminants. Nanofluid stability must be taken into account
in defining new nanofluids for heat transfer purposes.
3. Nanofluid characterisation
What is called nanofluid is generally a dilute suspension of
nanoparticles (volume fraction 65%). To extend the field of the
present study and to possibly relate our results to those obtained
with rheological fluids the decision was made to vary the nanopar-
ticle concentration beyond the 5% value.
The nanofluids used were colloidal suspensions of SiO2 nano-
particles in water (Fig. 1). They were prepared from a commercial
solution (Ludox
TMA colloidal silica from SigmaAldrich) with a
mass fraction of 34%. Three mass fractions were used: 34%, and
after dilution in demineralised water, 16% and 5%. They correspond
to volume fractions of 18.93%, 7.95%, and 2.3% respectively. Thephysical properties of SiO2 particles are shown in Table 2.
Table 1
Bibliography on experimental forced convective heat transfer with nanofluids.
Ref. Nanofluid Re Nunf/Nuf
Lee and Choi (1996) Metallic nanoparticle suspension Laminar +100%
Pak and Cho (1998) Al2O3water TiO2water 3 vol.% Turbulent 3% to 12% for constant average velocity
Li and Xuan (2002) Cuwater 2 vol.% 80023,000 +60%
Xuan and Li (2003) Cuwater 0.32 v ol.% Laminar and
turbulent
+30%
Wen and Ding (2004) Al2O3water 0.21.6% 6502050 Nu > Nu Shah especially near the entranceFaulkner et al. (2004) MW CNT (aspect ratio > 100) 1.1
4.4 vol.%
217 +48% to +221% with high volume concentration
Yang et al. (2005) Graphite 22.5 wt.% 5110 Nunf/Nuf < knf/kf (aspect ratio l/d = 0.02)
Lee et al. (2005) Agwater 2.5 wt.% 10002000 +17% to +25%
Ding et al. (2006) CNTwater (aspect ratio > 100) 0.1
1 wt.%
8001200 +350%
Zeinali Heris et al.
(2006a)
CuOwater 0.23 v ol.% 6502050 Enhancement of a with U and Pe
Zeinali Heris et al.
(2006b)
Al2O3water CuOwater 0.2 3 vol.% 6502500 Enhancement ofa with u and Pe. Al2O3 shows more enhancement than CuO
Zeinali Heris et al.
(2007)
Al2O3water 0.2-2.5 v ol.% 7002050 Enhancement of a with u and Pe
Nguyen et al. (2007) Al2O3water 16.8 vol.% 300015,500 +40% enhancement ofa with diameter decreases and U increasesDing et al. (2007) Nano-diamond 0.1 wt.% ethylene-
based titanium 24 wt.%
135 No significant enhancement
Chen et al. (2008) Titanate nanotubewater (aspect
ratio = 10) 0.52.5 wt.%
1700 a increases with aspect ratio (nanoparticle shape) increase
Williams et al. (2008) Al2O3water 0.93.6 vol.% ZrO2
water 0.20.9 vol.%
900063,000 No abnormal heat transfer enhancement using measured properties of the
nanofluid
Rea et al. (2009) Al2O3water 0.66.0 vol.% ZrO2
water 0.323.5 vol.%
Laminar No abnormal heat transfer enhancement using measured properties of the
nanofluid
He et al. (2007) TiO2water 0.242 v ol.% 8006000 Enhancement of a with u for a given Re and particle size but no abnormal heattransfer enhancement with particle size increase
Lai et al. (2008) Al2O3water 0.51.0 v ol.% Laminar Enhancement of a with u and volume flow rateKulkarni et al. (2008) SiO2ethylene glycol/water 2
10 vol.%
300012,000 +16% enhancement ofa with 10 vol.%, 20nm particle diameter at Re = 10000enhancement ofa with particle size increase
Jung et al. (2009) Al2O3water 0.61.8 v ol.% 5300 +32% enhancement of a with 1.8 vol.% without major friction lossSommers and Yerkes
(2009)
Al2O3propanol 0.53 wt.% 18002800 Small but significant enhancement for 1 wt.%
Yu et al. (2009) Silicon carbidewater 3.7vol.% 330010,000 +5060% for a given Re, but 7% for constant average velocity
Hwang et al. (2009) Al2O3water 0.010.3 v ol.% 550800 +8% at 0.3 v ol.%
426 S. Ferrouillat et al. / International Journal of Heat and Fluid Flow 32 (2011) 424439
-
7/28/2019 Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature bou
4/16
It is essential to use the correct thermal and physical properties
of nanofluids, since all correlations depend on these properties. The
thermal and physical properties of interest are discussed below.
3.1. Density
The density of the nanofluid is evaluated according to the stan-
dard formula:q 1uqf uqs 1where u is the volume fraction of the nanofluid, qf the density ofthe base fluid, and s is the density of the nanoparticles.
3.2. Specific heat
The formula for the specific heat of a mixture is given by:
Cp 1uwCpf uwCps 2where uw is the mass fraction of the nanofluid, Cpf the specific heatcapacity of the base fluid, and Cps the specific heat capacity of the
nanoparticles.
3.3. Thermal conductivity
Currently, there are no reliable theories to determine the effec-
tive conductivity of a flowing nanofluid. However, there exist
numerous theoretical studies for particle-fluid mixtures based on the
pioneering work of Maxwells effective medium theory (Maxwell,
1881). These studies are essentially concerned by relatively large
particles (down to micrometric sizes). The effective thermal con-
ductivity k for a mixture with spherical particles is given by
k kfks 2kf 2 kf ks
u
ks 2kf kf ks
u3
u is the volume fraction of the nanofluid, kf the thermal conductiv-
ity of the base fluid, and ks is the thermal conductivity of thenanoparticles.
