International Journal of Heat and Mass Transfer 54 (2011) 4051–4068

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer

journal homepage: www.elsevier .com/locate / i jhmt

A review of nanofluid stability properties and characterizationin stationary conditions

A. Ghadimi ⇑, R. Saidur, H.S.C. MetselaarDepartment of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia

a r t i c l e i n f o a b s t r a c t

Article history:Received 3 December 2010Received in revised form 1 April 2011Accepted 1 April 2011

Keywords:StabilityNanofluidCharacteristicsThermal conductivityViscosityThermo-physical properties

0017-9310/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.ijheatmasstransfer.2011.04.014

⇑ Corresponding author. Tel.: +60 3 79674451; fax:E-mail addresses: Azadeh_ghadimi@yahoo.com,

edu.my (A. Ghadimi).

A new engineering medium, called nanofluid attracted a wide range of researches on many cooling pro-cesses in engineering applications, which are prepared by dispersing nanoparticles or nanotubes in a hostfluid. In this paper, the stability of nanofluids is discussed as it has a major role in heat transfer enhance-ment for further possible applications. It also represents general stabilization methods as well as varioustypes of instruments for stability inspection. Characterization, analytical models and measurement tech-niques of nanofluids after preparation by a single step or two-step method are studied.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

One of the most significant scientific challenges in the industrialarea is cooling, which applies to many diverse productions, includ-ing microelectronics, transportation and manufacturing. Techno-logical developments such as microelectronic devices operatingat high speeds, higher-power engines, and brighter optical devicesare driving increased thermal loads, requiring advances in cooling.The conventional method for increasing heat dissipation is to in-crease the area available for exchanging heat to use a better heatconductive fluid. However, this approach involves an undesirableincrease in the size of a thermal management system; therefore,there is an urgent need for new and novel coolants with improvedperformance. The innovative concept of ‘nanofluids’ – heat transferfluids consisting of suspended of nanoparticles – has beenproposed as a prospect for these challenges [1].

Maxwell was the first presenter of a theoretical basis to predicta suspension’s effective conductivity about 140 years ago (1873)and his theory was applied from millimeter to micrometer sizedparticles suspensions but Choi and Eastman [2] introduced thenovel concept of nanofluids by applying the unique properties ofnanofluids at the annual Mechanical Engineering meeting ofAmerican Society at 1995. Goldstein et al. [3] added the conditionthat the particles must be in colloidal suspension. Choi and his

ll rights reserved.

+60 3 79675317.Azadeh_ghadimi@siswa.um.

colleagues have carried out experiments on heat transport in sys-tems with CuO nanoparticles in water and Al2O3 particles in ethyl-ene glycol and water. They found that the particles improve theheat transport by as much as 20%, and they interpreted their resultin terms of an improved thermal conductivity k/k0 which theynamed the effective thermal conductivity [3].

A nanofluid is a fluid produced by dispersion of metallic or non-metallic nanoparticles or nanofibers with a typical size of less than100 nm in a liquid. Nanofluids have attracted huge interest latelybecause of their greatly enhanced thermal properties. For instance,experiments showed an increase for thermal conductivity by dis-persion of less than 1% volume fraction of Cu nanoparticles or car-bon nanotubes in ethylene glycol or oil by 40% and 150%,respectively [1]. There are also various potential advantages fromnanofluid testing namely: better long-term stability and thermalconductivity compared to millimeter or even micrometer sizedparticle suspensions and less pressure drop and erosion particu-larly in microchannels. Though, there are still major applicationprospects in advanced thermal applications, they remain in theearly stages of development. About a decade ago, some researchersreported the heat transfer and flow characteristics of the differentnanofluids namely: Trisaksri and Wongwises [4], Beck [5], Wangand Mujumdar [6], Duangthongsuk and Wongwises [7], Godsonet al. [8], Li et al. [9] and Wen et al. [10], Leong et al. [11]. However,prior to use nanofluids for heat transfer, significant knowledgeabout their thermophysical properties is required, especially theirthermal conductivity and viscosity. Many researchers havemeasured the thermophysical properties of nanofluids while many

Nomenclature

E energyEl electrostatic repulsionx interparticle surface-to-surface distanceW weight/stability coefficientM molecular weightN Avogadro’s constantK thermal conductivityk constant rate of aggregationT temperature

Greek symbolsa collision efficiencyk mean free pathl dynamic viscosity

t viscosityq densityU volume fractionW surface potential

SubscriptsA van der Waalsd particleIEP iezo electric pointM maximumNf nanofluidPZC point of zero chargeS nanoparticletot sum

4052 A. Ghadimi et al. / International Journal of Heat and Mass Transfer 54 (2011) 4051–4068

others used well-known predictive correlations. Their works havebeen both experimental and theoretical [12].

This review focuses on the stability of nanofluids, which is crit-ical to eventual utilization of nanofluid in practice. The subject wasput into consideration recently since different investigators reachdifferent results with the same nanoparticles. Therefore, it wasconcluded that stability measurement and investigation for eachnanofluid preparation may be leading to a standard way of prepa-ration and unified data. Hence, experimental studies on prepara-tion and different stability methods of nanofluids are reviewed.Theoretical attempts made to explain the associated characteristicmechanisms are also outlined. In addition to these, the measure-ment methods proposed for the determination of stability are sum-marized and thermophysical property predictions of the modelsare compared with experimental findings, and significant discrep-ancies are specified.

2. Nanofluid preparation methods

Preparing a stable and durable nanofluid is a prerequisite opti-mizing its thermal properties. Therefore, many combinations ofmaterial might be used for particular applications, namely: nano-particles of metals, oxides, nitrides, metal carbides, and other non-metals with or without surfactant molecules which can bedispersed into fluids such as water, ethylene glycol, or oils [1]. Inthe stationary state, the sedimentation velocity of small sphericalparticles in a liquid follows the Stokes law [13]

V ¼ 2R2

9lðqp � qLÞ � g ð1Þ

where V is the particle’s sedimentation velocity; R is the sphericalparticle’s radius; l is the liquid medium viscosity; qP and qL arethe particle and the liquid medium density, respectively and g isthe acceleration of gravity. This equation reveals a balance of thegravity, buoyancy force, and viscous drag that are acting on the sus-pended nanoparticles. According to Eq. (1), the following measurescan be taken to decrease the speed of nanoparticles’ sedimentationin nanofluids, and henceforth to produce an improvement for thestability of the nanofluids: (1) reducing R, the nanoparticles size;(2) increasing l, the base fluid viscosity and (3) lessening the differ-ence of density between the nanoparticles and the base fluid(qP � qL). Clearly reducing the particle size should remarkably de-crease the sedimentation speed of the nanoparticles and improvethe stability of nanofluids, since V is proportional to the square ofR. According to the theory in colloid chemistry, when the size of

particle decreases to a critical size, Rc, no sedimentation will takeplace because of the Brownian motion of nanoparticles (diffusion).However, smaller nanoparticles have a higher surface energy,increasing the possibility of the nanoparticle aggregation. Thus,the stable nanofluids preparation strongly link up with applyingsmaller nanoparticles to prevent the aggregation process concur-rently [14].

Two different techniques apply to produce nanofluids namely:single-step and two-step method.

2.1. Two-step technique

In this method, dry nanoparticles/nanotubes are first produced,and then they are dispersed in a suitable liquid host, but as nano-particles have a high surface energy, aggregation and clustering areunavoidable and will appear easily. Afterward, the particles willclog and sediment at the bottom of the container. Thus, making ahomogeneous dispersion by two step method remains a challenge.However, there exist some techniques to minify this problem likehigh shear and ultrasound. Therefore, we will discuss differentmethods of making a stable nanofluid in the next section. Nanofl-uids containing oxide particles and carbon nanotubes are producedby this method. This method works well for oxide nanoparticlesand is especially attractive for the industry due to its simple pre-paring method. But its disadvantage due to quickly agglomeratedparticles brings about many challenges nowadays. As nanoparti-cles disperse partially, dispersion is poor and sedimentation hap-pens so a high volume concentration is needed increasing theheat transfer (10 times of single step) and accordingly the costwould be as much as loading [15]. The two-step method is usefulfor application with particle concentrations greater than 20 vol.%but it is less successful with metal nanoparticles. However, somesurface treated nanoparticles showed excellent dispersion [16].The first materials tried for nanofluids preparation were oxide par-ticles, mainly because they are easy to make and chemically stablein solution [17].

2.2. Single step technique

In this method nanoparticle manufacturing and nanofluid prep-aration are done concurrently. The single-step method is a processcombining the preparation of nanoparticles with the synthesis ofnanofluids, for which the nanoparticles are directly prepared byphysical vapor deposition (PVD) technique or a liquid chemicalmethod (condensing nanophase powders from the vapor phasedirectly into a flowing low-vapor–pressure fluid is called VEROS).

Fig. 1. Ultrasonic-aided submerged arc nanoparticle synthesis system to produceTiO2 nanofluid [18].

Fig. 2. Schematic diagram of the high-pressure homogenizer for producingnanofluids [18].

A. Ghadimi et al. / International Journal of Heat and Mass Transfer 54 (2011) 4051–4068 4053

In this method drying, storage, transportation, and dispersion ofnanoparticles are avoided, so the agglomeration of nanoparticles isminimized and the stability of the nanofluids is increased. A disad-vantage of this method is that it is impossible to scale it up forgreat industrial functions and is applicable only for low vapor pres-sure host fluids. This limits the application of the method[1,3,6,9,15]. Recently, Chang et al. [18] prepared nanofluids ofTiO2 nanoparticles dispersed in water by a one-step chemicalmethod using a high pressure homogenizer. This method is calledmodified magnetron sputtering. The schematic of the apparatuscan be seen in Fig. 1.

3. Importance of the stability of nanofluid

Preparing a homogeneous suspension is still a technical chal-lenge due to strong van der Waals interactions between nanopar-ticles always favoring the formation of aggregates. To obtainstable nanofluids, some methods are recommended, such as phys-ical or chemical treatment. They are listed as the addition of surfac-tant, surface modification of the suspended particles or applyingpowerful forces on the clustered nanoparticles. Spreading sur-face-active agents have been used to modify hydrophobic materi-als to enable dispersion in an aqueous solution [20–22].Otherwise clogging, aggregation and sedimentation happen andcause declining of suspension characteristics like thermal conduc-tivity, viscosity and increasing specific heat.

There exists a theory that clustering and aggregation is one ofthe main features in stability and extraordinary enhancement inthermal conductivity of nanofluids [23,140] although this theorymay be highly specific to the high aspect ratio nanoparticles,including single wall nanotubes. Philip et al. [24] and Evans et al.[23] claimed that the high aspect ratio structure of the fractal-likeaggregates is a key factor allowing rapid heat flow over large dis-tances. They also stated that well dispersed composites show lowthermal conductivity enhancement but composites with fractalaggregates show significant enhancements, even with considerableinterfacial resistance. Gharagozloo and Goodson [25] also mea-sured fractal dimensions for the 1%, 3% and 5% volume concentra-tions of Al2O3 in H2O and concluded that aggregation is a morelikely cause for the measured enhancements of nanofluid. Con-trarily, another theory shows that agglomeration and clustering re-duce stability and thermal conductivity improvement. Hong et al.[26,110] claimed that ultrasonicated Fe nanofluids, due to theirbroken clusters, got enhancement in thermal conductivityalthough this enhancement reduced as a function of elapsed timeafter production. Therefore, for classification of the stability theorymore experimental works are needed to clarify the role of aggrega-

tion in conductivity enhancement. But generally, to obtain a high-quality suspension, small particles have to meet these two princi-ples: (1) diffusion principle: particles are scattered by a liquidmedium and dispersed into the liquid medium. (2) Zeta potentialprinciple: the zeta potential absolute value among particles mustbe as large as possible, making a common repulsive force betweenthe particles [27].

