Thermophysical and electrokinetic properties of nanofluids – A critical review

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Applied Thermal Engineering 28 (2008) 2109–2125

Review

Thermophysical and electrokinetic properties ofnanofluids – A critical review

S.M.S. Murshed, K.C. Leong *, C. Yang

School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Republic of Singapore

Received 3 December 2007; accepted 9 January 2008Available online 16 January 2008

Abstract

In the past decade, nanofluids have attracted much interest because of their reported superior thermal performance and many poten-tial applications. However, there are many inconsistencies in reported experimental results of the thermophysical properties such as theeffective thermal conductivity of nanofluids and controversies in the underlying enhanced mechanisms. In this paper, various aspects ofnanofluids including synthesis, potential applications, experimental and analytical studies on the effective thermal conductivity, effectivethermal diffusivity, convective heat transfer, and electrokinetic properties are critically reviewed.� 2008 Elsevier Ltd. All rights reserved.

Keywords: Nanofluids; Effective thermal conductivity; Thermal diffusivity; Viscosity; Electrokinetic properties

Contents

1. Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2110

1359-4

doi:10.

* CoE-m

1.1. Development and concept of nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21101.2. Impact and potential benefits of nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21101.3. Potential applications of nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2111

1.3.1. Engineering applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21111.3.2. Medical applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2111

2. Synthesis of nanofluids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21123. Experimental studies on thermal conductivity of nanofluids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2112

3.1. Measurement method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21123.2. Effect of volume fraction and particle size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21133.3. Effect of fluid temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2115

4. Studies on thermal diffusivity of nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21165. Studies on viscosity of nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21176. Theoretical studies on nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2118

6.1. Underlying mechanisms for the enhanced thermal conductivity of nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . 21186.2. Models for the effective thermal conductivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2118

7. Electrokinetic phenomena of nanofluids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21218. Convective heat transfer studies of nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21219. Computational studies on heat transport of nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2122

311/$ - see front matter � 2008 Elsevier Ltd. All rights reserved.

1016/j.applthermaleng.2008.01.005

rresponding author. Tel.: +65 6790 4725; fax: +65 6792 2619.ail address: [email protected] (K.C. Leong).

mailto:[email protected]

F3

2110 S.M.S. Murshed et al. / Applied Thermal Engineering 28 (2008) 2109–2125

10. Summary and future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2123References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2123

1. Background

1.1. Development and concept of nanofluids

With ever-increasing thermal loads due to smaller fea-tures of microelectronic devices and higher power out-puts, thermal management of such devices to maintaintheir desired performance and durability is one of themost important technical issues in many high-technologyindustries such as microelectronics, transportation andmanufacturing. The conventional method of increasingthe cooling rate is to use extended heat transfer surfacesfor exchanging heat with a heat transfer fluid. However,this approach requires an undesirable increase in the sizeof the thermal management system. In addition, the inher-ently poor thermophysical properties of conventional heattransfer fluids such as water, ethylene glycol (EG) orengine oil (EO) greatly limit the cooling performance.Thus, conventional methods for increasing heat dissipa-tion are not suitable to meet the demand of these high-technology industries. There is therefore, a need todevelop advanced cooling techniques and innovative heattransfer fluids with better heat transfer performance thanthose presently available.

It is well known that at room temperature, metallic sol-ids possess an order-of-magnitude higher thermal conduc-tivity than fluids. For example, the thermal conductivityof copper at room temperature is about 700 times greaterthan that of water and about 3000 times greater than thatof engine oil (Fig. 1). Therefore, the thermal conductivitiesof fluids containing suspended solid metallic or nonmetallic(metallic oxide) particles would be expected to be signifi-cantly higher than those of conventional heat transfer flu-

Material1 2 3 4 5 6 7 8 9

The

rmal

con

duct

ivity

(W

/m-K

)

0

500

1000

1500

2000

2500

3000

35001- Engine oil2- Ethylene glycol3- Water4- Alumina5- Silicon6- Aluminum7- Copper8- Silver9- Multiwalled carbon nanotubes (MWCNT)