Hamilton and Crosser (1962), proposed a model for non-spher-
ical particles by introducing a shape factor b given by b = 3/w,where w is the particle sphericity, defined as the ratio of the sur-face area of a sphere with the same volume as that of the particle
and the surface area of the particle. The conductivity is expressed
as follows:
k kfks
b
1
kf
b
1
kf
ks u
ks b 1kf kf ks
u 4The Maxwell formula corresponds to sphericity equals one. Sev-
eral authors have proposed other models to take into account
either the effects of the interface between the nanoparticle and
the base fluid or several micro-convection phenomena. They will
not be evoked here.
The available experimental data on conductivity from different
research groups vary widely, and the proposed theories to explain
such dispersion vary from one author to the other. It seems that the
different preparation methods and the different measurement
techniques of each research group contribute to this dispersion.
Due to these problems, the thermal conductivity of our nanofluids
was measured using two techniques: The first by using the hot
wire classical transient method with an industrial instrument(Kd2 Pro) and the second by using a steady-sate method in a coax-
ial cylinder cell (Glory et al., 2008). The results from this instru-
ment were validated by using demineralised water. The values
obtained (shown in Fig. 2) were found to be close to the Maxwell
theory in accordance with the molecular dynamics simulation of
heat flow in a well-dispersed nanofluid (Evans et al., 2006). For
the analysis of our experiments we used the conductivity values
obtained from measurements.
3.4. Dynamic viscosity
The viscosity of nanofluids was measured using a MCR300 An-
ton PAAR rheometer as a function of temperature for the three
mass fractions. The results obtained were compared with currenttheories.
The limiting case for dilute suspensions of small, rigid, spherical
particles was treated by Einstein (1906), and extended to ellipsoi-
dal particles. The viscosity is given by:
l lf1 Bu 5
where B depends on the ratio of the revolution ellipsoid axes and is
equal to 2.5 for spherical particles.
Measurements revealed that all the tested fluids have a dy-
namic viscosity nearly constant from shear rates varying from
100 to 1000 s1. However, Einsteins formula does not allow us
to predict the experimental values.
Results obtained as a function of temperature are given in Fig. 3
for a shear rate of 1000 s
1
which is a mean value in ourexperiments.
4. Experimental set-up and data reduction
4.1. Experimental set-up
4.1.1. Test loop and test section
A test loop was constructed to measure pressure loss and con-
vective heat transfer coefficients with fixed wall temperature
boundary conditions. The experimental apparatus is shown sche-
matically in Fig. 4.
A 1 l copper vessel equipped with drain valves was used as
the nanofluid reservoir. After injection in the reservoir tank,
the nanofluid, with specified concentration, was circulated usinga gear pump (Micropump, Ismatec, 0200 l h1). Assuming that
Fig. 1. SEM picture of SiO2 nanoparticles used (34 wt%)
Table 2
Physical properties of SiO2 particles.
Nanoparticles Meandiameter
(nm)
Density(kgm3)
Thermal conductivityat 25 C (Wm1 K)
Specificheat at
25 C
(J/kg K)
SiO2 22 2200 1.38 740
S. Ferrouillat et al. / International Journal of Heat and Fluid Flow 32 (2011) 424439 427
-
7/28/2019 Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature bou
5/16
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
20 30 40 50 60 70 80
Temperature (C)
Thermalconductiv
ity(W/(m.K
)
SiO2 5%w SSSiO2 16%w SSSiO2 34%w SSSiO2 5%w THWSiO2 34%w THWWaterMaxwell 5%wMaxwell 16%wMaxwell 34%w
Fig. 2. Thermal conductivity versus temperature(SS: Steady State Method, THW: Transient Hot Wire Method).
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
10 20 30 40 50 60 70
Temperature (C)
Viscosity(cP)
SiO2/Water 5%w
SiO2/Water 16%w
SiO2/Water 34%w before destabilizing
SiO2/Water 34%w after destabilizing
Fig. 3. Viscosity versus temperature for SiO2/water nanofluids.
Pump
Gearpump
Nanofluid
reservoir
Test sectionP
T
P Mixer
TPump
AcquisitionSystem
T T
Sewer
heat
exchanger
Heated bath
T
Coriolis
flow
TT T
T T T T
pH meter
Heated bath
Tap water
Fig. 4. Schematic diagram of the experimental loop.
428 S. Ferrouillat et al. / International Journal of Heat and Fluid Flow 32 (2011) 424439
-
7/28/2019 Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature bou
6/16
nanofluids are considered as homogeneous fluids, the flow rate
was measured by a Coriolis flow meter (Micro Motion ELITE,CFM10) that was calibrated with 0.1% accuracy over the range
of 080kg h1. The pressure drop was measured directly by
three differential strain-gauge pressure transducers operating
over a range of 01620 kPa with uncertainty within 0.075% f.s.,
as calibrated by the manufacturer (Rosemount). A pH meter (Eu-
tech Instruments) was inserted downstream of the test section
to follow the nanofluid pH change with a maximum accuracy
of 0.01.
The test section (Fig. 5) consisted of a 0.5 m long tube-in-tube
heat exchanger, the tested nanofluid flowing into the 4 mm diam-
eter and 1 mm thick inner copper tube (CuA1) and heating or cool-
ing water flowing into a 10 mm diameter and 1 mm thick stainless
steel annular tube. The test section was preceded by a 0.5 m (125
diameters) adiabatic section.The nanofluid was circulated inside the inner tube (primary
loop) with a temperature varying between 15 and 90 C. To ob-
serve the potential influence of the transverse temperature gradi-
ent, the water temperature was varied within the same range
allowing us to change the temperature difference between the
fluid and the wall. The fluid could be heated or cooled thanks to
various valves in the experimental loop, and then the gradient
direction could be modified. After passing through the test section,
the nanofluid entered a heat exchanger in which water was used as
a cooling or heating fluid depending on nanofluid heating or cool-
ing tests. For both primary and secondary loops, temperature was
controlled using two thermostatic baths (Polystat 37, Fischer Sci-
entific) and a second heat exchanger.
The entire test section was insulated with polyurethane foam
(Armaflex) in order to minimize heat losses.