According to the literature, there are three effective tactics usedto manage stability of suspension against sedimentation of nano-particles. Some of the researchers applied all of these methods togain better stability [28–30] but others just applied one [31] ortwo techniques [32–34] with satisfaction. There is no standard torecognize the superlative mix up of combining methods. This areaacquires more experiments to be clarified. The techniques are sum-marized below:

3.1. Surfactant or activator adding

This is one of the general methods to avoid sedimentation ofnanoparticles. Addition of surfactant can improve the stability ofnanoparticles in aqueous suspensions. The reason is that thehydrophobic surfaces of nanoparticles/ nanotubes are modified tobecome hydrophilic and vice versa for non-aqueous liquids. Arepulsion force between suspended particles is caused by the zetapotential which will rise due to the surface charge of the particlessuspended in the base fluid [35,36]. However, care should be takento apply enough surfactant as inadequate surfactant cannot make asufficient coating that will persuade electrostatic repulsion andcompensate the van der Waals attractions [37]. The effect of sur-factant on aggregated particle size distribution can be demon-strated as shown in Fig. 3.

Popular surfactants that have been used in literature can be listedas sodium dodecylsulfate (SDS) [35,37–41], SDBS [21,28,29,39],salt and oleic acid [38,42,139], cetyltrimethylammoniumbr-omide (CTAB) [32,138], dodecyl trimethylammonium bromide(DTAB) and sodium octanoate (SOCT) [43], hexadecyltrimeth-ylammoniumbromide (HCTAB), polyvinylpyrrolidone (PVP)[22,44,45] and Gum Arabic [39]. Choosing the right surfactant isthe most important part of the procedure. It could be anionic,cationic or nonionic [46].

Fig. 3. Particle size distributions of nano-suspensions. (a) Al2O3–H2O without SDBS, (b) Al2O3–H2O with SDBS, (c) Cu–H2O without SDBS and (d) Cu–H2O with SDBS.Concentration of nanoparticles and SDBS surfactant are 0.05% weight fraction, respectively [29].

4054 A. Ghadimi et al. / International Journal of Heat and Mass Transfer 54 (2011) 4051–4068

The disadvantage of surfactant addition is for applications at thehigh temperatures [10,14,47] as above than 60 �C [32,48] thebonding between surfactant and nanoparticles can be damaged.Therefore, the nanofluid will lose its stability and sedimentationof nanoparticles will occur [6].

3.2. pH control (surface chemical effect)

The stability of an aqueous solution nanofluid directly links toits electrokinetic properties. Through a high surface charge density,strong repulsive forces can stabilize a well-dispersed suspension[27–29,49–53]. Xie et al. [54] showed that by simple acid treat-ment a carbon nanotube suspension gained a good stability inwater. This was caused by a hydrophobic-to-hydrophilic conver-sion of the surface nature due to the generation of a hydroxylgroup. The isoelectric point (IEP) is the concentration of potentialcontrolling ions at which the zeta potential is zero. Thus, at theIEP, the surface charge density equals the charge density, whichis the start point of the diffuse layer. Therefore, the charge densityin this layer is zero. Critical to nanoparticle nucleation and stabil-ization in solution is that the repulsive energy is smaller for smallparticles, so a larger zeta potential is required for suspension sta-bility [18]. As the pH of the solution departs from the IEP of parti-cles the colloidal particles get more stable and ultimately modifythe thermal conductivity of the fluid. The surface charge state isa basic feature which is mainly responsible for increasing thermalconductivity of the nanofluids [52,53]. Also in some experimentsparticles’ shape conversion was related to the pH variation [49,55].

In the liquid suspension, particles attract or repel each other.This interaction depends on the distance between particles andthe total interface energy Etot that is the sum of the van der Waalsattraction EA and the electrostatic repulsion Eel between them. TheEel between two charged particles with the surface potentials Wd1

and Wd2 is approximated by the DLVO theory:

Fig. 4. The interaction potentials at various pHs as a function of interparticle

Eel ¼�0�1r1r2

r1 þ r22Wd1Wd2In

1þ expð�kxÞ1� expð�kxÞ

� �þ ðW2

d1 þW2d2Þ ln½1� expð�2kxÞ�

� �ð2Þ

where r is the radius of particles, x is an interparticle surface-to-sur-face distance, and the other symbols have their conventionalmeanings.

It is notable that higher potentials (Wd or f) lead to a bigger po-tential barrier for agglomeration. In aqueous nanofluid of CuO with0.3 vol.% and PZC of about 8.5–9.5, the interparticle distance isabout 100 nm for mobility-equivalent spherical particles. At thiscondition, the second term in the bracket of above equation is neg-ligible compared to the first. Thus, the repulsion energy of thesame-sized particles goes up approximately in proportion to f2.

The attraction energy between the same particles is given bythe Hamaker equation: EA = �A132r/(12x). The Hamaker constantA132 of metal oxide is typically on the order of 10�20 J. Using theabove equation, the Hamaker equation, and the estimated Wd, Etot

is calculated as a function of x at different pHs as shown in Fig. 4. Inthis condition, the repulsion barrier gets bigger than the attractionas pH goes from the PZC, which makes the colloids more stable. AtpH 8 or 10 when W is small, however, the repulsion barrier disap-pears, and particles are only subjected to the attractions. Strongparticle agglomeration is expected in that situation. Here, we needto quantify the suspension stability in terms of collision efficiency,

distance [53].

A. Ghadimi et al. / International Journal of Heat and Mass Transfer 54 (2011) 4051–4068 4055

a, which is responsible for colloidal particle growth. The a, a reci-procal value of stability coefficient W, is related to the rate con-stant of aggregation, k = akdiff = kdiff/W.

The kdiff represents the rate constant of the coagulation betweenuncharged particles. Then a general relation of stability coefficientW to total interaction energy Etot can be derived [53]

W ¼ 2rZ 1

0exp

Etot

kbT

� �dx

ð2r þ xÞ2ð3Þ

For example, as the pH of the nanofluid goes far from the isoelectricpoint, the surface charge increases by applying SDBS surfactant inCu–H2O nanofluid. Since more frequent attacks occur to the surfacehydroxyl and phenyl sulfonic group by potential-determining ions(H+, OH� and phenyl sulfonic group), zeta potential and the colloi-dal particles increase. So the suspension gets more stable and even-tually changes the thermal conductivity of the fluid [21].

Lee [56] also worked on different pH of nanofluids with Al2O3.The experiments indicated that when the nanofluid had a pH of1.7, the agglomerated particle size was reduced by 18% and whenthe nanofluid had a pH of 7.66, the agglomeration size was in-creased by 51%. More particles aggregated in pH of 7.66 becauseof reduction in electric repulsion force. When Al2O3 particles areimmersed in water, hydroxyl groups (–OH) are produced at thesurface of the Al2O3 particle. The relevant reactions depend onthe solution pH. When the pH of the solution is lower than thePZC, the hydroxyl groups react with H+ from water which leadsto a positively charged surface. Alternatively, when the pH of thesolution is higher than the PZC, the hydroxyl groups react withOH� from water and create a negatively charged surface [107]. Inaddition, as it is demonstrated from Table 1, the particle sizes differwhen the pH of nano-suspensions change [39].The optimized pH isdifferent for different nanoparticles. For example, the proper pH foralumina is around 8 meanwhile for copper and graphite nanopar-ticles are 9.5 [57] and about 2.0 respectively. The pH for the pointof zero charge also changes by temperature variation as is shownin Table 2 [50].

3.3. Ultrasonic vibration

All the mentioned techniques aim to change the surface proper-ties of suspended nanoparticles and to suppress forming clusters ofparticles, with the purpose of attaining stable suspensions. Ultra-sonic bath, processor and homogenizer are powerful tools forbreaking down the agglomerations in comparison with the otherslike magnetic and high shear stirrer as experienced by researchers

Table 1Particle size change of Al2O3/distilled water nanofluids with two pH values [39].

Nanofluid Al2O3/DI Al2O3/DI/PBSa/HCl Al2O3/DI/PBS

pH 1.7 7.66Mean particle size (nm) 170 139 1033

a Phosphate buffered saline contains sodium chloride, sodium phosphate andpotassium phosphate and helps to keep a constant pH.

Table 2Values of pHpzc of the TiO2 between 5 and 55 �C [50].

Temperature (�C) PHPZC

5 6.6215 6.3925 6.1735 5.9745 5.7855 5.61

[38]. However occasionally after passing the optimized duration ofthe process, it will cause more serious problems in agglomerationand clogging resulting in fast sedimentation. Furthermore, there isa new method to get stable suspensions proposed by Hwang et al.[38] which consists of two micro-channels, dividing a liquid streaminto two streams. Both streams are then recombined in a reactingchamber. Breaking the clusters of nanoparticles was studied usingthe high-energy of cavitations [58]. This work was conducted forCarbon Black with water and silver with silicon oil nanofluids.When the suspension contacted with the interior walls of theinteraction chamber, it will flow through the microchannel. There-fore, the flow velocity of the suspension through the microchannelshould be increased according to Bernoulli’s theorem, and concur-rently cavitations extensively occurred. In this fast flow region,particle clusters must be broken by the combination of variousmechanisms, including (i) strong and irregular shock on the wallinside the interaction chamber, (ii) microbubbles formed by cavita-tion-induced exploding energy, and (iii) high shear rate of flow.This leads to obtain homogeneous suspensions with fewer aggre-gated particles at high-pressure. This procedure can be repeateda number of three times to achieve the required homogeneousnanoparticle distribution in the base fluids. A schematic of thismethod is presented in Fig. 2.

An ultrasonic disruptor is a more general accessible apparatusthan the one prepared by Hwang et al. [38]. Many researchers usedthis technique to obtain a stable nanosuspension. In some cases,they mixed different methods of stabilization to fine-tune the re-sults. A summary of investigators who reached diverse durationof stability using ultrasonic methods is given in Table 3. Althoughit was noted that typically it is rare to maintain nanofluids synthe-sized by the traditional one-step and two-step methods in a homo-geneous stable state for more than 24 h (Peterson & Li, 2006) [107]we gathered.

4. Stability inspection instruments

There are some instruments and methods that can rank the rel-ative stability of nanosuspension. The list includes UV–Vis spectro-photometer, zeta potential, sediment photograph capturing, TEM(Transmission Electron Microscopy) and SEM (Scanning ElectronMicroscopy), light scattering, three omega and sedimentation bal-ance method. Therefore, the rate or percentage of sedimentationwill be identified by analyzing gathered data.

4.1. UV–Vis spectrophotometer

Even though the stability of a nanofluid is the key issue for itsapplication, there are limited studies on estimating the stabilityof a suspension. Ultra Violet–Visible spectrophotometer (UV–Vis)measurements have been used to quantitatively characterize col-loidal stability of the dispersions. One of the most striking featuresof this apparatus is its applicability for all base fluids, whereas zetapotential analysis has restrictions for the viscosity of the host fluid.

An UV–Vis spectrophotometer exploits the fact that the inten-sity of the light becomes different by absorption and scatteringof light passing through a fluid. At 200–900 nm wavelength, theUV–Vis spectrophotometer measures the absorption by liquidand is used to analyze various dispersions in the fluid [56]. Typi-cally, suspension stability is resolved by measuring the sedimentvolume versus the sediment time. However, this method is unsuit-able for nanofluid dispersions with a high concentration and espe-cially for CNT solutions. These dispersions are too dark todifferentiate the sediment visibly. Jiang et al. [37] were the firstinvestigators who proposed sedimentation estimation using UV–Vis spectrophotometer for nano suspensions. In this method, the

Table 3Summary of different ultrasonic processes.