0.25 0.610.15

ig. 1. Thermal conductivity of typical materials (solids and liquids) at00 K [2].

ids. As the thermal conductivity of a fluid plays a vitalrole in the development of energy-efficient heat transferequipment, numerous theoretical and experimental studieson increasing the thermal conductivity of liquids by sus-pending small particles have been conducted since the trea-tise by Maxwell more than a century ago [1]. However, allsuch studies on thermal conductivity of suspensions havebeen confined to millimeter- or micrometer-sized particles.The main problems of using such suspensions are the rapidsettling of particles, clogging of flow channels, andincreased pressure drop in the fluid. If the fluid is kept cir-culating rapidly enough to prevent much settling, themicroparticles would damage the walls of the heat transferdevices (e.g. pipes and channels) and wear them out. Incontrast, nanoparticles due to their high surface to volumeratio can remain in suspension and thereby reduce erosionand clogging. Nanoparticles are also suitable for use inmicrosystems because they are many orders of magnitudesmaller than the microsystems.

Over the last several decades, scientists and engineershave attempted to develop fluids, which offer better coolingor heating performance for a variety of thermal systemscompared to conventional heat transfer fluids. Applyingnanotechnology to thermal engineering, the novel conceptof a ‘‘nanofluid” which was coined at Argonne NationalLaboratory of USA by Choi in 1995 [3] has been proposedto meet these cooling challenges. This new class of heattransfer fluids (nanofluids) is engineered by dispersingnanometer-sized (one billionth of a meter) solid particles,rods or tubes in traditional heat transfer fluids. From theinvestigations in the past decade, nanofluids were foundto exhibit significantly higher thermal properties, in partic-ular, thermal conductivity, than those of base fluids [4–12].Thus, nanofluids have attracted great interest from theresearch community due to their potential benefits andapplications in numerous important fields such as micro-electronics, transportation, manufacturing, medical, andHVAC.

1.2. Impact and potential benefits of nanofluids

The impact of nanofluid technology is expected to begreat considering that heat transfer performance of heatexchangers or cooling devices is vital in numerous indus-tries. For example, the transport industry has a need toreduce the size and weight of vehicle thermal managementsystems and nanofluids can increase thermal transport ofcoolants and lubricants. When the nanoparticles are prop-erly dispersed, nanofluids can offer numerous benefits [2,13]besides the anomalously high effective thermal conductiv-ity. These benefits include:

S.M.S. Murshed et al. / Applied Thermal Engineering 28 (2008) 2109–2125 2111

(1) Improved heat transfer and stability: Because heattransfer takes place at the surface of the particles, itis desirable to use particles with larger surface area.The relatively larger surface areas of nanoparticlescompared to microparticles, provide significantlyimproved heat transfer capabilities. In addition, par-ticles finer than 20 nm carry 20% of their atoms ontheir surface, making them instantaneously availablefor thermal interaction [2]. With such ultra-fine parti-cles, nanofluids can flow smoothly in the tiniest ofchannels such as mini- or micro-channels. Becausethe nanoparticles are small, gravity becomes lessimportant and thus chances of sedimentation are alsoless, making nanofluids more stable.

(2) Microchannel cooling without clogging: Nanofluidswill not only be a better medium for heat transferin general, but they will also be ideal for microchan-nel applications where high heat loads are encoun-tered. The combination of microchannels andnanofluids will provide both highly conducting fluidsand a large heat transfer area. This cannot beattained with macro- or micro-particles because theyclog microchannels.

(3) Miniaturized systems: Nanofluid technology will sup-port the current industrial trend toward componentand system miniaturization by enabling the designof smaller and lighter heat exchanger systems. Minia-turized systems will reduce the inventory of heattransfer fluid and will result in cost savings.