A simplified test section of identical dimensions in which
only inlet and outlet fluid temperatures were measured, was alsoused in order to estimate the influence of thermocouple
insertions on heat transfer (Section 4.1.2) and on pressure losses
(Section 5.1).
4.1.2. Temperature measurements in the test section
Two (K-type) thermocouples were inserted into the flow at the
inlet and outlet of the test section for measuring bulk tempera-
tures of nanofluid. In order to increase the outlet temperature
accuracy for laminar flow, a static mixer was inserted down-
stream of the test section. To record the temperature at the
outer surface of the copper tube and the bulk temperature, four
(K-type) thermocouples were brazed on the inner tube wall and
four (K-type) thermocouples were inserted into the inner tube
at equally spaced 10 cm distances. The thermocouples werecalibrated before tests and had a maximum accuracy of 0.1 C.
All the data were recorded by an Agilent 34970 A data acquisition
unit.
To determine inner wall temperature, the thermal resistance
due to conduction through the tube (Fig. 5) was taken into account
(Eq. (8)). To determine inner flow bulk temperature we added a
corrective term by writing an energy balance between forced con-
vective flow perpendicular to the thermocouple and conduction in
the thermocouple between its extremity and the wall. The thermo-
couple is considered as a fin of constant area, and if the heat loss
from its end is negligible, the temperature at the fin tip is given
by the equation (Kaka et al., 1985):
T
TbTw Tb
1
cosh dl 6
4 mm6 mm10 mm12 mm
Copper
Copper
Stainless steel
Stainless steel
TWall (K-type thermocouple)
TBulk (K-type thermocouple)
Fig. 5. Schematic diagram of the test section with thermocouple locations.
S. Ferrouillat et al. / International Journal of Heat and Fluid Flow 32 (2011) 424439 429
-
7/28/2019 Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature bou
7/16
where d is given by:
d ffiffiffiffiffiffiffiffiffi
htP
ktAt
s7
Pis the perimeter of the thermocouple, kt is the average conductiv-
ity of the thermocouple (15 W m1 K1) and At, its cross section
area.
The heat transfer coefficient ht is calculated from the followingcorrelation developed by Churchill and Bernstein (1977):
NuD 0:3 0:62Re1=2D Pr
1=3
1 0:4=Pr2=3h i1=4 1 ReD282000
5=8" #4=58
where NuD = htD/kt, with D being the thermocouple diameter. This
formula holds for all values of ReD and Pr, provided the Peclet num-
ber PeD = ReD Pr is greater than 0.2. As thermocouple temperatures
are close to bulk temperatures, physical properties in dimensionless
numbers are evaluated at Tb.
4.2. Data reduction
The heat flow rate _Q was determined from the mass flow rate _m
and the inlet and outlet temperatures of the fluid:
_Q _mCpTin Tout 9The internal heat transfer coefficient hi between the nanofluid
and the wall was derived from the following expression of the heat
flow rate:
_Q 11hi
Rw
S Twe Tbi 10
where S is the heat exchange area (m2), Twe the average external
wall temperature of the four K-type thermocouples brazed on the
inner tube (K), Tbi the average internal bulk temperature of the four
K-type thermocouples inserted into the inner tube (K), and Rw is thethermal resistance of the copper tube wall (m K W1).
This thermal resistance Rw is given by:
Rw di2kw
lndedi
11
where di and de are respectively the inner and outer diameters of
the inner tube (m),
kw is the thermal conductivity of the inner tube (W m1 K1).
The internal heat transfer coefficient hi (W m2 K1) can thus be
calculated from
hi S Twe Tbi _Q
Rw 1
12
Once the experimental heat transfer coefficient hi is deter-
mined, the experimental Nusselt number must be compared with
the value obtained experimentally with pure water, which is the
base fluid. This comparison is done by plotting the ratio of the Nus-
selt number measured with the nanofluid Nunf and the Nusselt
number measured with pure water Nuf. In each case, the Reynolds
number was deduced from the mass flow rate measurement by:
Re 4 _mpdil
13
where l is the measured fluid dynamic viscosity taken at averagebulk temperature. Knowing the exact value of viscosity is crucial
because incorrect determination of the Reynolds number can cause
a shift in the curves and lead to misinterpretation of the Nunf/Nufratio.
Using three differential strain-gauge pressure transducers, the
pressure drop measurement enables the Darcy coefficient to be de-
duced with the following expression:
Kexp 2DPdhL
qS2pi_m2
14
where the Darcy coefficient is 4 times larger than the fanning
friction factor f. The maximum relative uncertainties of the Rey-nolds number and Darcy coefficient were estimated and are respec-
tively less than 1.9% and 4.3%. The maximum relative uncertainty of
the Nusselt number is highly dependent on the Reynolds number.
For example, this uncertainty is between 78% and 5% for a Reynolds
number between 100 and 12,000. Details of uncertainty calcula-
tions are given in Appendix A.
5. Results and discussion
5.1. Pressure drop
5.1.1. Preliminary tests
To be confident in the experimental loop and its instrumenta-
tion, the pressure drop of pure demineralised water flowingthrough the entire length of the copper tube was measured. Several
measurement conditions were studied as shown in Table 3. Fig. 6
shows experimental results in isothermal, heating and cooling
conditions at several temperature levels (20 C, 50 C, 70 C). In
the heating and cooling conditions, the temperature of one fluid
was 20 C, the other being at 50 or 70 C. These results were
compared with classical relationships.
In laminar flow regime (Re < 2300), the following Poiseuille
equation is used in the calculations:
K 64Re
15
In turbulent flow regime, the Blasius equation is used:
K 0:316Re0:25 16In heat transfer conditions, the Poiseuille and the Blasius laws
are followed provided that the experimental Darcy coefficient is
modified by using a corrective factor as indicated by Petukhov
(1970):
K Kexp lw=l m 17
where lw is the viscosity of the fluid near the wall and l is the vis-cosity of the bulk temperature.
The m exponent was experimentally found to be equal to the
following:
for heating conditions, m = 0.58 for laminar flow and
m = 0.25 in turbulent flow;
for cooling conditions, m = 0.50 for laminar flow and
m = 0.25 for turbulent flow.