Investigator Nanoparticle Base fluid Concentration Stability process Duration Sedimentation

[59] Al2O3 (45 nm) DW 1–5.5 vol.% Ultrasonic cleaner 15 h Minutes after preparationEG 1–8 vol.%

[60] Al2O3 (11 nm) DW 0.8 vol.% Ultrasonication 6 h N/A[61] Al2O3 (38.4 nm) DW 1–4 vol.% Ultrasonication 11 h After 12 hours

CuO (28.6 nm) 1–4 vol.%[62] CuO (10 nm) DI 0.003 vol.% Ultrasonication 2–7 h N/A[35] MWCNT DI + SDS 0–1.6 vol.% N/A N/A N/A

(10�50 � 10�30 nm) Oil + SDSFullerene (10 nm) DI + SDS 0–1.6 vol.% N/A N/A N/A

Oil + SDSMixed fullerene (10 nm) EG + SDS 0–1.6 vol.% N/A N/A N/AC70 and C60 Oil + SDS

DI + SDSCuO (33 nm) EG + SDS 0–1.6 vol.% N/A N/A N/A

DI + SDSSiO2 (12 nm) DI + SDS 0–1.6 vol.% N/A N/A N/A

[29] Al2O3 (25 nm) DW + SDBS 0–0.08(N.P) wt.%

Ultrasonication, pH control and Surfactantadding

15 min N/A

DW 0–0.14 wt.%(SDBS)

1 h

Cu (25 nm) DW + SDBS 15 minDW 1 h

[12] TiO2 (21 nm) DW 0–1.2 vol.% Ultrasonication 2 h N/A[31] Al2O3 (43 nm) DW (0.33–5) vol.% Ultrasonication 6 h N/A[63] TNT (10 � 100 nm) EG (0.5-8) wt.% Ultrasonic bath 48 h More than 2 months stability[26] Fe (10 nm) EG (0.2–

0.55) vol.%Ultrasonic 10–

70 minOptimized 30 min

cell disrupter[53] CuO (25 nm) DW 0.3 vol.% N/A N/A[21] CuO (25 nm) DW + SDBS 0.1 wt.% Ultrasonic vibrator, pH control and

surfactant addition1 h N/A

[22] Graphite (nm) DW + PVP 0.5 wt.% Ultrasonic vibration 30 min N/A[42] Fe3O4 (15 nm) Kerosene + oleic

acid0–1.2 vol.% Ultrasonication 0–

80 minStable

[64] ZnO (20 nm) ammonium poly 0.02 vol.% Horn ultrasonic 0–60 min

Stable over 10,000 h

(40–100 nm) methacrylate + DI[39] Al2O3 (40–50 nm) DW 1 vol.% Horn ultrasonic 0–

30 minParticle size reduction

Ultrasonic bath 8 h[40] MWCNT

(10�30 nm � 10�50 lm)DW + SDS 0–1 vol.% Ultrasonic disruptor 2 h Surfactant adding avoid

entanglementSiO2 (7 nm) DW StableCuO (35.4 nm) DW StableCuO (35.4 nm) EG Stable

Table 4Summary of different nanofluids peak absorption measured by UV–Visspectrophotometer.

Nanoparticle Base fluid Peak wavelength Investigator

MWCNT and fullerene Oil 397 [35]Aligned CNT DW 210 [67]CNT DW 253 [37]Tio2 DW 280–400 nm [18]Cu DW 270 [27]CuO DW 268 [27]Ag DW 410 [44]

4056 A. Ghadimi et al. / International Journal of Heat and Mass Transfer 54 (2011) 4051–4068

first step is to find the peak absorbance of the dispersed nanopar-ticles at very dilute suspension by scanning. As the concentrationof suspension has a linear relation with absorbance, preparing astandard to fit a linear relation to at least three different dilute con-centrations (0.01–0.03%) will be the next step in this method. Rel-ative stability measurement will be followed by preparing thedesired concentration of nanofluid and put aside for a couple ofdays. Whenever it is needed to check the relative stability, thesupernatant concentration will be measured by UV–Vis spectro-photometer and the concentration can be plotted against time. Thismethod was used by Refs. [35,56,65,66]. There also exist a sum-mary from different nanofluid peak absorptions by UV–Vis spec-trophotometer in Table 4.

According to Mie’s theory [68], the surface plasmon absorptionand the plasmon bandwidth are dependent on the size of metallicparticles in the solution. Consequently, the peak value representsthe most populated nanoparticle size in the solution. Additionally,by increasing the particle size especially smaller than 20 nm, thebandwidth decreases. Contrarily, the bandwidth of the surfacePlasmon for the particles larger than 20 nm, increases with the par-ticle size [69,70]. As the particle size increases, the local peak in theUV–Vis spectra shifts towards longer wavelength [71]. Tsai et al.[71] have conducted a series of tests on this theory. The sizes of

Au nanoparticles from different preparation methods measuredby TEM and peak wavelength are summarized in Table 5.

4.2. Zeta potential test

Zeta potential measurement is one of the most critical tests tovalidate the quality of the nanofluids stability via a study of itselectrophoretic behavior [53,72]. According to the stabilizationtheory [7], the electrostatic repulsions between the particles in-crease if zeta potential has a high absolute value which then leadsto a good stability of the suspensions [22].

Table 5Volumes of gold nanofluid in different synthesis conditions [71].

Condition Basefluid Na3

citrate(ml)

Tannicacid(ml)

HAuCl4

(ml)Particlesize(nm)

Peakwavelength

A DW 0.2 2.5 3 21.3 528B DW 0.2 5 6 43.7 530.5C DW 3 0.1 1 8 568.5E DW 3 2.5 6 9.3 647G DW 3 0.1 3 15.6 721.5

Fig. 6. Octahedral-Cu2O nanofluids 24 h after their preparation (CuSO4 molarconcentration from 0.0025 mol/L to 0.002 mol/L) [49].

A. Ghadimi et al. / International Journal of Heat and Mass Transfer 54 (2011) 4051–4068 4057

The experiments are conducted by using a 0.05% weight fractionof nanosuspension to measure zeta potential and particle size [29].

The relationship between suspension stability and zeta-poten-tial arises from the mutual repulsion that occurs between like-charged particles. For this reason, particles with a high surfacecharge tend not to agglomerate, since contact is opposed. Typicallyaccepted zeta-potential values are summarized below in Table 6.Generally, a suspension with a measured zeta-potential above30 mV (absolute value) is considered to have good stability[73,74] this is one of the most common methods among theresearchers to determine the stability as mentioned above.

4.3. Sediment photograph capturing

A primary method to find out about sedimentation of nanofluidsis photo capturing. After preparation, some amounts of the suspen-

Table 6Zeta potential and associated suspension stability [74].

Z potential (absolute value [mv]) Stability

0 Little or no stability15 Some stability but settling lightly30 Moderate stability45 Good stability, possible settling60 Very good stability, little settling likely

Fig. 5. Variation of the nanofluids viscosity with pH and nanoparticles weight fraction atviscosity with nanoparticles concentration, (c) the sediment photograph of Al2O3–H2O sususpensions after depositing for seven days [57].

sion will put aside to capture photos after certain period of time. Bycomparing these photos of nano suspensions, sedimentation of sus-pension will be apparent. Different sets of nanofluid preparation forthe photo capturing can be seen at Figs. 5–7. Clearly variable pH, vis-cosity and weight fractions for Al2O3 and Cu and Cu2O were investi-gated after seven days and 24 h by photo capturing.

4.4. TEM (Transmission Electron Microscopy) and Scanning ElectronMicroscope (SEM)

TEM and SEM are very useful tools to distinguish the shape, sizeand distribution of nanoparticles. Nevertheless, it cannot presentthe real situation of nanoparticles in nanofluids when dried sampleare needed. Cryogenic electron microscopy (Cryo-TEM, Cryo-SEM)might provide a method to resolve this problem if the microstruc-ture of nanofluids is not changed during cryoation. Nanoparticles

temperature 303 K: (a) the variation of the viscosity with pH, (b) the variation of thespensions after depositing for seven days, (d) the sediment photograph of Cu–H2O

Fig. 7. TEM pictures of (left) Cu nanofluids, (middle) CuO nanoparticles and (right) alkanethiol terminated AuPd colloidal particles [1].

Fig. 8. SEM of carbon nanotube (a) single-walled carbon nanotubes obtained by arc discharge and (b) multiwalled carbon nanotubes obtained by chemical vapor depositiongrowth [1].

Fig. 9. TEM micrograph of nanoparticles (a) nano-alumina (b) nano-copper [29].

4058 A. Ghadimi et al. / International Journal of Heat and Mass Transfer 54 (2011) 4051–4068

aggregation structure in nanofluids could be directly monitored bythis instrument as well [14].

The following procedure is attributed to the standard SEM/TEMmicrographs of nanoparticles [75]:

(1) Obtain stable nanofluid in solution form.(2) Drop one drop of the solution on sticky tape of top surface of

the SEM specimen holder (carbon grid in the case of TEM).(3) Heat in the vacuum oven to dry the liquid drop or dried in

the air naturally.(4) Obtain solid particle.(5) Bring into the vacuum chamber of SEM/TEM for picture after

coating with Au and Pd.

The stable nanofluids have different shapes after preparation asare shown in TEM and SEM images in Figs. 7–11.

4.5. Light scattering method

The single-particle analysis from which the light scatteringtheory can be approached has been used to visualize polymer mol-ecule structure in solutions or colloidal particles in suspension. Theintensity of scattered light for a single particle is related to theparticle volume. While the interaction of electromagnetic radiationwith a small particle is weak in light scattering, most of the inci-dent light is transmitted and only a little amount of light is distrib-uted. In one study, the average size of the clusters was obtainedevery five minutes after the sonication stopped [26].

4.6. Sedimentation balance method

The stability of the nano-suspension can be also measured byanother method named a sedimentation balance. The tray of a sed-

Fig. 10. TEM photographs of Au, Al2O3, TiO2 and CuO particles and carbon nanofibers [41].

A. Ghadimi et al. / International Journal of Heat and Mass Transfer 54 (2011) 4051–4068 4059

imentation balance is immersed in the fresh nano-suspension. Theweight of sediment nanoparticles during a certain period of time ismeasured. The suspension fraction (Fs) of nanoparticles at an ac-cepted time is calculated by the formula Fs = (W0 �W)/W0 in whichW0 is the total weight of all nanoparticles in the measured space,and W is the weight of the sediment nanoparticles at a certain time[22].

4.7. Three omega method

The colloidal stability of nanofluid can also be determined bythe three omega method. It can be evaluated by detecting the ther-mal conductivity growth caused by the nanoparticle sedimentation

in a wide nanoparticle volume fraction range. There are a few sta-bility measurements attributed to this method in the literature[59,76,111].

5. Characteristic measurement

There are four major thermophysical properties that changetheir values due to nanoparticle addition to the host fluid whichis thermal conductivity, viscosity, density and specific heat. Differ-ent investigators have unlike ideas about the effect of nanoparticledispersion. Typically, these nanofluid properties will increase ex-cept for the specific heat which decreases. The percentage of incre-

Fig. 11. Bright field TEM micrographs of ZnO aggregates from (a) As-mixed suspension from powder A, (b) same suspension, ultrasonically agitated for 60 min with horn, (c)as-mixed suspension from powder B and (d) same suspension, ultrasonically agitated for 60 min with horn [64].

4060 A. Ghadimi et al. / International Journal of Heat and Mass Transfer 54 (2011) 4051–4068

ment will vary as the function of dispersion, volume concentration,temperature, base fluid. There is not a standard for preparation ofnanofluid since then it would be obvious if the data will vary fromtime to time.

5.1. Thermal conductivity

Thermal conductivity is the most important factor that can beinvestigated to prove the heat transfer enhancement of a preparednanofluid. Reviewing available literature explains that the rise inthermal conductivity of the nanofluids is large. Addition of only asmall volume percent of solids produces a dramatic enhance ofthermal conductivity [4,6,77,78].

Several mechanisms for this strange enhancement of thermalconductivity have been already discussed. Among them, Brownianmotion, interfacial layer and aggregation of particles have beentalked about comprehensively [79–88]. Some researchers dis-cussed a nanofluid as a two-phase flow mixture and utilized theo-ries of a two-phase mixture or properties of nanofluid, such asMaxwell’s theory [89] and the Hamilton and Crosser approach

Fig. 12. Aggregation effect on the effective thermal conductivity [10].

[90]. These models are based on an effective medium theory thatpresumes well dispersed particles in a fluid medium. If aggregatedparticles in the fluid bring about particle chains or clusters, the pre-dicted thermal conductivity would be significantly higher as wasobserved by many researchers [10,91] and might be of a strongfunction of the aggregates dimension and the radius of gyrationof the aggregates. This result is based on the three-level homogeni-zation theory, validated by MC (Monte Carlo) simulation of heatconduction on model fractal aggregates [23,25,92]. As it can beseen in Fig. 12, they related the enhancement of thermal conduc-tivity to nanoparticle aggregation. It is seen that there should bean optimized aggregation structure for achieving maximum ther-mal conductivity, which is far beyond the prediction from homoge-neous dispersions. Such an argument eliminates thermalconductivity as an intrinsic physical characteristic. Possible influ-ence of particle aggregation on conduction highlights the colloidchemistry’s significant role in optimizing this property of nanofl-uids. Meanwhile, there exists another theory of lowering thermalconductivity of aggregation forming as found by Hong et al.[26,110] from experiments by light scattering of Fe nanoparticlesaggregate.