(4) Reduction in pumping power: To increase the heattransfer of conventional fluids by a factor of two,the pumping power must usually be increased by afactor of 10. It was shown that by multiplying thethermal conductivity by a factor of three, the heattransfer in the same apparatus was doubled [3]. Therequired increase in the pumping power will be verymoderate unless there is a sharp increase in fluid vis-cosity. Thus, very large savings in pumping powercan be achieved if a large thermal conductivityincrease can be achieved with a small volume fractionof nanoparticles.

The better stability of nanofluids will prevent rapid set-tling and reduce clogging in the walls of heat transfer devices.The high thermal conductivity of nanofluids translates intohigher energy efficiency, better performance, and lower oper-ating costs. They can reduce energy consumption for pump-ing heat transfer fluids. Miniaturized systems require smallerinventories of fluids where nanofluids can be used. Thermalsystems can be smaller and lighter. In vehicles, smaller com-ponents result in better gasoline mileage, fuel savings, loweremissions, and a cleaner environment [14].

1.3. Potential applications of nanofluids

With the aforementioned highly desired thermal proper-ties and potential benefits, nanofluids can be seen to have a

wide range of industrial and medical applications, whichare elaborated here.

1.3.1. Engineering applications

Nanofluids can be used to improve thermal managementsystems in many engineering applications including:

(a) Nanofluids in transportation: The transportationindustry has a strong demand to improve perfor-mance of vehicle heat transfer fluids and enhance-ment in cooling technologies is also desired.Because engine coolants, engine oils, automatic trans-mission fluids, and other synthetic high temperaturefluids currently possess inherently poor heat transfercapabilities, they could benefit from the high thermalconductivity offered by nanofluids. Nanofluids wouldallow for smaller, lighter engines, pumps, radiators,and other components. Lighter vehicles could travelfurther on the same amount of fuel i.e. more mileageper liter. More energy-efficient vehicles would savemoney. Moreover, burning less fuel would result inlower emissions and thus reduce environment pollu-tion. Therefore, in transportation systems, nanofluidscan contribute greatly.

(b) In micromechanics and instrumentation: Since 1960s,miniaturization has been a major trend in scienceand technology. Microelectromechanical systems(MEMS) generate a lot of heat during operation.Conventional coolants do not work well with high-power MEMS because they do not have enough cool-ing capability. Moreover, even if large-sized solidparticles were added to these coolants to enhancetheir thermal conductivity, they still could not beapplied in practical cooling systems, because the par-ticles would be too big to flow smoothly in the extre-mely narrow cooling channels required by MEMS.Since nanofluids can flow in microchannels withoutclogging, they would be suitable coolants. They couldenhance cooling of MEMS under extreme heat fluxconditions.

(c) In heating, ventilating and air-conditioning (HVAC)

systems: Nanofluids could improve heat transfercapabilities of current industrial HVAC and refriger-ation systems. Many innovative concepts are beingconsidered; one involves pumping of coolant fromone location where the refrigeration unit is housedin another location. Nanofluid technology couldmake the process more energy efficient and costeffective.

1.3.2. Medical applications

Magnetic nanoparticles in body fluids (biofluids) can beused as delivery vehicles for drugs or radiation, providingnew cancer treatment techniques. Due to their surfaceproperties, nanoparticles are more adhesive to tumor cellsthan normal cells. Thus, magnetic nanoparticles excited


by an AC magnetic field is promising for cancer therapy.The combined effect of radiation and hyperthermia is dueto the heat-induced malfunction of the repair process rightafter radiation-induced DNA damage. Therefore, in futurenanofluids can be used as advanced drug delivery fluids.

2. Synthesis of nanofluids

Preparation of nanofluids is the first key step to investi-gate the heat transfer performance of nanofluids. A nano-fluid does not mean a simple mixture of liquid and solidnanoparticles. Techniques for good dispersions of nano-particles in liquids or directly producing stable nanofluidsare crucial. Nanofluids are produced by dispersing nano-meter-sized solid particles into liquids such as water, ethyl-ene glycol, or oils. Modern fabrication technologiesprovide great opportunities to process materials at nano-meter scales. Nanostructured materials exhibit new orenhanced properties, which are not exhibited by the bulksolids. There are mainly two techniques for synthesizingnanofluids, which are the two-step process and the directevaporation technique or single-step process [3,4].