Table 3
Measurement conditions.
Reference Measurement
conditions
Inlet internal
temperature (C)
Inlet external
temperature (C)
1 Isothermal 20 20
2 Isothermal 50 50
3 Isothermal 70 70
4 Heating 20 50
5 Heating 20 70
6 Cooling 50 20
7 Cooling 70 20
430 S. Ferrouillat et al. / International Journal of Heat and Fluid Flow 32 (2011) 424439
-
7/28/2019 Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature bou
8/16
-
7/28/2019 Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature bou
9/16
Fig. 8 shows the Darcy coefficient for water and several nano-
fluids versus the Reynolds number. As for demineralised pure
water, using the measured viscosities, nanofluid results correlate
quite well with Poiseuilles law for Re < 1000. Then, Poiseuilles
law underpredicts the measurements for 1000 < Re < 2300 be-
cause of inserted thermocouples. Finally, for Re > 2300, the Cole-
brook correlation seems to concord with experimental results
better than the Blasius law. It should be noted that the greatest
difference between experimental results and the Blasius law or
Colebrook correlation is observed for some results with the
34 wt.% nanofluid. These differences with the Blasius law or
Colebrook correlation are respectively slightly higher than 25%and 10%.
5.2. Heat transfer coefficient
5.2.1. Preliminary tests
As for pressure drop analyses, in order to be confident in the
experimental loop and its instrumentation, the heat transfer
coefficient of pure demineralised water was measured. Several
measurement conditions were studied, as shown in Table 3.
Fig. 9 shows the measured Nusselt number versus the predicted
Nusselt number calculated with the classical correlation of
Gnielinski valid for Re > 2300 in transition and turbulent regime
in heating and cooling conditions (measured conditions 4, 5, 6
and 7) (Gnielinski, 1976):
Nu K=8Re 1000Pr1 12:7
ffiffiffiffiffiffiffiffiffiffiffiffiffiK=8p Pr2=3 1 Pr
Prw
0:111 dh
L
2=3" #19
In this formula, the Darcy coefficient is given by K = (1.82log10-Re 1.64)2, where Re is the Reynolds number, Pr and Prw are the
Prandtl numbers calculated at the water bulk temperature and at
the inner wall temperature respectively, L is the tube length and
dh the hydraulic diameter. The bulk temperature is an average be-
tween the inlet and outlet fluid temperatures.
It can be seen that experimental data correspond well with the
predictions of the correlation to within 20%. It can be noted that
20% is also the Gnielinski range of validity.
0.01
0.1
1
10
10000100010010
Reynolds number
Darcycoefficient
Poiseuille
Blasius
Colebrook 20 m
SiO2/Water 5%w (heating and cooling)
SiO2/Water 16%w (heating and cooling)
SiO2/Water 34%w (heating and cooling)
Water (heating and cooling)
Fig. 8. Darcy coefficient as a function of the Reynolds number for several measurement conditions with water and nanofluids.
0
10
20
30
40
50
60
70
80
90
0 10 20 30 40 50 60 70 80 90
Predicted Nuf
MeasuredNuf
20%
-20%
Water heating (4)
Water heating (5)
Water cooling (6)
Water cooling (7)
Fig. 9. Tube averaged Nusselt number for water tests.
432 S. Ferrouillat et al. / International Journal of Heat and Fluid Flow 32 (2011) 424439
-
7/28/2019 Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature bou
10/16
5.2.2. Results with nanofluids
Figs. 1012 present the Nusselt number versus the Reynolds
number for the three mass fraction nanofluids and pure deminer-
alised water for both heating and cooling conditions.
Significant enhancement of the nanofluid Nusselt number com-
pared to the base fluid in the turbulent regime with nanofluid con-
centration can be observed. There is a strong particle concentration
influence in that the larger the mass fraction, the higher theenhancement is.
Considering Fig. 10, these results can be divided into three
parts. A first part, for Re > 1000, shows that the heat transfer is con-
trolled by turbulence regime flow. As previously observed on pres-
sure drop results, heat transfer results seem to show turbulent flow
regime development below the classical value (Re = 2300) due to
thermocouples inserted in the test section.
A second part, for 200 < Re < 1000, characterises the heat trans-
fer controlled by laminar regime flow.
A third part for Re < 200 shows a probable longitudinal con-
duction effect which implies a Nusselt number decrease (Bontemps,
2005). Indeed, the elementary theory of heat exchangers assumes
that heat is transferred locally from the hot to the cold fluid
through an interposed solid wall which only acts as a thermal
resistance, while conduction along the wall is neglected. In real
equipment, however, heat transfer is actually a multi-dimensional
conjugate problem, in which heat conduction may play a rolenot only in the direction orthogonal to the walls (transverse
conduction), but also in that parallel to them (longitudinal
conduction). As it can be observed in Fig. 10, a strong scattering
of data occurs for Re < 1000. The uncertainty on measured values
was calculated (see Appendix A) and relative errors vary from
78% to 5% from low to high Reynolds numbers. In Fig. 10, an
example of uncertainty for low Reynolds numbers is given. For
high Reynolds numbers, uncertainty is of the order of magnitude
of point sizes.
1
10
100
10000010000100010010
Reynolds number
Nusseltnumber
SiO2/Water 5%w (heating and cooling)
SiO2/Water 16%w (heating and cooling)
SiO2/Water 34%w (heatind and cooling)
Water (heating and cooling)
200
Part 3 Part 2 Part 1
Fig. 10. Nusselt number versus Reynolds number.
0
10
20
30
40
50
60
70
80
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Reynolds number
Nusseltnumber
Water (heating 4)
SiO2/Water 5%w (heating 4)
SiO2/Water 16%w (heating 4)
SiO2/Water 34%w (heating 4)
Water (heating 5)
SiO2/Water 5%w (heating 5)
SiO2/Water 16%w (heating 5)
SiO2/Water 16%w (heating 5)
Fig. 11. Nusselt number versus Reynolds number for heating condition.