The effective thermal conductivity increment may also dependson the shape of nanoparticles as discussed by Zhou and Gao [93–95]. They proposed a differential effective medium theory basedon Bruggeman’s model [79] to approximate the effective thermalconductivity of nano-dispersion with nonspherical solid nanoparti-cles with consideration of the interfacial thermal resistance acrossthe solid particles and the host fluids. They found that a highenhancement of effective thermal conductivity can be gained ifthe shape of nanoparticles deviates greatly from spherical.

Many of the researchers suggested altogether new mechanismsfor the transport of thermal energy [79]. There is another idea pro-posed by Keblinski et al. [1] of an ordered liquid layer at particleinterfaces and ‘tunneling’ of heat-carrying phonons from one par-ticle to another. The subsequent simulation work from the samegroup of investigators concludes that these mechanisms do notcontribute considerably to heat transfer. Koo and Kleinstreuer[96] found that the role of Brownian motion is much more signif-icant than the thermophoretic and osmo-phoretic motions. In con-

A. Ghadimi et al. / International Journal of Heat and Mass Transfer 54 (2011) 4051–4068 4061

clusion, some investigators believe that nanoparticle aggregationplays an important role in thermal transport due to their chainshape [23,97] but some others believe that the time-dependentthermal conductivity in the nanofluids proves the reduction ofthermal conductivity by passing time due to clustering of nanopar-ticles with time [98].

Vadasz [72] showed that heat transfer enhancement may becaused by a transient heat conduction process in nanofluids. Exper-iments demonstrate that a nanofluids thermal conductivity de-pends on a great number of parameters, such as the chemicalcomposition of the solid particle and the base fluid, surfactants,particle shape, size, concentration, polydispersity, etc., though theexact variation trend of the conductivity with these factors hasnot yet been found. Additionally, the temperature influences thethermal conductivity of a nanofluid as shown in several studiesthat have been carried out to see that effect on CuO, Al2O3, TiO2,

ZnO dispersed nanofluids by Mintsa et al. [38], Duangthongsukand Wongwises [39], Vajjha and Das [40], Murshed et al. [41], Yuet al. [42] and Karthikeyan et al. [98]. A temperature increase im-proves the thermal conductivity of the nanofluids. However, theactual mechanism of this increment has not been revealed yet. Adeficiency of reliable data for the conductivity of nanofluid is themajor problem of non-commercialization for this product.

The other influencing factor for the thermal conductivity in-crease of nanosuspension is the volume fraction which has been di-rectly proportional with this characteristic [31], although thisrelationship is generally nonlinear for nanoparticles with a high as-pect ratio [99]. Thermal conductivity increment data for DI (De-Ionized) water based suspensions were investigated by Wanget al. [80], which showed a high rise in comparison with the resultsof Lee et al. [100] and Das et al. [101]. Moreover, experiments con-ducted by Oh et al. [59] for EG based nanofluids data showed rel-atively low thermal conductivity values compared to those of Leeet al. [100] and Wang et al. [80].

It has been found that the thermal conductivity of a base fluid isnearly constant at different doses of surfactant or base. Hence itseems that this property improvement is related only to the parti-cles when dispersing the nanoparticles into water. The generalbehavior of the particle-water interaction depends on the proper-ties of the particle surface. Addition of surfactant may cause highor low pH value, which result in a lower surface charge and aweaker repulsion between particles. Therefore, this action leadsto a stronger coagulation [29].

Yimin et al. [81] developed a classic theory of Brownian motionand the Diffusion Limited Aggregation (DLA) model for randommovement of suspended nanoparticles. This theory does not

Table 7Summary of different tests that conduct to a theory.

Investigator Nanofluid type Concentration(%)

Thermal conductivityenhancement

Karthikeyanet al. [98]

CuO(8 nm) + DW + EG

1 vol.% 31.6%54%

Kwak et al. [102] CuO (10–30 nm) + EG

<0.002 vol.%

Lee et al. [53] CuO(25 nm) + DW

0.3 vol.% 3 times increasing

pH from 8 to 3Wang et al. [57] Al2O3 (15–

50 nm) + DW0.4 wt.% 13%

Cu(25–60 nm) + DW

15%

Li et al. [21] Cu + DW 0.1 wt.% 10.7%Zhu et al. [22] Graphite

(106 nm) + DW2.0 vol.% 34%

Wei et al. [49] Cu2O(200.5 nm) + DW

0.01–0.05 vol.%

24%

describe the experimentally determined thermal conductivity sat-isfactorily, however, the dependence of this characteristic on tem-perature is also mentioned in their work.

The effect of particle surface charge and IEP is also exposed invarying thermal conductivity experiment sets conducted by Leeet al. [53]. They proved that the colloidal particles get more stableand enhance thermal conductivity of nanofluid when the pH ofthe solution goes far from the IEP of particles. Moreover, research,demonstrated that there is a priority factor in controlling nano-fluid aggregation by surface charge. They proposed a new inter-pretation of the charged sites and ion densities in the diffuselayer as the number and efficiency of channels for phonon trans-port, respectively. The same theory was accepted by Wang et al.[57,29,21].

In conclusion, understanding the mechanism and magnitude ofeffective thermal conductivity (keff) of nano-scale colloidal suspen-sions still continues to be an active research area. A summary ofexperiments and proposed theories is given in Table 7.

5.1.1. Analytical modelEven though many models have been developed to predict the

nanofluid thermal conductivity, all presented models can be classi-fied into two general groups, as follows:

i. static models such as those of Maxwell and Hamilton–Crosser, which presume immobile nanoparticles in the hostfluid in which conduction-based models predict the thermaltransport properties, and

ii. dynamic models, which are based on the idea that nanopar-ticles have sideways, arbitrary movement in the fluid. Theparticle motion is believed to be responsible for energytransport directly through collision between nanoparticlesor indirectly through micro liquid convection that enhancesthe thermal energy transfer.

A simple relationship suggested by Weber shows the thermalconductivity of liquids with accuracy usually within 15% and theequation is:

k ¼ 3:59� 10�9CpqqM

� 13 ð4Þ

This formula has been developed previously to calculate the ther-mal conductivity of nanofluids [28], as:

knf ¼ 3:59� 10�9Cp;nf qnf

qnf

Mnf

� �13

ð5Þ

Theory

Nanoparticle size, polydispersity, particle clustering and the volume fraction ofparticlesThermal conductivity enhancement due to viscosity increase

Setting pH far from isoelectric point getting 3 times effective thermalconductivity and better dispersion

pH control and adding surfactant far from isoelectric point

pH control and adding surfactant far from isoelectric pointpH control and adding surfactant far from isoelectric point

Thermal conductivity can be controlled by either the synthesis parameters orits temperature

4062 A. Ghadimi et al. / International Journal of Heat and Mass Transfer 54 (2011) 4051–4068

By supposing well dispersed nanoparticles, the thermo-physicalproperties of the particle fluid mixture can be evaluated usingEqs. (6)–(8). Properties with subscript ‘‘s’’ are for nanoparticleswhile without subscripts are for base fluid

qnf ¼ ð1�UÞqþUqs ð6ÞðqCpÞnf ¼ ð1�UÞqCp þUqsCp;s ð7ÞMnf ¼ ð1�UÞM þUMs ð8Þ

The effective thermal conductivity is defined as the ratio of the ther-mal conductivity of nanofluid to that of the base fluid. Therefore,from Eqs. (4) and (5), the generalized form of relative thermal con-ductivity can be given as:

knf

k¼ Cp;nf

Cp

� �a qnf

q

� �b MMnf

� �c

ð9Þ

In which a, b and c should be defined from experiments and areequal to �0.023, 1.358 and 0.126, respectively for Al2O3/waternanofluids. Yimin et al. [81,103] proposed a formula for the effec-tive thermal conductivity in conjugate with Brownian motion andDLA theory as follows:

keff

kf¼ kp þ 2kf � 2Uðkf � kpÞ

kp þ 2kf þUðkf � kpÞþ

qpUCp

2kf

ffiffiffiffiffiffiffiffiffiffiffiffiffikBT

3prcg

sð10Þ

where kf, kp, q, Cp, T, g, U and rc are the actual thermal conductivityof the base liquid and the nanoparticle, density, specific heat, tem-perature (K), viscosity, volume concentration and the radius of thecluster, respectively.

Meibodi et al. [104] described the model of thermal barrierresistance and claimed that the most important factor for thermalconductivity enhancement of nanofluids might be MFP (Mean FreePath), the distance between particles that can be calculated by

Fig. 13. Schematic modeling of a homogeneous suspension contain

Table 8Most applicable models for viscosity of nanofluids [31].

No. Model Equation Remarks

1 Einsteinmodel

lr ¼lnf

l ¼ 1þ gU Applicable when U < 1

2 Batchelormodel

lr ¼lnf

l ¼ 1þ gUþ ðgUÞ2 Brownian motion of thmodel and it is an exte

3 Ward model lr ¼lnf

l ¼ 1þ gUþ ðgUÞ2 þ ðgUÞ3 An exponential model

4 RenewedWard model

lr ¼lnf

l ¼ 1þ gUe þ ðgUeÞ2 þ ðgUeÞ3 The influence of liquid

Brownian approach for very low nanoparticle volume fractionsand by effective diameter for micro-particles and/or high particlevolume fractions [104]. The schematic of this model is presentedin Fig. 13. Likewise, Hadjov et al. [55] assumed a flux jump and adiscontinuity between the inclusion and the matrix as well whichis called the thermal conductive interface. This assumption con-flicts with the previous model. They stated that the thermal con-ductivity depends strongly on the morphology via the kind ofparticle packing.

5.1.2. Measurement apparatusThe measurement of thermal conductivity of liquids is a chal-

lenging task. In general, Fourier’s law of heat conduction isexploited for the measurement of thermal conductivity.

The thermal conductivity of nanofluids can be measured by dif-ferent methods, including transient hot-wire (THW, also calledtransient line heat source method) which are further categorizedinto a basic transient hot-wire method, insulated wire methodand liquid metal wire method [5,108,109]. A detailed explanationof the transient hot wire method in measuring the thermal conduc-tivity of nanofluids is given by Lee et al. [100]. Also, a summary ofthe apparatus utilized for thermophysical properties by differentinvestigators is given in Table 9.

Among the stated techniques, the steady state parallel platemethod used by Wang et al. [80] seems to be least affected bythe particle sedimentation for their thickness of the loaded samplefluid is less than one mm. The sedimentation of nanofluids can af-fect the THW method used by Lee et al. [100]. An increment of thetemperature gradient within the vertical hot wire may be causedby non-homogeneous nanoparticle concentration which might bea source of measurement errors. This is also true for thetemperature oscillation technique by Das et al. [101] where the

ing spherical mono-sized particle with resistance model [104].

% and when there is no interaction between the particles

e nanoparticles and the interaction between them was taken into account in thisnsion of the Einstein modelfor U up to 35%

layering is taken into account to calculate U, U is replaced by Ue

Table 9Equipments used for characteristic measurements.

Investigator Nanofluid Thermal conductivity Viscosity Specific heat Density Surface tension

[132] CuO + CTAB

THW (Assael et al., 2004) Rheometer with coaxial cylinders(HaakeRheostress RS600)

DSC (SetaramC80D)

Weighting a knownvolume of nanofluid

Pendant drop (KSVCAM 200)

Al2O3

CNTTiO2

[31] Al2O3 + DW KD2 Pro (DecagonDevices, Inc., USA)

Brookfield cone and plate viscometer(LVDV-I PRIME C/P)

– – –

[12] TiO2 + DW THW Bohlin rotational rheometer

[57] Al2O3 + DW TPS Capillary viscometer – – –Cu + DW

[49] Cu2O + DW KD2 system[133] KD2 system Bohlin CVO rheometer[134] KD2 pro Ubbeholder capillary viscometer (Fisher

Scientific)

A. Ghadimi et al. / International Journal of Heat and Mass Transfer 54 (2011) 4051–4068 4063

thermocouple that measures the fluid temperature oscillation liesin the upper half of the nanofluid chamber [59].