In the two-step process, dry nanoparticles are first pro-duced by an inert gas condensation method and they arethen dispersed into a fluid. Fig. 2 shows TEM images ofseveral types of commercial nanoparticles (Nanostructuredand Amorphous Materials, Inc., USA). This method mayresult in a large degree of nanoparticle agglomeration.Thus, proper dispersion techniques and small volume frac-tion of nanoparticles are important to produce stable nano-fluids by this technique. An advantage of the two-stepprocess in terms of eventual commercialization of nanofl-uids is that the inert gas condensation technique can pro-duce tonnage quantities of nanopowders.

The direct evaporation technique synthesizes nanoparti-cles and disperses them into a fluid in a single step. As withthe inert gas condensation technique, this technique

Fig. 2. TEM photographs of nanoparticles from Nanostructured and Amo

involves the vaporization of a source material under vac-uum conditions. An advantage of this process is that nano-particle agglomeration is minimized. The disadvantages arethat the liquid must have a very low vapor pressure andthat this technique can produce very limited amounts ofnanofluids. At present, most researchers use the two-stepprocess to produce nanofluids by dispersing commercialor self-produced nanoparticles in a liquid. The optimiza-tion (i.e. improvement) of thermal properties of nanofluidsrequires stable nanofluids, which can be ensured by propersynthesis and dispersion procedures.

3. Experimental studies on thermal conductivity of nanofluids

3.1. Measurement method

Since the transient hot-wire (THW) method was first sug-gested by Stalhane and Pyk (Horrocks and McLaughlin [15])in 1931 to measure the absolute thermal conductivity of pow-ders, many researchers have modified the method to make itmore accurate. With development of modern electronicinstrumentation and use of a proper theoretical basis, thismethod has evolved into an accurate means of determiningthe thermal conductivity of fluids. Attempts have been madeby several researchers to extend the THW method to mea-sure the thermal conductivity of electrically conductingmedia. Nagasaka and Nagashima [16] performed thermalconductivity measurements of electrically conducting liquidsby considering the electrical insulation layer effect on heattransfer in their experimental facility. No significant negativeeffect of insulation layer was found.

Although several studies reported the use of the steady-state technique [7,17], temperature oscillation technique [9],and the 3x-wire method [18] to determine the effective ther-mal conductivity of nanofluids, these techniques are not asaccurate as the THW method. The temperature oscillationtechnique measures the thermal diffusivity and derives the

rphous Materials, Inc., USA: (a) TiO2 (15 nm) and (b) Al2O3 (80 nm).


thermal conductivity from this measured value and the vol-umetric specific heat of sample. Similar to the hot-wiremethod, the 3x-wire method uses a metal wire suspendedin a liquid. A sinusoidal current at frequency x passesthrough the metal wire and generates a heat wave at fre-quency 2x, which is deduced by the voltage componentat frequency 3x. The 3x-wire method may be suitable tomeasure temperature-dependent thermal conductivity.

The THW method has proved to be one of the mostaccurate techniques of determining the thermal conductiv-ity of a fluid [15,16]. The advantage of this method lies inits near elimination of natural convection effects. In addi-tion, this method is very fast compared to other techniques.The conceptual design of the hot-wire apparatus is alsosimple when compared to other techniques.