S. Ferrouillat et al. / International Journal of Heat and Fluid Flow 32 (2011) 424439 433
-
7/28/2019 Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature bou
11/16
Taking into account the measurement accuracy, it is difficult
to know whether or not some heat transfer intensification/dete-
rioration occurs in laminar regime. For the following analyses,
results below Re < 1000 will not be considered. In Figs. 11 and
12, results in linear scales for heating and cooling conditions
are indicated respectively. It is clearly seen that in turbulent re-
gime and compared to pure water, heat transfer enhancement
occurs when using nanofluids. In order to quantify the possible
intensification of the heat transfer coefficient due to nanofluids
compared to that of the base fluid (pure demineralised water),
the ratio Nunf/Nuf versus the Reynolds number is given in
Fig. 13 (heating and cooling conditions 4, 5, 6 and 7). For
Re > 1000, whatever the measurement conditions, significant
heat transfer enhancement with nanofluid concentration up to+50% with 34 wt.% nanofluid can be observed.
The temperature gradient direction effect (comparison of heat-
ing and cooling condition) must be analysed with caution. Heating
and cooling conditions were not realized at the same bulk temper-
ature. Nevertheless, in most cases, the cooling condition seems to
lead to equal or better heat transfer performance characteristics
than the heating condition.
To compare theses results with the prediction of classical corre-
lation, Fig. 14 shows the experimental ratio Nunf/Nuf versus the
predicted ratio Nunf/Nuf calculated with the classical correlation
of Gnielinski valid for Re > 2300 in transition and turbulent regime.
It can be observed that heat transfer performance characteristics
for all nanofluids concentrations are predicted by the Gnielinski
correlation within 20% if the nanofluid mixture properties are ta-
ken into account.
5.3. Nanofluid stability
We have seen in the selected bibliography that heat transfer
enhancement in various nanofluids has been attributed to different
0
10
20
30
40
50
60
70
80
90
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
Reynolds number
Nusseltnum
ber Water (cooling 6)
SiO2/Water 5%w (cooling 6)
SiO2/Water 16%w (cooling 6)
SiO2/Water 34%w (cooling 6)
Water (cooling 7)
SiO2/Water 5%w (cooling 7)
SiO2/Water 16%w (cooling 7)
SiO2/Water 34%w (cooling 7)
Fig. 12. Nusselt number versus Reynolds number for cooling condition.
0%
20%
40%
60%
80%
100%
120%
140%
160%
0 2000 4000 6000 8000 10000 12000 14000
Reynolds number
Nunf/Nuf
5%w heating (4) 5%w heating (5) 5%w cooling (6) 5%w cooling (7)
16%w heating (4) 16%w heating (5) 16%w cooling (6) 16%w cool ing (7)
34%w heating (4) 34%w heating (5) 34%w cooling (6) 34%w cool ing (7)
Fig. 13. Nunf/Nuf versus Reynolds number.
434 S. Ferrouillat et al. / International Journal of Heat and Fluid Flow 32 (2011) 424439
-
7/28/2019 Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature bou
12/16
mechanisms. There have recently been further discussions thatpoint to particle coatings on heat transfer surfaces as being impor-
tant (Yu et al., 2009) and nanofluid discoloration (Sommers and
Yerkes, 2009).
Studying the thermal performance of the nanofluid at the Rey-
nolds number was difficult due to the increase in fluid viscosity
and the limitations imposed by the pump. However, in order to
collect results at higher Reynolds number for 34 wt.% nanofluids,
some tests were carried out by increasing the nanofluid inlet tem-
perature to higher than 80 C to reduce the apparent viscosity of
the nanofluid. These measurement conditions show the 34 wt.%
nanofluid to be destabilized, leading to a modification of hydraulic
performance. Fig. 15 shows the Darcy coefficient increase after the
nanofluid destabilization, by 1.5 in laminar flow and 3.0 in turbu-
lent flow. According to Ludox product information, most Ludoxapplications involve the use of sols at room temperature, thereby
minimizing concentration by evaporation. Higher temperaturesnot only increase the loss of water by evaporation but also the
movement of the colloidal particles in suspension and the dissoci-
ation of electrolytes present in the system and surfactants avoiding
particle agglomeration. Each of these factors contributes to gela-
tion or formation of silica aggregates.
To validate the hypothesis of the formation of silica aggregates,
after emptying the test section, other tests with pure deminera-
lised water were conducted. Fig. 16 also shows an increase of the
Darcy coefficient after nanofluid destabilizing. These results seem
to indicate that 34 wt.% nanofluid destabilization leads to a coating
of the test surface.
Another test for assessing fluid stability involved analysing fluid
samples after different periods of time and at different tempera-
ture conditions. The 34 wt.% nanofluid was stored in two differentsealed glass beakers for two weeks. The first one was heated to
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
Predicted Nunf/Nuf
MeasuredNunf/Nuf
5%w heating (4 and 5)
5%w cooling (6 and 7)
16%w heating (4 and 5)
16%w cooling (6 and 7)
34%w heating (4 and 5)
34%w cooling (6 and 7)
20%
-20%
Fig. 14. Measured (Nunf/Nuf) versus predicted (Nunf/Nuf).
0.01
0.1
1
10
10000100010010
Reynolds number
Darc
ycoefficient
Poiseuille
Blasius
Colebrook 20 m
Before destabilizing
After destabilizing
Fig. 15. Darcy coefficient evolution after 34%w nanofluid destabilizing.
S. Ferrouillat et al. / International Journal of Heat and Fluid Flow 32 (2011) 424439 435
-
7/28/2019 Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature bou
13/16
88 C for 24 h, the second was left at room temperature. It was
observed that the heated nanofluid showed some particleaggregates with sediment on the beaker bottom confirming the
temperature effect. This type of effect was already observed with
Al2O3 nanoparticles in water by Lee and Mudawar (2007), who
observed sedimentation in long-term use and by Nguyen et al.