The 3x method is exploited by the small number of investiga-tors; a thin film heater is powered by an AC power source so thereis an oscillating heat transfer rate through the material, whosethermal conductivity is to be measured. The three omega wiremethod may be suitable to measure temperature-dependent ther-mal conductivity [112].

5.2. Viscosity

The viscosity is the other vital factor in designing dynamicnanofluid for heat transfer applications as the pressure drop andthe resulting pumping power depend on it. In comparison withthe works carried out on thermal conductivity of nanofluids, onlya few studies have been reported on the rheological behavior ofnanofluids. Kang et al. [113] measured the viscosities of UDD(ultradispersed diamond)/ethylene glycol, silver/water, and silica/water nanofluids and found the viscosity increment of 50%, 30%and 20% for UDD/EG, silver/water and silica/water nanofluids atvolume concentrations of 1%, 2% and 3%, respectively. Prasheret al. [114] showed the independence of the viscosity to shear ratefor alumina/propylene glycol (PG) nanofluids. This proves theNewtonian nature of nanofluid and viscosity growth by increasingnanoparticle volume concentration. They found a 30% increase inviscosity at 3% volume concentration and related this phenomenonto aggregation of the nanoparticles in the nanofluid with the size ofthe aggregates of around three times the size of the individualnanoparticles. The effect due to temperature and particle volumeconcentration on the dynamic viscosity for an Al2O3/water nano-fluid has been experimentally investigated by Nguyen et al.[115]. They found a significant increase in nanofluid dynamic vis-cosity with particle volume concentration and an obvious declinewith a temperature increase. In their experiments, another factoremerged, which is known as a critical temperature. Beyond thattemperature, the properties of particle suspension seem to be var-ied, which leads to a hysteresis phenomenon. This fact has raisedserious doubts about the reliability of using nanofluids for heattransfer enhancement purposes. Murshed et al. [48] measured rel-ative viscosity data for TiO2 and Al2O3/water-based nanofluids, andreported a maximum increase of 80% at 4% and 5% particle volumefraction, respectively. Similar increments in viscosity were re-ported earlier by Masuda et al. [116] and Wang et al. [80]. Xieet al. [117] ran experiments for nanoparticles dispersed in organicfluids like EG and showed that the increase for the viscosity ofAl2O3/EG nanofluids is smaller than those of water based suspen-sions, indicating the important effect of the base fluid on nanofluid

viscosity. They also studied the dependence of the viscosity on thepH values. But when the pH value is close to PZC, it causes coagu-lation of nanoparticles and therefore a viscosity increment. Namb-uru et al. [118] presented some experiments for rheologicalbehavior of CuO/EG and water based nanofluid over temperaturesranging from �35 �C to 50 �C. Kwak and Kim [102] demonstratedthat large thermal conductivity enhancements are accompaniedby sharp viscosity increases at low (<1%) nanoparticle volume frac-tions, which is a logical consequence of aggregation effects.

There are theoretical models to calculate the ratio of effectiveviscosity of nanofluids to that of base fluid. A few of the frequentlyused models [119,120] which have their limitations and applica-tions are listed in Table 8. Murshed et al. [48] showed that themeasured viscosities of Al2O3/water and TiO2/water nanofluidswere under predicted by the Krieger–Dougherty (K–D) model. Incontrast, Chen et al. [121] showed that the viscosity of nanofluidscan be predicted by the Krieger–Dougherty model if the volumeconcentration is replaced by the volume concentration of nanopar-ticle aggregates. In relation to their experiments, for sphericalnanoparticles, an aggregate size of approximately three times theprimary nanoparticle size gives the best fit with the experimentaldata. Chen et al. [121] proposed a categorization for the rheologicalbehavior of nanofluids into four groups as (i) dilute nanofluids(with volume concentration less than 0.1%) whose viscosity fitsthe Einstein equation and there is no visible shear-thinning behav-ior; (ii) semi-dilute nanofluids (with 0.1–5% volume concentration)with aggregation of nanoparticles, whose viscosity fits the modi-fied K–D equation and there is no obvious shear-thinning behavior;(iii) semi-concentrated nanofluids (with 5–10% volume concentra-tion) with aggregation of nanoparticles whose viscosity fits themodified K–D equation and there is noticeable shear-thinningbehavior; and (iv) concentrated nanofluids (with volume concen-tration more than 10%) with interpenetration of aggregationand this is out of the normal concentration range of nanofluids[31,63].

There is a concern about different experimental results for vis-cosity as shown by Pak and Cho [122] for 13 nm particle-size dataare much higher than all other results while Wang et al. [80] dataare relatively low. Nguyen et al. [123] claimed that it is compli-cated to sketch any certain clarification about such results, apartfrom saying that this interesting behavior may be related to vari-ous factors such as different nanofluid preparation methods.

5.2.1. Analytical modelsIn the case of aqueous nanofluid preparation, viscosity data col-

lection should be accompanied with distilled water in which mea-sured data have to be compared by the following correlation [124]:

4064 A. Ghadimi et al. / International Journal of Heat and Mass Transfer 54 (2011) 4051–4068

lbf � 104 ¼ exp1:12646� 0:039638 � ðTÞ

1� 0:00729769 � ðTÞ

� �ð11Þ

where T (K) is the fluid temperature and l in cP [123,125].There are a few theoretical formulas that can be used to approx-

imate nanofluid viscosities. Almost all such formulas have been de-rived from the original work of Einstein (1906) which is based onthe assumption of a linearly viscous fluid containing a dilute, sus-pension of spherical particles. The energy dissipated by the fluidflow around a single particle was calculated by Einstein in this arti-cle, and associated with that the work required moving this parti-cle relatively to the surrounding fluid, he obtained:

lr ¼lnf

lbf¼ 1þ 2:5U ð12Þ

Einstein’s formula was found to be applicable to relatively low par-ticle volume fractions, U < 2%. Beyond this value, it underestimatesthe effective viscosity of the resulting mixture as it ignores particle–particle interaction. Since the publication of Einstein’s work, manyresearchers have contributed to the ‘correction’ of his formula.Based on the assumption of a very slow flow, inertial effect in thefluid has been considered negligible by the authors in most of theseworks, which technicality makes linearity for the equations of mo-tion. Two factors were frequently employed to ‘correct’ Einstein’sresult: the first is that the particles may not be small, and the sec-ond is that the structure of the particles within the continuousphase may also affect the viscosity of the mixture. A brief reviewof the relevant works is given below. There exists an extended Ein-stein’s formula for use with moderate particle concentrations pro-posed by Brinkman [126], as follows:

lnf

lbf¼ 1

ð1�UÞ2:5ð13Þ

Frankel and Acrivos [127] proposed the following formula:

lnf

lbf¼ 9

8� ðU=UmÞ1=3

1� ðU=UmÞ1=3

" #ð14Þ

where Um is the experimental value for the maximum particle vol-ume fraction. Alternatively, Lundgren [128] has offered the subse-quent equation as a Taylor series in U:

lnf

lbf¼ 1þ 2:5Uþ 25

4U2 þ 0ðU3Þ ð15Þ

Clearly, if the terms O (U2) or higher are neglected, the above for-mula reduces to that of Einstein. Batchelor [129], in his notionalanalysis, considered the effect due to the Brownian motion of parti-cles on the bulk stress of an approximately isotropic suspension ofrigid and spherical particles. He proposed the following formula:

lnf

lbf¼ 1þ 2:5Uþ 6:5U2 ð16Þ

Graham [130] has proposed the following formula as a generalizedform of the Frankel and Acrivos [127] formula that agrees well withEinstein’s for small U:

lnf

lbf¼ 1þ 2:5Uþ 4:5

1

hdP

� � 2þ h

dP

� � 1þ h

dP

� 2

264

375 ð17Þ

where dp is the particle radius and h is the inter-particle spacing.In fact, practically none of the above mentioned models can de-

scribe the viscosity of nanofluids exactly in a wide range of thenanoparticle volume fractions. Nguyen et al. [115] found that theconditional formula, including Einstein’s formula and the ones pro-posed by Brinkman[126], Lundgren [128] and Batchelor had all

underestimated the nanofluids viscosity even for a relatively lowparticle fraction. They also suggested two correlations for Al2O3

aqueous nanofluids consisting of 47 and 36 nm nanoparticles asfollows:

lnf

lbf¼ 0:904e0:483U for 47 nm Al2O3 ð18Þ

lnf

lbf¼ ð1þ 0:025Uþ 0:015U2Þ for 36 nm Al2O3 ð19Þ

Lee [73] synthesized aqueous nanofluids containing low volumeconcentrations of Al2O3 nanoparticles in the 0.01–0.3 volume per-centage. His viscosity measurements showed that there was a con-siderable decline with temperature increase. In addition, themeasured viscosities of the mentioned nanofluids showed a nonlin-ear relation with the concentration even in the low volume concen-tration (0.01–0.3%) range, in contrast with the Einstein model whichpredicts a linear relation and therefore it severely underestimatesthe viscosity.

The temperature as another important factor other than the vol-ume fraction influences the viscosity of nanofluids. There are lim-ited researches about the dependence of viscosity on temperature;whereas it is interesting to observe that for particle concentrationslower than 4%, all tested nanofluids exhibit almost constant rela-tive viscosities that are independent of temperature. Between thetwo alumina–water nanofluids, just a slight difference in the levelsof relative viscosity arises. Such differences, however, becomemuch more visible at higher particle fractions, e.g. for 7% and 9%,where we can observe not only a temperature dependence, but aparticle-size-dependence as well. The effect of particle-size ap-pears somewhat paradoxical: for a particle fraction of 7% for exam-ple, viscosities for 36 nm are slightly higher than those of 47 nm;while for a 9% volume fraction, the reverse behavior is found.

For Al2O3–water and CuO–water nanofluids, the following for-mulas have been proposed to compute the dynamic viscosity forall three nanofluids and particle concentrations tested [123]:

lnf

lbf¼ 1:1250� 0:0007 � T ð20Þ

lnf

lbf¼ 2:1275� 0:0215 � T þ 0:0002 � T2 ð21Þ

There are also other correlations proposed for dependence of viscos-ity to temperature by investigators. The correlation of Kulkarni et al.[131] related the viscosity of CuO–water nanofluids with the tem-perature in the range of 5–50 �C:

lnls ¼ A1T

� �� B ð22Þ

Here A and B are the functions of volume percentage U. Since thiscorrelation is obtained for an aqueous solution, it is not valid forsubzero temperature range. Praveen [132] derived an exponentialmodel for CuO–water nanofluids with base fluid of 60:40 (byweight) ethylene glycol and water mixture as follows:

logðlsÞ ¼ Ae�BT ð23Þ

where ls is the CuO-water nanofluid viscosity in (cP), T is the tem-perature in K and A, B are functions of particle volume percentageU. It should be noted that some discrepancy appeared among afew studies on the rheology of nanofluids [114,133] which showedthe Newtonian behavior of nanofluids while others observednoticeable non-Newtonian behavior [134]. Prasher’s results [114]depicted that the normalized shear viscosity has a linear relation-ship with the nanoparticle volume fractions, whereas investigationsof Nguyen et al. [115] for particle volume fractions lower than 4%,the viscosity of CuO–water is approximately the same as that of

A. Ghadimi et al. / International Journal of Heat and Mass Transfer 54 (2011) 4051–4068 4065

the alumina–water nanofluids considered earlier, though for higherparticle loading, the increase in viscosity with respect to particleconcentration is clearly much greater. Such great values of viscositymay result from the intrinsic molecular structure of the mixture it-self and the particular chemical dispersing agents used.