Table 1Summarized results for thermal conductivity of different types of nanofluids

Researchers Nanofluids [particle(size in nm)/base fluid]

Measurement techniq

Eastman et al. [4] Al2O3 (33)/water THW methodCuO (36)/waterCu (35)/oil

Lee et al. [6] Al2O3 (38)/water/EG THW methodCuO (23.6)/water/EG

Wang et al. [7] Al2O3 (28)/water/EG Steady-state methodCuO (23)/water/EG

Xuan and Li [8] Cu (100)/water/TO THW methodChoi et al. [19] MWCNT (25 nm � 50 lm)/oil THW methodEastman et al. [5] Cu (<10)/EG THW method

CuO (35)/EGXie et al. [20] Al2O3 (60.4)/water/EG THW methodWang et al. [21] Al2O3 (29)/EG Steady-state parallel

plate methodTiO2 (40)/EGWang et al. [17] CuO (50)/DIW Quasi-steady stateXuan and Li [22] Cu (10)/water THW methodPatel et al. [23] Au (10–20)/toluene/water THW methodKumar et al. [24] Au (4)/water/toluene THW methodMurshed et al. [10] TiO2 (15)/DIW THW method

TiO2 (10 � 40)/DIWHong et al. [11] Fe (10)/EG THW methodKwak and Kim

[25]CuO (12)/EG THW method

Li and Peterson[12]

CuO (29)/water Steady-state methodAl2O3 (36)/water

Zhu et al. [26] Fe3O4 (10)/water THW methodHwang et al. [27] CuO (35.4)/water/EG THW methodXuan et al. [28] Cu (35.4)/water THW methodMurshed et al. [29] Al2O3 (80)/DIW THW methodLiu et al. [30] CuO (29)/EG THW methodKrishnamurthy

et al. [31]Al2O3 (20)/water Unspecified

Wen and Ding [32] TiO2 (34)/water THW methodPutnam et al. [33] Au (4)/ethanol Optical beam deflect

techniqueKang et al. [34] Diamond (30–40)/EG THW method

Ag (8–15)/waterMurshed et al. [35] TiO2 (15)/EG THW method

Al (80)/EG

Notation: DIW, EG, TO, and MWCNT stand for deionised water, ethylene gTHW stands for transient hot-wire.

3.2. Effect of volume fraction and particle size

In the past few years, many experimental investigationson the thermal conductivity of nanofluids have beenreported. The effective thermal conductivities of nanofluidscontaining different concentrations, materials and sizes ofnanoparticles dispersed in different base fluids have beenexperimentally investigated. The published results on thethermal conductivity of nanofluids at room temperatureare summarized in Table 1.

Reported results of the effective thermal conductivity ofnanofluids as a function of nanoparticle volume fractionfrom various research groups are shown in Fig. 3. It canbe seen that even for the same nanofluids, different groupsreported different enhancements.

ue Observed significant enhancement of thermalconductivity (k) with particle volume percentage

29% for 5 vol%60% for 5 vol%44% for 0.052 vol%CuO/EG: 22% for 4 vol%Al2O3/EG: 18% for 5 vol%Al2O3/water: 12% for 3 vol%Al2O3/EG: 26% for 5 vol%Cu/water: 54% for 5 vol%160% for 1 vol%40% for 0.3 vol%22% for 4 vol%Al2O3/EG: 30% for 5 vol%18% for 4 vol%13% for 5 vol%17% for 0.4 vol%70% for 3 vol%Au/toluene: 5.5% for 0.008 vol% at 30 �CAu/water: 20% for 0.00013 vol% at 30 �C30% for 5 vol%33% for 5 vol%18% for 0.55 vol%6% for 1 vol%

52% for 6 vol% at 34 �C30% for 10 vol% at 34 �C38% for 4 vol%CuO/EG: 9% for 1 vol%24% for 2 vol%24% for 5 vol%23% for 5 vol%16% for 1 vol%

6% for 0.66 vol%ion 1.3% ± 0.8% for 0.018 vol%

75% for 1.32 vol%11% for 0.4 vol%18% for 5 vol%45% for 5 vol%

lycol, transformer oil, and multi-wall carbon nanotubes, respectively and

Particle volume fraction0.00 0.01 0.02 0.03 0.04 0.05

k nf/

k f

1.0

1.2

1.4

1.6

1.8

Al2O3 (33 nm)/water [4]

Al2O3 (20 nm)/water [31]

Al2O3 (60.4 nm)/water [20]

Al2O3(38 nm)/EG [6]

Al2O3 (28 nm)/EG [7]

Al2O3 (60.4 nm)/EG [20]

CuO (36 nm)/water [4]CuO (50 nm)/water [17]Cu (35 nm)/oil [4]Au (4 nm)/water [24]TiO2 (15 nm)/DIW [10]

Al (80 nm)/EG [35]

Fig. 3. Comparison of experimental results of the enhanced thermal conductivity of nanofluids.