(2008), who found a critical temperature beyond which the
particle suspension properties seem to be drastically altered.
Moreover, viscosity measurements of the 34 wt.% nanofluid
after destabilization show a decrease which confirms a formation
of silica aggregates which lead to sedimentation and thus to
coating. By interpolation, we deduce from Fig. 3 a new concen-
tration at roughly 31 wt.%. With this new mass concentration,
we deduce the other new thermal and physical properties of
nanofluids.
From results after nanofluid destabilization presented in Fig. 16,we have estimated a new hydraulic diameter of the test section in
laminar flow regime thanks the following equation deduced from
Eqs. (13) and (14):
dh 128Lp :lm:
qDPexp
14
20
The new hydraulic diameter is roughly 3.5 mm instead of
4.0 mm.
The results after destabilization presented in the Fig. 15 were
modified to take into account the new thermal and physical
properties and hydraulic diameter. The new results are presented
in Fig. 17. It can be observed that in laminar flow regime, the re-
sults follow Poiseuille classical laws up toRe < 1000. But for
1000 < Re < 2300, the Poiseuille law underpredicts the measure-
ments. This deviation may also be associated with the presence
of the four (K-type) thermocouples inserted into the inner tube.
For Re> 2300, the Blasius law underpredicts the Darcycoefficient measurement. It should be noted that the Colebrook
0.01
0.1
1
10
10000100010010Reynolds number
Darcycoefficie
nt
Poiseuille
Blasius
Colebrook 20 m
1 before destabilizing
1 after destabilizing
4 before destabilizing
4 after destabilizing
7 before destabilizing7 after destabilizing
Fig. 16. Darcy coefficient evolution after 34%w nanofluid destabilizing with pure demineralised water.
0.01
0.1
1
10
10000100010010
Reynolds number
Darcy
coefficient
PoiseuilleBlasiusColebrook 20 mColebrook 250 m7 before destabilizing7 after destabilizing7 after destabilizing with new properties and hydraulic diameter
Fig. 17. Darcy coefficient evolution after 34%w nanofluid destabilizing with new physical properties and hydraulic diameter.
436 S. Ferrouillat et al. / International Journal of Heat and Fluid Flow 32 (2011) 424439
-
7/28/2019 Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature bou
14/16
correlation with e = 250 lm absolute roughness seems to concordbetter with the results. This absolute roughness corresponds well
with the estimation of the new hydraulic diameter. Nevertheless,
the above explanation requires further experimental validation
through copper tube roughness measurements, for instance.
5.4. Energetic performance evaluation criterion (PEC)
In general, the results on SiO2/water nanofluids are apparently
attractive in terms of their thermal performance. Nevertheless,
an important point must be discussed. Indeed, the strong increase
of dynamic (and kinematic) viscosity of nanofluids inevitably in-
volves an increase of the pressure losses inside the system. Conse-
quently, even if a heat transfer enhancement is observed, the
required power for the pumping is increased compared to the base
fluid. This is the reason why a significant increase of viscosity may
lead to an unfavourable energetic balance. There are several ways
to characterise the energetic or thermal performance of a fluid
flowing in a specific device (Colburn, AP, 1933) (Sahiti et al.,
2006). We can use the PEC (performance evaluation criterion) de-
fined below and based on an energetic global approach.
It is defined as the ratio of heat transferred to the required
pumping power in the test section:
PEC _m CpTout Tin_v DP 21
where_
m is the mass flow rate (kg/s),_v the volumic flow rate
(m3/s), Tin and Tout the tube inlet and outlet temperatures and DP
the pressure drop (Pa).
Fig. 18 shows the evolution of this energetic criterion with the
Reynolds number in the case of water and of the SiO2/water nano-
fluids. We can notice that all measurements lead to PEC values be-
neath those corresponding to the case of water, which means that
the energy budget is unfavourable.
For specific applications in which the energetic cost is not
important, the use of such nanofluids could be relevant.
6. Conclusions
As seen in the literature survey, heat transfer coefficient
enhancement was generally observed in using nanofluids. However,in a recent experiment it was shown that by using measured
thermophysical properties, the heat transfer in forced convection
experiments with nanofluids was quite similar to that of conven-
tional fluids (Williams et al., 2008). To find possible effects in con-
vection to interpret the literature data we performed experiments
with several conditions: mass fraction varying from a small value
corresponding to that of a nanofluid to a high value, different wall
boundary conditions, imposed flux and, as described in this paper,
imposed temperature.
In this paper, the convective heat transfer of colloidal suspen-
sion of SiO2 nanoparticles in water was studied experimentally.
The flow regime was varied from laminar to turbulent and constant
wall temperature was considered as a thermal boundary condition.
Both flow cooling and flow heating were studied. Results have
shown that with the presence of nanoparticles, heat transfer of
the resulting nanofluid significantly increases compared to the
base fluid (water) in turbulent regime. Such an enhancement has
been found more pronounced with the increase of particle concen-
tration. The Nusselt number increases from 10% to about 50% when
volume concentration varies from 2.3% to 18.93%.
It is shown that, if the measured thermal and physical proper-
ties of the nanofluid were taken into account to calculate the
dimensionless numbers, the existing correlations reproduce the
convective heat transfer and pressure loss behaviour in tubes with-
in the correlations range of validity. Therefore, the merits of nano-
fluids for heat transfer enhancement depend on the compromise
between thermal conductivity increase and viscosity increase. In
this objective, a Performance Evaluation Criterion (PEC) was de-
fined, which indicates that the global energy budget is not favour-able to the studied nanofluid.
Finally, this paper examines nanofluid destabilizing with high
temperature. A temperature influence on fluid stability was
observed.
Based on these results, the use of nanofluids seems to remain
suitable for applications in which an increase in pumping power
is not of great concern. Nevertheless, nanofluid stability must be
carefully studied for an industrial application.
Acknowledgments
This work was partially supported by the Programme Interdis-
ciplinaire Energie Microcond of the CNRS (National Scientific
Research Centre) and the Environment and Energy ManagementAgency (ADEME) under grant No. 0566C00.