These discrepancies between investigations might be due to dif-ferent volume concentration, type of nanoparticles, chemical prop-erties of base fluids and nanoparticle preparation method. Asshown by Ko et al. [135], nanofluids prepared by the acid treat-ment (TCNT) have much lower viscosity than the ones made withsurfactant (PCNT). Also, we can see that the use of the Batchelor[129] and Brinkman [126] formulas for CuO–water nanofluid isinappropriate. Therefore, the following correlation was proposedfor computing CuO–water viscosity:

lr ¼ 1:475� 0:319Uþ 0:051U2 þ 0:009U3 ð24Þ

Fullman [136] and Noni et al. [137] derived a formula from themodel of the mean free path for relative viscosity of suspensionsof solid particles in a liquid medium as:

lr ¼ 1þ a1kn ð25Þ

where the constants a and n depend on material characteristicswhile the mean free path (k) is defined as:

k ¼ 23

dð1�UÞ

Uð26Þ

Substituting Eq. (26) in Eq. (25) and for a given particle size,

lr ¼ 1þ bU

1�U

� �n

ð27Þ

This model (Eq. (27)) which considers the mean free path is used topredict the effective viscosity of Al2O3/water nanofluids [31].

5.3. Density

The key parameters for assessing the heat transfer merits ofnanofluids are their thermo physical properties. The mixture prop-erties of nanofluids are normally expressed in volume percent Uwhile the loading analysis was obtained in weight percent (wt).The conversion between the weight and volume fractions is donethrough the bulk density qp

U ¼wqf

qPð1�wÞ þwqfð28Þ

5.4. Specific heat

Thermal conductivity studies have been the main focus of nano-fluid investigations, and certain efforts have also been done on theviscosity of nanofluids. The density has been reported to be consis-tent with the mixing theory. However, the specific heat Cp of nano-fluids has received very little attention [141].

The heat capacity of the nanofluid is incorporated into theenergy equation, so it is important to be able to calculate it accu-rately. Most researchers use one of two correlations, which are inEqs. (29) and (30), The first model is based on the volume fractionwhereas the second model is based on heat capacity concept. Bothmodels are often cited by a number of researchers for calculatingthe specific heat of nanofluid.

Pak and Cho model [122]

c ¼ ð1�UÞcbf þUcp ð29Þ

and Xuan and Roetzel model [142].

c ¼ð1�UÞðqcÞbf þUðqcÞp

qð30Þ

Where c is the heat capacity, U is the volume fraction of nanopar-ticles, and q is the density. The subscript bf refers to properties ofthe base fluid, and the subscript p refers to properties of the nano-particles. Eq. (29) is simply the rule of mixtures applied to heatcapacity; while Eq. (30) is an altered form. It clearly shows thatthe specific heat decreased with increasing nanoparticle concentra-tions [10,141].

In some investigations, the influence of nanoparticles on thespecific heat of nanofluid seems too small to be considered dueto the low nanoparticle volume fraction.

6. Conclusion

The present outlook is the first and inclusive review on the re-search progress made in the stability of the nanofluids. Nanofluidpreparation with a single and two-step method would definitelyaffect the stability as the two-step method needs a higher nanopar-ticle concentration to equalize the heat transfer enhancementreached by single step. A higher concentration causes more sedi-mentation. However, unfortunately, the single step method is notindustrialized in a wide range so experiments are mostly con-ducted by two-step method. Therefore, higher costs and lower sta-bility are inevitable.

Major factors influencing the extraordinary enhancement ofheat transfer are listed as chemical composition of the solid parti-cle and the basefluid, particle source and concentration, particleshape and size, surfactants, temperature, pH value (surfacecharge), monodispersity, IEP and elapsed time.

Comparing several studies in the literature, some discrepanciesappear among the results. At this moment, it cannot be clearly ex-plained why incongruities take place among the measurements ofthe nanofluid characteristics such as thermal conductivity and vis-cosity. However, at least we are able to mention that differentsources of measurement uncertainties such as sedimentation andaggregation of nanoparticle, lack of a standard for nanofluid prep-aration, different source of nanoparticle manufacturing, variousstabilization methods, and time duration between the nanofluidspreparation and measurement in which cause the aggregate togrow with time, could be the most important reasons for the dis-persed data. Furthermore, the timing for the ultrasonic processessuch as horn processor or ultrasonic bath is not optimized properlywith respect to different nanoparticles and base fluids.

There is also another important result regarding stability andthermal conductivity that more stable nanofluid does not necessar-ily have more enhanced characteristics.

Three methods of homogenization are used by researchers andbring about various results. It can be mentioned that differentnanoparticles need their own stability method. Sometimes, thesemethods have to be combined together while in other cases justone method would be adequate to obtain the preferred stability.

Surfactant selection in nanofluid preparation has an importantrole in improving heat transfer. Temperature is considered as a re-stricted factor in case of nanofluid application for exploiting at thehigh temperatures. Likewise, the optimum percentage of surfac-tant should be considered as a factor in stable nanofluid prepara-tion as well.

Ultrasonication method, particularly the more effective onenamed horn ultrasonic, attracts much attention for its short timingpreparation among the other homogenization techniques. It has tobe considered that if a critical time is exceeded, it may have an in-verse effect and cause agglomeration and speedy sedimentation ofnanoparticles.

4066 A. Ghadimi et al. / International Journal of Heat and Mass Transfer 54 (2011) 4051–4068

The pH control, which has an important role in stability control,places the IEP of the suspension, far from the PZC in order to avoidcoagulation and instability. It should be taking into account thatacidic or alkaline pH is corrosive to metals. Therefore, it can leadto damage to the piping and instrumentation in long termapplications.

In support of stability measurement, it is better to examine atleast three different tests with the different stability measurementapparatus to come out with a reasonable result regarding stability.Furthermore, reproducibility is important in experiments so thesamples have to be run at least three times to meet the require-ments of uncertainties.

Among the characteristics discussed in the literature, thermalconductivity and viscosity have a major role in nanofluid charac-terization. To reach the best hypothesis for thermal conductivityenhancement, different theories were discussed such as Brownianmotion, interfacial layer and aggregation of particles. Additionally,some researchers discussed nanofluid as a two-phase flow mixtureand utilized certain formulas of two-phase mixtures for propertiesof nanofluid. However, still none of the proposed theories can ex-actly predict the improvement of thermal conductivity of nano-fluid. Although there are some results regarding the viscosity ofnanofluids, none is usable across a wide range of volume fractionsof nano particles so further experiments are required.

Systematic experiments are needed that will show the effect ofthe stability on heat transfer mechanism and characteristicsenhancement in stationary condition. Refer to other thermophysi-cal properties, including, specific heat and density, a few research-ers conducted tests as the correlations satisfied the result ofexperiments.

References

[1] P. Keblinski, J.A. Eastman, D.G. Cahill, Nanofluids for thermal transport, Mater.Today 8 (6) (2005) 36–44.

[2] S.U.S. Choi, J.A. Eastman, Enhancing thermal conductivity of fluids withnanoparticles, in: Conference: 1995 International Mechanical EengineeringCongress and Exhibition, San Francisco, CA (United States), 12-17 Nov 1995,ASME, San Francisco, 1995, pp. 99–105.

[3] R.J. Goldstein, D.D. Joseph, D.H. Pui, Convective Heat Transport in Nanofluids,proposal, Faculty of Aerospace Engineering and Mechanics, University ofMinnesota, Minnesota, September 2000.

[4] V. Trisaksri, S. Wongwises, Critical review of heat transfer characteristics ofthe nanofluids, Renew. Sustain. Energy Rev. 11 (2007) 512–523.

[5] M.P. Beck, Thermal Conductivity of Metal Oxide Nanofluids, Georgia Instituteof Technology, Georgia, 2008.

[6] X.-Q. Wang, A.S. Mujumdar, Heat transfer characteristics of nanofluids: areview, Int. J. Therm. Sci. 46 (1) (2007) 1–19.

[7] W. Duangthongsuk, S. Wongwises, A critical review of convective heattransfer of nanofluids, Renew. Sustain. Energy Rev. 11 (2007) 797–817.

[8] L. Godson, B. Raja, D. Mohan Lal, S. Wongwises, Enhancement of heat transferusing nanofluids – an overview, Renew. Sustain. Energy Rev. 14 (2) (2010)629–641.

[9] Y. Li, J.e. Zhou, S. Tung, E. Schneider, S. Xi, A review on development ofnanofluid preparation and characterization, Powder Technol. 196 (2) (2009)89–101.

[10] D. Wen, G. Lin, S. Vafaei, K. Zhang, Review of nanofluids for heat transferapplications, Particuology 7 (2) (2009) 141–150.

[11] K.Y. Leong, R. Saidur, S.N. Kazi, A.H. Mamun, Performance investigation of anautomotive car radiator operated with nanofluid-based coolants (nanofluidas a coolant in a radiator), Appl. Therm. Eng. 30 (17-18) (2010) 2685–2692.

[12] W. Duangthongsuk, S. Wongwises, Comparison of the effects of measured andcomputed thermophysical properties of nanofluids on heat transferperformance, Exp. Therm. Fluid Sci. 34 (5) (2010) 616–624.

[13] P.C. Hiemenz, M. Dekker, Principles of colloid and surface chemistry, Seconded., Dekker, New York, 1986.

[14] D. Wu, H. Zhu, L. Wang, L. Liua, Critical issues in nanofluids preparation,characterization and thermal conductivity, Curr. Nanosci. 5 (2009) 103–112.

[15] S.K. Das, S.U.S. Choi, W.H. Yu, T. Pradeep, nanofluid: Science and Technology,John Wiley & Sons Inc., 2007.

[16] E.J. Swanson, J. Tavares, S. Coulombe, Improved dual-plasma process for thesynthesis of coated or functionalized metal nanoparticles, IEEE Trans. PlasmaSci. 36 (4) (2008) 886–887.

[17] S.K. Das, S.U.S. Choi, H.E. Patel, Heat Transfer in Nanofluids – a review, HeatTransfer Eng. 27 (10) (2006) 3–19.

[18] H. Chang, C. Jwo, P. Fan, S. Pai, Process optimization and material propertiesfor nanofluid manufacturing, Int. J. Adv. Manuf. Technol. 34 (3) (2007) 300–306.

[20] Y. Hwang, H.S. Park, J.K. Lee, W.H. Jung, Thermal conductivity and lubricationcharacteristics of nanofluids, Curr. Appl Phys. 6 (Suppl. 1) (2006) e67–e71.

[21] X.F. Li, D.S. Zhu, X.J. Wang, N. Wang, J.W. Gao, H. Li, Thermal conductivityenhancement dependent pH and chemical surfactant for Cu–H2O nanofluids,Thermochim. Acta 469 (1–2) (2008) 98–103.

[22] H. Zhu, C. Zhang, Y. Tang, J. Wang, B. Ren, Y. Yin, Preparation and thermalconductivity of suspensions of graphite nanoparticles, Carbon 45 (1) (2007)226–228.

[23] W. Evans, R. Prasher, J. Fish, P. Meakin, P. Phelan, P. Keblinski, Effect ofaggregation and interfacial thermal resistance on thermal conductivity ofnanocomposites and colloidal nanofluids, Int. J. Heat Mass Transfer 51 (5-6)(2008) 1431–1438.

[24] J. Philip, P.D. Shima, B. Raj, Enhancement of thermal conductivity inmagnetite based nanofluid due to chainlike structures, Appl. Phys. Lett. 91(20) (2007) 203103–203108.

[25] P.E. Gharagozloo, K.E. Goodson, Aggregate fractal dimensions and thermalconduction in nanofluids, J. Appl. Phys. 108 (7) (2010) 074307–074309.

[26] K.S. Hong, T.K. Hong, H.S. Yang, Thermal conductivity of Fe nanofluidsdepending on the cluster size of nanoparticles, Appl. Phys. Lett. 88 (3) (2006)1–3.

[27] H. Chang, Y.C. Wu, X.Q. Chen, M.J. Kao, Fabrication of Cu Based Nanofluid withSuperior Dispersion, 2006, www.ntut.edu.tw.

[28] D. Zhu, X. Li, N. Wang, X. Wang, J. Gao, H. Li, Dispersion behavior and thermalconductivity characteristics of Al2O3–H2O nanofluids, Curr. Appl Phys. 9 (1)(2009) 131–139.

[29] X.-j. Wang, D.-s. Zhu, S. yang, Investigation of pH and SDBS on enhancementof thermal conductivity in nanofluids, Chem. Phys. Lett. 470 (1–3) (2009)107–111.

[30] M.N. Pantzali, A.G. Kanaris, K.D. Antoniadis, A.A. Mouza, S.V. Paras, Effect ofnanofluids on the performance of a miniature plate heat exchanger withmodulated surface, Int. J. Heat Fluid Flow 30 (4) (2009) 691–699.