From the reported results shown in Table 1 and Fig. 3, itis clear that nanofluids exhibit much higher thermal con-ductivities than their base fluids even when the concentra-tions of suspended nanoparticles are very low and theyincrease significantly with nanoparticle volume fraction.Several representative studies on the thermal conductivityof nanofluids are elaborated below.

The first results on the enhanced effective thermal con-ductivity of nanofluids were reported by Eastman et al.[4]. By dispersing Al2O3 and CuO nanoparticles in water,the reported increase in thermal conductivity were 29%and 60%, respectively for a nanoparticle volumetric load-ing of 5%. Surprisingly, in the case of Cu/oil-basednanofluids, the thermal conductivity was increased byabout 44% by dispersing only 0.052 vol% of Cu nanopar-ticles in HE-200 oil. The same group [6] later showed amoderate enhancement of thermal conductivity for thesame ceramic nanoparticles (Al2O3 and CuO) dispersedin water and ethylene glycol. For instance, a 20%enhancement in the thermal conductivity of ethylene gly-col was observed for 4.0 vol% of CuO nanoparticles.Wang et al. [17] reported a significant 17% increase inthe thermal conductivity for a loading of 0.4 vol% of50 nm sized same nanoparticles (CuO) in water.Recently, Li and Peterson [12] measured the thermal con-ductivity of the same ceramic nanofluids i.e. CuO(29 nm)/water and Al2O3 (36 nm)/water by using asteady-state method named as ‘‘cut-bar apparatus”. Theirresults were more astounding as both the CuO andAl2O3 nanoparticles increased the thermal conductivityof water by 52% and 22%, respectively at a volume frac-tion of just 6% at 34 �C.

Choi et al. [19] measured the thermal conductivity of oilsuspensions containing multi-walled carbon nanotubes(MWCNT). At 1% volumetric loading, the thermal con-ductivity was increased by 160%. Interestingly, the conduc-tivity increase as a function of nanotubes loading is

nonlinear even at very low volume fractions. The possiblereason was thought to be strong interactions of thermalfields associated with different fibers.

Thermal conductivities of several types of nanofluidswere experimentally studied by Wang et al. [21]. In theirstudy, nanofluids were prepared by suspending CuO(33 nm), Al2O3 (29 nm) and TiO2 (40 nm) in ethylene glycoland their thermal conductivities were measured by thesteady-state parallel plate method. The Al2O3/EG-basednanofluids showed 18% increase in the thermal conductiv-ity at particle vol% of 4. In contrast, Xie et al. [20] observedabout 30% increase in the thermal conductivity for 5 vol%of Al2O3 (60.4 nm) nanoparticles in the same base fluid.Although the particle size used by Xie et al. was doublethat of the particles of Wang et al., their results showed amuch higher thermal conductivity than that of Wanget al. for this nanofluid. This discrepancy could be due todifferent measurement methods and adjustment of pH val-ues of the nanofluids used by Xie et al. However, Xieet al.’s [20] study showed that the effective thermal conduc-tivity of nanofluids depends on the particle size and the pHvalues of the suspension.

Patel et al. [23] used gold and silver nanoparticles to pre-pare water and toluene-based nanofluids. Their resultsshowed that at room temperature, the conductivity ofAu/toluene nanofluid was enhanced by 4–7% for verylow volumetric loading of 0.005–0.011%, whereas theenhancement for Au/water nanofluid was about 3.2–5%for a vanishingly small concentration of 0.0013–0.0026%.The reason for such anomalously high thermal conductiv-ities was the small size of nanoparticles and high thermalconductivity of particle materials. Later, a larger enhance-ment in thermal conductivity of Au (4 nm)/water-basednanofluids was reported by the same group [24]. At extre-mely low volumetric loading of 1.3 � 10�4% of ultra-fineAu nanoparticles, the thermal conductivity was found toincrease by 20% at 30 �C.