1000
10000
100000
1000000
10000000
100000100001000100
Reynolds number
PEC
Water
SiO2/Water 5%w
SiO2/Water 16%w
SiO2/Water 34%w
Fig. 18. Evolution of the PEC versus Reynolds number in cooling condition (6).
S. Ferrouillat et al. / International Journal of Heat and Fluid Flow 32 (2011) 424439 437
-
7/28/2019 Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature bou
15/16
The authors thank Olivier PONCELET from CEA L2T for his work
preparing nanofluids and Marco BONETTI from CEA IRAMIS for
thermal conductivity measurements.
Appendix A
The internal heat transfer coefficient is given by:
hi 1S TweTbi _Q
Rw
If Ui S TweTbi
_Q S TweTbi
_mCpTinTout; the uncertainty of the internal heat
transfer coefficient hi was determined using Moffats method:
dhi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
@hi@Ui
dUi
2 @hi
@RwdRw
2s
where @hi@Ui
1U2i
1Ui
Rw 2
hiUi
2and @hi
@Rw 1
Ui Rw
2 h
2i
In the same way, the uncertainty of Ui is written as:
where @Ui@ _m
Cp TinToutj j
TweTbi jj S Ui
_m
@Ui@S
_mCp Tin Toutj jTwe Tbijj S2
UiS
@Ui@Cp
_m Tin Toutj jTwe Tbijj S2
UiCp
@Ui@ Twe Tbi
_mCp Tin Toutj jTwe Tbijj 2S
UiTwe Tbijj
@Ui@ Tin Tout
_mCpTwe Tbijj S
UiTin Toutj j
The internal heat transfer area S is given by: S= pdiLThus, the uncertainty of S is written as:
dSffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffi
@S
@diddi
2 @S
@LdL
2s
where @S@di
pL and @S@L
pdi
The thermal resistance of the copper tube wall Rw is given by:
Rw di2kCu
ln de
di
In the same way, the uncertainty of the thermal resistance Rc is
written as:
dRw ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
@Rw@di
ddi
2 @Rw
@dedde
2s
where @Rw@di
12kCu
ln dedi
1
and @Rw@de
12kCu
dide
References
Bontemps, A., 2005. Measurements of single-phase pressure drop and heat transfercoefficient in micro and minichannels in Microscale He at transfer:
fundamentals and applications, NATO science series, II: mathematics. Physicsand Chemistry 193, 2548.
Bontemps, A., Ribeiro, J.P., Ferrouillat, S., Gruss, J.A., Soriano, O., Wang, B., 2008a.Experimental study of convective heat transfer and pressure loss of SiO2/waternanofluids. Part 1: nanofluid characterization imposed wall temperature.Thermal Issues in Emerging Technologies, ThETA 2, Cairo, Egypt, 1720thDecember, pp. 275284.
Bontemps, A., Ribeiro, J.P., Ferrouillat, S., Gruss, J.A., Soriano, O., Wang, B., 2008b.Experimental study of convective heat transfer and pressure loss of SiO2/waternanofluids. Part 2: imposed uniform heat flux, energetic performance criterion.Thermal Issues in Emerging Technologies, ThETA 2, Cairo, Egypt, 1720thDecember, 2008, pp. 285292.
Chen, H., Yang, W., Ding, Y., Zhang, L., Tan, C., Lapkin, A.A., Bavykin, D.V., 2008. Heattransfer and flow behaviour of suspensions of titanate nanotubes. PowderTechnology 183, 6372.
Churchill, S.W., Bernstein, M., 1977. A correlating equation for forced convectionfrom gases and liquids to a circular cylinder in cross-flow. Journal of HeatTransfer 99, 300306.
Colebrook, C.F., White, C.M., 1965. Experiments with fluid friction-factor equations.Chemical Engineering 29, 8687.
Ding, Y., Alias, H., Wen, D., Williams, R.A., 2006. Heat transfer of aqueoussuspensions of carbon nanotubes (CNT nanofluids). International Journal ofHeat and Mass Transfer 49, 240250.
Ding, Y., Chen, H., He, Y., Lapkin, A., Yeganeh, M., Siller, L., Butenko, Y.V., 2007.Forced convective heat transfer of nanofluids. Advanced Powder Technology 18(6), 813824.
Einstein, A., 1906. Eine neue Bestimmung der Molekldimensionen (a newdetermination of molecular dimensions). Annalen der Physik 19, 289306.
Evans, W., Fish, J., Keblinski, P., 2006. Role of Brownian motion hydrodynamics onnanofluid thermal conductivity. Applied Physics Letters 88, 093116-1093116-3.
Faulkner, D.J., Rector, D.R., Davidson, J., Shekarriz, R., 2004, Enhanced heat transferthrough the use of nanofluids in forced convection. In: Proceedings of IMECE2004. Anaheim, California, USA.
Glory, J., Bonetti, M., Helezen, M., Mayne-LHermite, M., Reynaud, C., 2008. Thermaland electrical conductivity of water-based nanofluids prepared withlong multi-walled carbon nanotubes. Journal of Applied Physics 103, 094309.
Gnielinski, V., 1976. New equations for heat andmass transfer in turbulent pipe andchannel flow (translated from German). International Chemical Engineering 16
(2), 359368.Hamilton, R.L., Crosser, O.K., 1962. Thermal conductivity of heterogeneous two-
component systems. Industrial & Engineering Chemistry Fundamentals 1 (3),187191.
He, Y., Jin, Y., Chen, H., Ding, Y., Cang, D., Lu, H., 2007. Heat transfer and flowbehaviour of aqueous suspensions of TiO2 nanoparticles (nanofluids) flowingupward through a vertical pipe. International Journal of Heat and Mass Transfer50, 22722281.
Hwang, K.S., Jang, S.P., Choi, S.U.S., 2009. Flow and convective heat transfercharacteristics of water-based Al2O3 nanofluids in fully developed laminar flowregime. International Journal of Heat and Mass Transfer 52, 193199.