[31] M. Chandrasekar, S. Suresh, A. Chandra Bose, Experimental investigations andtheoretical determination of thermal conductivity and viscosity of Al2O3/water nanofluid, Exp. Therm. Fluid Sci. 34 (2) (2010) 210–216.

[32] M.J. Assael, I.N. Metaxa, J. Arvanitidis, D. Christofilos, C. Lioutas, Thermalconductivity enhancement in aqueous suspensions of carbon multi-walledand double-walled nanotubes in the presence of two different dispersants,Int. J. Thermophys. 26 (3) (2005) 647–664.

[33] X. Wei, T. Kong, H. Zhu, L. Wang, CuS/Cu2S nanofluids: synthesis and thermalconductivity, Int. J. Heat Mass Transfer 53 (9-10) (2010) 1841–1843.

[34] M.E. Meibodi, M. Vafaie-Sefti, A.M. Rashidi, A. Amrollahi, M. Tabasi, H.S. Kalal,The role of different parameters on the stability and thermal conductivity ofcarbon nanotube/water nanofluids, Int. Commun. Heat Mass Transfer 37 (3)(2010) 319–323.

[35] Y. Hwang, J.K. Lee, C.H. Lee, Y.M. Jung, S.I. Cheong, C.G. Lee, B.C. Ku, S.P. Jang,Stability and thermal conductivity characteristics of nanofluids, Thermochim.Acta 455 (1-2) (2007) 70–74.

[36] H. Jin, W. Xianju, L. Qiong, W. Xueyi, Z. Yunjin, L. Liming, Influence of pH onthe Stability Characteristics of Nanofluids, in: Symposium on Photonics andOptoelectronics, 2009, SOPO 2009, 2009, pp. 1–4.

[37] L. Jiang, L. Gao, J. Sun, Production of aqueous colloidal dispersions of carbonnanotubes, J. Colloid Interface Sci. 260 (1) (2003) 89–94.

[38] Y. Hwang, J.-K. Lee, J.-K. Lee, Y.-M. Jeong, S.-i. Cheong, Y.-C. Ahn, S.H. Kim,Production and dispersion stability of nanoparticles in nanofluids, PowderTechnol. 186 (2) (2008) 145–153.

[39] J. Lee, Convection Performance of Nanofluids for Electronics Cooling, Ph.D.,Stanford University, United States – California, 2009.

[40] Y.J. Hwang, Y.C. Ahn, H.S. Shin, C.G. Lee, G.T. Kim, H.S. Park, J.K. Lee,Investigation on characteristics of thermal conductivity enhancement ofnanofluids, Curr. Appl Phys. 6 (6) (2006) 1068–1071.

[41] X. Zhang, H. Gu, M. Fujii, Effective thermal conductivity and thermaldiffusivity of nanofluids containing spherical and cylindrical nanoparticles,Exp. Thermal Fluid Sci. 31 (6) (2007) 593–599.

[42] W. Yu, H. Xie, L. Chen, Y. Li, Enhancement of thermal conductivity ofkerosene-based Fe3O4 nanofluids prepared via phase-transfer method,Colloids Surface A: Physicochem. Eng. Aspects 355 (1–3) (2010) 109–113.

[43] I. Madni, C.-Y. Hwang, S.-D. Park, Y.-H. Choa, H.-T. Kim, Mixed surfactantsystem for stable suspension of multiwalled carbon nanotubes, ColloidsSurface A: Physicochem. Eng. Aspects 358 (1–3) (2010) 101–107.

[44] M. Sato, Y. Abe, Y. Urita, R. Di Paola, A. Cecere, R. Savino, Thermal performanceof self-rewetting fluid heat pipe containing dilute solutions of polymer-capped silver nanoparticles synthesized by microwave-polyol process, in:Proceedings of the ITP2009, 2009.

[45] C. Walleck, Development of Steady-State, Parallel-Plate Thermal ConductivityApparatus for Poly-Nanofluids and Comparative Measurements withTransient HWTC Apparatus, M.S., Northern Illinois University, United States– Illinois, 2009.

[46] H.-t. Zhu, Y.-s. Lin, Y.-s. Yin, A novel one-step chemical method forpreparation of copper nanofluids, J. Colloid Interface Sci. 277 (1) (2004)100–103.

[47] X.-Q. Wang, A.S. Mujumdar, A review on nanofluids. Part II: Experiments andapplications, Braz. J. Chem. Eng. 25 (2008) 631–648.

A. Ghadimi et al. / International Journal of Heat and Mass Transfer 54 (2011) 4051–4068 4067

[48] S.M.S. Murshed, K.C. Leong, C. Yang, Investigations of thermal conductivityand viscosity of nanofluids, Int. J. Therm. Sci. 47 (2008) 560–568.

[49] X. Wei, H. Zhu, T. Kong, L. Wang, Synthesis and thermal conductivity of Cu2Onanofluids, Int. J. Heat Mass Transfer 52 (19–20) (2009) 4371–4374.

[50] J.-C. Chou, L.P. Liao, Study on pH at the point of zero charge of TiO2 pH ion-sensitive field effect transistor made by the sputtering method, Thin SolidFilms 476 (1) (2005) 157–161.

[51] Y. Fovet, J.-Y. Gal, F. Toumelin-Chemla, Influence of pH and fluorideconcentration on titanium passivating layer: stability of titanium dioxide,Talanta 53 (5) (2001) 1053–1063.

[52] J. Huang, X. Wang, influence of pH on the stability characteristics of nanofluid,IEEE, 2009.

[53] D. Lee, J.-W. Kim, B.G. Kim, A new parameter to control heat transport innanofluids: surface charge state of the particle in suspension, J. Phys. Chem.(2006) 4323–4328.

[54] H. Xie, H. Lee, W. Youn, M. Choi, Nanofluids containing multiwalled carbonnanotubes and their enhanced thermal conductivities, J. Appl. Phys. 94 (8)(2003) 4967–4971.

[55] K.B. Hadjov, Modified self-consisted scheme to predict the thermalconductivity of nanofluids, Int. J. Therm. Sci. 48 (12) (2009) 2249–2254.

[56] K. Lee, Y. Hwang, S. Cheong, L. Kwon, S. Kim, J. Lee, Performance evaluation ofnano-lubricants of fullerene nanoparticles in refrigeration mineral oil, Curr.Appl Phys. 9 (2, Suppl. 1) (2009) e128–e131.

[57] X.-J. Wang, X.-F. Li, Influence of pH on nanofluids’ viscosity and thermalconductivity, Chin. Phys. Lett. 26 (5) (2009) 056601.

[58] B.R. Munson, D.F. Young, T.H. Okiishi, Fundamentals of Fluid Mechanics, JohnWiley & Sons Inc., 1998.

[59] D.-W. Oh, A. Jain, J.K. Eaton, K.E. Goodson, J.S. Lee, Thermal conductivitymeasurement and sedimentation detection of aluminum oxide nanofluids byusing the 3omega method, Int. J. Heat Fluid Flow 29 (5) (2008) 1456–1461.

[60] H. Patel, T. Sundararajan, T. Pradeep, A. Dasgupta, N. Dasgupta, S. Das, Amicro-convection model for thermal conductivity of nanofluids, Pramana 65(5) (2005) 863–869.

[61] P.N. Das Sarit Kumar, Thiesen Peter, R. Wilfried, Temperature dependence ofthermal conductivity enhancement for nanofluids, J. Heat Transfer 125 (2003)8.

[62] L.G. Asirvatham, N. Vishal, S.K. Gangatharan, D.M. Lal, Experimental study onforced convective heat transfer with low volume fraction of CuO/waternanofluid, Energies 2 (1) (2009) 97–119.

[63] H. Chen, Y. Ding, A. Lapkin, Rheological behaviour of nanofluidscontaining tube/rod-like nanoparticles, Powder Technol. 194 (1–2)(2009) 132–141.

[64] S.J. Chung, J.P. Leonard, I. Nettleship, J.K. Lee, Y. Soong, D.V. Martello, M.K.Chyu, Characterization of ZnO nanoparticle suspension in water:Effectiveness of ultrasonic dispersion, Powder Technol. 194 (1–2) (2009)75–80.

[65] X.F. Li, D.S. Zhu, X.J. Wang, J.W. Gao, H. Li, Proceedings of the InternationalSymposium on Biophotonics, Nanophotonics and Metamaterials, 2006.

[66] S.H. Kim, S.R. Choi, D. Kim, Thermal conductivity of metal-oxide nanofluids:particle size dependence and effect of laser irradiation, J. Heat Transfer 129(3) (2007) 298–307.

[67] Z.-Q. Liu, J. Ma, Y.-H. Cui, Carbon nanotube supported platinum catalysts forthe ozonation of oxalic acid in aqueous solutions, Carbon 46 (6) (2008) 890–897.

[68] U. Kreibig, L. Genzel, Optical absorption of small metallic particles, SurfaceSci. 156 (Part 2) (1985) 678–700.

[69] S. Link, M.A. El-Sayed, Optical properties and ultrafast dynamics of metallicnanocrystals, Annu. Rev. Phys. Chem. 54 (1) (2003) 331–366.

[70] U.V. Kreibig, M. Vollmer, Optical Properties of Metal Clusters, Springer, 1995.[71] C.Y. Tsai, H.T. Chien, P.P. Ding, B. Chan, T.Y. Luh, P.H. Chen, Effect of structural

character of gold nanoparticles in nanofluid on heat pipe thermalperformance, Mater. Lett. 58 (9) (2004) 1461–1465.

[72] P. Vadasz, Heat conduction in nanofluid suspensions, J. Heat Transfer 128 (5)(2006) 465–477.

[73] J.-H. Lee, K.S. Hwang, S.P. Jang, B.H. Lee, J.H. Kim, S.U.S. Choi, C.J. Choi,Effective viscosities and thermal conductivities of aqueous nanofluidscontaining low volume concentrations of Al2O3 nanoparticles, Int. J. HeatMass Transfer 51 (11–12) (2008) 2651–2656.

[74] L. Vandsburger, Synthesis and Covalent Surface Modification of CarbonNanotubes for Preparation of Stabilized Nanofluid Suspensions, M.Eng.,McGill University (Canada), Canada, 2009.

[75] M.-S. Liu, M.C.-C. Lin, C.Y. Tsai, C.-C. Wang, Enhancement of thermalconductivity with Cu for nanofluids using chemical reduction method, Int. J.Heat Mass Transfer 49 (17–18) (2006) 3028–3033.

[76] D.-W. Oh, A. Jain, J.K. Eaton, K.E. Goodson, J.S. Lee, Thermal conductivitymeasurement of aluminum oxide nanofluids using the 3-omega method, in:ASME Conference Proceedings, ASME, 2006, pp. 343–349.

[77] G. Paul, M. Chopkar, I. Manna, P.K. Das, Techniques for measuring the thermalconductivity of nanofluids: a review, Renew. Sustain. Energy Rev. 14 (7)(2010) 1913–1924.

[78] S.M.S. Murshed, K.C. Leong, C. Yang, Thermophysical and electrokineticproperties of nanofluids – a critical review, Appl. Therm. Eng. 28 (17–18)(2008) 2109–2125.

[79] P. Keblinski, S.R. Phillpot, S.U.S. Choi, J.A. Eastman, Mechanisms of heat flowin suspensions of nano-sized particles (nanofluids), Int. J. Heat Mass Transfer45 (4) (2002) 855–863.

[80] X. Wang, X. Xu, S.U.S. Choi, Thermal conductivity of nanoparticles–fluidmixture, J. Thermophys. Heat Transfer 4 (1999) 474–480.

[81] Y. Xuan, Q. Li, W. Hu, Aggregation structure and thermal conductivity ofnanofluids, AIChE J. 49 (4) (2003) 1038–1043.

[82] A. Amrollahi et al., The effects of temperature, volume fraction and vibrationtime on the thermo-physical properties of a carbon nanotube suspension(carbon nanofluid), Nanotechnology 19 (31) (2008) 315701.

[83] B.-X. Wang, L.-P. Zhou, X.-F. Peng, A fractal model for predicting the effectivethermal conductivity of liquid with suspension of nanoparticles, Int. J. HeatMass Transfer 46 (14) (2003) 2665–2672.

[84] R. Yajie et al., Effective thermal conductivity of nanofluids containingspherical nanoparticles, J. Phys. D: Appl. Phys. 38 (21) (2005) 3958.

[85] H. Xie, M. Fujii, X. Zhang, Effect of interfacial nanolayer on the effectivethermal conductivity of nanoparticle–fluid mixture, Int. J. Heat Mass Transfer48 (14) (2005) 2926–2932.

[86] Q. Xue, W.-M. Xu, A model of thermal conductivity of nanofluids withinterfacial shells, Mater. Chem. Phys. 90 (2–3) (2005) 298–301.

[87] P. Tillman, J.M. Hill, Determination of nanolayer thickness for a nanofluid, Int.Commun. Heat Mass Transfer 34 (4) (2007) 399–407.

[88] L. Li, Y. Zhang, H. Ma, M. Yang, An investigation of molecular layering at theliquid–solid interface in nanofluids by molecular dynamics simulation, Phys.Lett. A 372 (25) (2008) 4541–4544.

[89] C. Maxwell, A treatise on electricity and magnetism 1 (1904) 435.[90] R.L. Hamilton, O.K. Crosser, Thermal conductivity of heterogeneous two-

component systems, Ind. Eng. Chem. Fundam. 1 (3) (1962) 187–191.[91] A. Sommers, K. Yerkes, Experimental investigation into the convective heat

transfer and system-level effects of Al2O3–propanol nanofluid, J. Nanopart.Res. 12 (3) (2009) 1003–1014.

[92] P.E. Gharagozloo, J.K. Eaton, K.E. Goodson, Diffusion, aggregation, and thethermal conductivity of nanofluids, Appl. Phys. Lett. 93 (10) (2008) 103110–103113.

[93] X.F. Zhou, L. Gao, Effective thermal conductivity in nanofluids of nonsphericalparticles with interfacial thermal resistance: differential effective mediumtheory, J. Appl. Phys. 100 (2) (2006) 024913–024916.

[94] L. Gao, X.F. Zhou, Differential effective medium theory for thermalconductivity in nanofluids, Phys. Lett. A 348 (3–6) (2006) 355–360.

[95] L. Gao, X. Zhou, Y. Ding, Effective thermal and electrical conductivity ofcarbon nanotube composites, Chem. Phys. Lett. 434 (4–6) (2007) 297–300.

[96] J. Koo, C. Kleinstreuer, Laminar nanofluid flow in microheat-sinks, Int. J. HeatMass Transfer 48 (13) (2005) 2652–2661.

[97] H.T. Zhu, C.Y. Zhang, S.Q. Liu, Y.M. Tang, Y.S. Yin, Effects of nanoparticleclustering and alignment on thermal conductivities of Fe3O4 aqueousnanofluids, Appl. Phys. Lett. (2006).

[98] N.R. Karthikeyan, J. Philip, B. Raj, Effect of clustering on the thermalconductivity of nanofluids, Mater. Chem. Phys. 109 (1) (2008) 50–55.

[99] H. Zhu, C. Zhang, S. Liu, Y. Tang, Y. Yin, Effects of nanoparticle clustering andalignment on thermal conductivities of Fe3O4 aqueous nanofluids, Appl. Phys.Lett. 89 (2) (2006).

[100] S. Lee, S.U.S. Choi, S. Li, J.A. Eastman, Measuring thermal conductivity offluids containing oxide nanoparticles, J. Heat Transfer 121 (2) (1999) 280–289.

[101] K. Das, N. Putra, P. Thiesen, W. Roetzel, Temperature dependence of thermalconductivity enhancement for nanofluids, J. Heat Transfer 125 (4) (2003)567–574.

[102] K. Kwak, C. Kim, Viscosity and thermal conductivity of copper oxide nanofluiddispersed in ethylene glycol, Korea Aust. Rheol. J. 17 (2) (2005) 35–40.

[103] X. Yimin, L. Qiang, H. Weifeng, Aggregation structure and thermalconductivity of nanofluids, AIChE J. 49 (4) (2003) 1038–1043.

[104] M.E. Meibodi, M. Vafaie-Sefti, A.M. Rashidi, A. Amrollahi, M. Tabasi, H.S. Kalal,Simple model for thermal conductivity of nanofluids using resistance modelapproach, Int. Commun. Heat Mass Transfer 37 (5) (2010) 555–559.

[107] G.P. Peterson, C.H. Li, Heat and mass transfer in fluids with nanoparticle, Adv.Heat Transfer Suspensions 39 (2006) 257–376.

[108] P. Vadász, Nanofluid suspensions and bi-composite media as derivatives ofinterface heat transfer modeling in porous media, in: Emerging Topics inHeat and Mass Transfer in Porous Media, 2008, pp. 283–326.

[109] S. Tavman, I.H. Tavman, Measurement of effective thermal conductivity ofwheat as a function of moisture content, Int. Commun. Heat Mass Transfer 25(5) (1998) 733–741.

[110] S. Özerinç, S. Kakaç, A. Yazıcıoglu, Enhanced thermal conductivity ofnanofluids: a state-of-the-art review, Microfluid. Nanofluid. 8 (2) (2010)145–170.

[111] H. Wang, M. Sen, Analysis of the 3-omega method for thermal conductivitymeasurement, Int. J. Heat Mass Transfer 52 (7–8) (2009) 2102–2109.

[112] S.M.S. Murshed, K.C. Leong, C. Yang, Thermophysical and electrokineticproperties of nanofluids – a critical review, Appl. Therm. Eng. 28 (2008)2109–2125.

[113] H.U. Kang, S.H. Kim, J.M. Oh, Estimation of thermal conductivity of nanofluidusing experimental effective particle volume, Exp. Heat Transfer 19 (2006)181–191.

[114] R. Prasher, D. Song, J. Wang, P.E. Phelan, Measurements of nanofluid viscosityand its implications for thermal applications, Appl. Phys. Lett 89 (2006).

[115] C.T. Nguyen, F. Desgranges, N. Galanis, G. Roy, T. Maré, S. Boucher, H. AngueMintsa, Viscosity data for Al2O3–water nanofluid-hysteresis: is heat transferenhancement using nanofluids reliable?, Int J. Therm. Sci. 47 (2) (2008) 103–111.

4068 A. Ghadimi et al. / International Journal of Heat and Mass Transfer 54 (2011) 4051–4068

[116] H. Masuda, A. Ebata, K. Teramae, N. Hishinuma, Alteration of thermalconductivity and viscosity of liquid by dispersing ultra-fine particles(dispersion of Al2O3, SiO2 and TiO2 ultra-fine particles), Netsu Bussei(Japan) 7 (1993) 227–233.

[117] H. Xie, L. Chen, Q. Wu, Measurements of the viscosity of suspensions(nanofluids) containing nanosized Al2O3 particles, High Temp. – High Press.37 (2008) 127–135.

[118] P.K. Namburu, D.P. Kulkarni, D. Misra, D.K. Das, Viscosity of copper oxidenanoparticles dispersed in ethylene glycol and water mixture, Exp. Therm.Fluid Sci. 323 (2007) 97–402.

[119] W. Duangthongsuk, S. Wongwises, Measurement of temperature-dependentthermal conductivity and viscosity of TiO2–water nanofluids, Exp. ThermalFluid Sci. 33 (4) (2009) 706–714.

[120] I.M. Krieger, T.J. Dougherty, A mechanism for non-Newtonian Flow insuspensions of rigid spheres, Trans. Soc. Rheol. 3 (1) (1959) 137–152.

[121] H. Chen, Y. Ding, C. Tan, Rheological behaviour of nanofluids, New J. Phys. 9(2007) 367-1–367-24.

[122] B.C. Pak, Y.I. Cho, Hydrodynamic and heat transfer study of dispersed fluidswith submicron metallic oxide particles, Exp. Heat Transfer 11 (2) (1998)151–170.

[123] C.T. Nguyen, F. Desgranges, G. Roy, N. Galanis, T. Maré, S. Boucher, H. AngueMintsa, Temperature and particle-size dependent viscosity data for water-based nanofluids – hysteresis phenomenon, Int. J. Heat Fluid Flow 28 (6)(2007) 1492–1506.

[124] K. Hagen, Heat Transfer with Applications, Prentice-Hall, New Jersey, USA,1999.

[125] H.A. Mintsa, G. Roy, C.T. Nguyen, D. Doucet, New temperature dependentthermal conductivity data for water-based nanofluids, Int. J. Therm. Sci. 48(2) (2009) 363–371.

[126] H.C. Brinkman, The viscosity of concentrated suspensions and solutions, J.Chem. Phys. 20 (4) (1952) 571.

[127] N.A. Frankel, A. Acrivos, On the viscosity of a concentrated suspension of solidspheres, Chem. Eng. Sci. 22 (6) (1967) 847–853.

[128] T.S. Lundgren, Slow flow through stationary random beds and suspensions ofspheres, J. Fluid Mech. 51 (02) (1972) 273–299.

[129] G.K. Batchelor, The effect of Brownian motion on the bulk stress in asuspension of spherical particles, J. Fluid Mech. 83 (01) (1977) 97–117.

[130] A.L. Graham, On the viscosity of suspensions of solid spheres, Appl. Sci. Res.37 (3) (1981) 275–286.

[131] D.P. Kulkarni, D.K. Das, G.A. Chukwu, Temperature dependent rheologicalproperty of copper oxide nanoparticles suspension (nanofluid), J. Nanosci.Nanotechnol. 6 (2006) 1150–1154.

[132] P.K. Namburu, D.P. Kulkarni, D. Misra, D.K. Das, Viscosity of copper oxidenanoparticles dispersed in ethylene glycol and water mixture, Exp. Therm.Fluid Sci. 32 (2) (2007) 397–402.

[133] Y. Yang, Z.G. Zhang, E.A. Grulke, W.B. Anderson, G. Wu, Heat transferproperties of nanoparticle-in-fluid dispersions (nanofluids) in laminar flow,Int. J. Heat Mass Transfer 48 (6) (2005) 1107–1116.

[134] Y. He, Y. Jin, H. Chen, Y. Ding, D. Cang, H. Lu, Heat transfer and flow behaviorof aqueous suspensions of TiO2 nanoparticles (nanofluids) flowing upwardthrough a vertical pipe, Int. J. Heat Mass Transfer 50 (11–12) (2007) 2272–2281.

[135] G.H. Ko, K. Heo, K. Lee, D.S. Kim, C. Kim, Y. Sohn, M. Choi, Anexperimental study on the pressure drop of nanofluids containing carbonnanotubes in a horizontal tube, Int. J. Heat Mass Transfer 50 (23–24)(2007) 4749–4753.

[136] R.L. Fullman, Measurement of particle sizes in opaque bodies, J. Metals 5(1953) 447–452.

[137] A.D. Noni Jr., D.E. Garcia, D. Hotza, A modified model for the viscosity ofceramic suspensions, Ceram. Int. 28 (2002) 731–735.

[138] M.N. Pantzali, A.A. Mouza, S.V. Paras, Investigating the efficacy of nanofluidsas coolants in plate heat exchangers (PHE), Chem. Eng. Sci. 64 (14) (2009)3290–3300.

[139] Y. Ding, H. Chen, Y. He, A. Lapkin, M. Yeganeh, L. Siller, Y.V. Butenko, Forcedconvective heat transfer of nanofluids, Adv. Powder Technol. 18 (6) (2007)813–824.

[140] E.V. Timofeeva, A.N. Gavrilov, J.M. McCloskey, Y.V. Tolmachev, S. Sprunt, L.M.Lopatina, J.V. Selinger, Thermal conductivity and particle agglomeration inalumina nanofluids: Experiment and theory, Phys. Rev. E 76 (6) (2007)061203.

[141] S.-Q. Zhou, R. Ni, Measurement of the specific heat capacity of water-basedAl2O3 nanofluid, Appl. Phys. Lett. 92 (9) (2008) 093123.

[142] Y. Xuan, W. Roetzel, Conceptions for heat transfer correlation of nanofluids,Int. J. Heat Mass Transfer 43 (19) (2000) 3701–3707.