Jung, J.Y., Oh, H.S., Kwak, H.Y., 2009. Forced convective heat transfer of nanofluids inmicrochannels. International Journal of Heat and Mass Transfer 52, 466472.
Kaka, S., Yener, Y., 1985. Heat Conduction. Hemisphere Publishing Corporation,Washington.
Kulkarni, D.P., Namburu, P.K., Bargar, H.E., Das, D.K., 2008. Convective heat transferandfluid dynamic characteristics of SiO2ethylene-glycol/water nanofluid. HeatTransfer Engineering 29 (12), 10271035.
Lai, W.Y., Phelan, P.E., Vinod, S., 2008, Convective heat transfer for water-basedalumina nanofluids in single 1.02 mm tube. In: 11th IEEE IntersocietyConference on Thermal and Thermomechanical Phenomena in ElectronicSystems, vols. 13, Intersociety Conference on Thermal andThermomechanical Phenomena in Electronic Systems, pp. 970978.
Lee, C.H., Kang, S.-W., Kim, S.H., 2005. Effects of nano-sized Ag particles on heattransfer of nanofluids. Journal of Industrial Engineering Chemistry 11 (1), 152158.
Lee, S., Choi, S.U.S., 1996, Application of metallic nanoparticle suspensions inadvanced cooling systems. In: International Mechanical Engineering Congressand Exhibition. Atlanta, USA.
Lee, J., Mudawar, I., 2007. Assessment of the effectiveness of nanofluids for single-phase and two-phase heat transfer in micro-channels. International Journal ofHeat and Mass Transfer 50, 452463.
Li, Q., Xuan, Y., 2002. Convective heat transfer and flow characteristics of Cuwaternanofluid. Science in China Series E 45, 408416.
Maxwell, J.C., 1881, 2nd ed. A Treatise on Electricity and Magnetism, vol. 1Clarendon press, Oxford.
Nguyen, C.T., Roy, G., Gauthier, C., Galanis, N., 2007. Heat transfer enhancement
using Al2O3water nanofluid for an electronic liquid cooling system. AppliedThermal Engineering 27, 15011506.
dUi
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
@Ui@ _m
d _m
2 @Ui
@SdS
2 @Ui
@CpdCp
2 @Ui
@ Twe Tbi d Twe Tbi 2
@Ui@ Tin Tout d Tin Tout
2s
438 S. Ferrouillat et al. / International Journal of Heat and Fluid Flow 32 (2011) 424439
-
7/28/2019 Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature bou
16/16
Nguyen, C.T., Desgranges, F., Galanis, C.N., Roy, G., Mar, T., Boucher, S., AngueMintsa, H., 2008. Viscosity data for Al2O3water nanofluid hysteresis: is heattransfer enhancement using nanofluid reliable? International Journal ofThermal Science 47, 103111.
Pak, B.C., Cho, Y. Lee, 1998. Hydrodynamic and heat transfer study of dispersedfluids with submicronic metallic oxide particles. Experimental Heat Transfer 11,151170.
Petukhov, B.S., 1970, Heat transfer and friction in turbulent pipe flow withvariable physical properties. In: Irvine, T.F., Hartnett, J.P. (Eds.), Advances inHeat Transfer Vol. 6. New York, pp. 503564.
Rea, U., McKrell, T., Hu, L.W., Buongiorno, J., 2009. Laminar convective heat transferand viscous pressure loss of aluminawater and circoniawater nanofluids.International Journal of Heat and Mass Transfer 52, 20422048.
Sahiti, N., Lemouedda, A., Stojkovic, D., Durst, F., Franz, E., 2006. Performancecomparison of pin fin in-duct flow arrays with various pin cross-sections.Applied Thermal Engineering 26 (1112), 11761192.
Sommers, A.D., Yerkes, K.L., 2009, Experimental investigation into the convectiveheat transfer and system-level effects of Al2O3propanol nanofluid. Journal ofNanoparticle Research (Published on line).
Wen, D., Ding, Y., 2004. Experimental investigation into convective heat transfer ofnanofluids at the entrance region under laminar flow conditions. International
Journal of Heat and Mass Transfer 47 (24), 51815188.
Williams, W., Buongiorno, J., Hu, L.-W., 2008. Experimental Investigation ofturbulent convective heat transfer and pressure loss of alumina/water andzirconia/water nanoparticle colloids (nanofluids) in horizontal tubes.Transactions on ASME, Journal of Heat Transfer 130, 042412-1042412-7.
Xuan, Y., Li, Q., 2003. Investigation on convective heat transfer and flowfeatures of nanofluids. Transactions on ASME, Journal of Heat Transfer 125,151155.
Yang, Y., Zhang, Z.G., Grulke, E.A., Anderson, W.B., Wu, G., 2005. Heat transferproperties of nanoparticles-in-fluid dispersions (nanofluids) in laminar flow.International Journal of Heat and Mass Transfer 48 (6), 11071116.
Yu, W., France, D.M., Smith, D.S., Singh, D., Timofeeva, E.V., Routbort, J.L., 2009. Heattransfer to a silicon carbide/water nanofluid. International Journal of He at andMass Transfer 52, 36063612.
Zeinali Heris, S., Nasr Esfahany, M., Eternad, S.G., 2006a. Investigation of CuO/waternanofluid laminar convective heat transfer through a circular tube. JournalEnhanced Heat transfer 13 (4), 279289.
Zeinali Heris, S., Nasr Esfahany, M., Eternad, S.G., 2006b. Experimental investigationof oxide nanofluids laminar flow convective heat transfer. InternationalCommunications in Heat and Mass Transfer 33 (4), 529535.
Zeinali Heris, S., Nasr Esfahany, M., Eternad, S.G., 2007. Experimental investigationof convective heat transfer of Al2O3/water nanofluid in circular tube.nternational Journal of Heat and Fluid Flow 28, 203210.
S. Ferrouillat et al. / International Journal of Heat and Fluid Flow 32 (2011) 424439 439