Murshed et al. [10] measured the thermal conductivity ofTiO2 of 15 nm and 10 � 40 nm sized spherical and cylindri-cal shape nanoparticles in deionized water. For the low vol-ume fraction (<1%), their results showed a nonlinearincrease in thermal conductivity. They, however, found sig-nificant increase i.e. 32% (for 5 vol%) in thermal conductiv-ity with volume fraction. Furthermore, their results showedthat cylindrical shape nanoparticles exhibit slightly higherthermal conductivity compared to spherical shape nano-particles. Subsequently, Murshed et al. [29,35] and Leonget al. [67] presented more results for several types of nano-fluids i.e. Al2O3/DI water, TiO2/EG, and Al/EG to vali-date their thermal conductivity models. For a particlevolumetric loading of 5%, the maximum enhancement ofthermal conductivities of TiO2 (15 nm)/EG- and Al(80 nm)/EG-based nanofluids are 18% and 45%, respec-tively. Nanofluids having higher thermally conductivenanoparticles (Al) exhibit much higher thermal conductiv-ity compared to the nanofluids having lower thermally con-ductive nanoparticles (TiO2).

For Fe (10 nm)/EG-based nanofluids, a large increase inthermal conductivity was reported by Hong et al. [11].They obtained an enhancement of 18% with just0.55 vol% of Fe nanoparticles. They also noticed that son-ication has a significant effect on the thermal conductivityof nanofluids. Nonetheless, their observed enhancementfor this nanofluid was even much higher than that of theCu/EG-based nanofluids obtained by Eastman et al. [5].This indicates that the suspension of high conductivitymaterials is not always effective to improve thermal con-ductivity of nanofluids.

By using the co-precipitation method, Zhu et al. [26]prepared Fe3O4 (10 nm)/water-based nanofluids and mea-sured the thermal conductivity by the THW method. Theyfound a 38% increase in the thermal conductivity for thenanoparticle volume fraction of 0.04. Zhu et al. ascribedsuch anomalously high thermal conductivity to the nano-particle alignment in clusters.

Putnam et al. [33] performed experiments to measure thethermal conductivity of Au (4 nm)/ethanol-based nanofl-uids by the optical beam deflection technique. For the firsttime, their results showed no anomalous enhancement ofthermal conductivity of nanofluids with very low particlevolume fraction. Their observed maximum enhancementin thermal conductivity was 1.3% ± 0.8% for 0.018% volu-metric loading of 4 nm Au particles in ethanol. This resultis directly in conflict with the anomalous result of Patelet al. [23] for the same nanofluid.

From a comparison of the reported studies, the incre-ments of thermal conductivities are different for differenttypes of nanofluids. The thermal conductivity of nanofluidsvaries with the size, material of nanoparticles as well asbase fluids. For instance, nanofluids with metallic nanopar-ticles were found to have a higher thermal conductivitythan nanofluids with nonmetallic (oxide) nanoparticles.The smaller the particle size, the larger the thermal conduc-tivities of nanofluids. Furthermore, several studies reported

that high conductivity nanoparticles are not always effec-tive in enhancing the thermal conductivity of nanofluids[11,36].

The particle size is important because shrinking it downto nanoscale not only increases the surface area relative tovolume but also generates some nanoscale mechanisms inthe suspensions [14,37–39]. Theoretical evidence [37,38,40]indicate that the effective thermal conductivity of nanofl-uids increases with decreasing particle size. Chon andKihm [41] experimentally measured the thermal conductiv-ity of nanofluids with nanoparticles of different sizes. Theyshowed that the 47 nm Al2O3 nanoparticles in water gave alarger increase in thermal conductivity compared to the150 nm nanoparticles.

3.3. Effect of fluid temperature

Fluid temperature may play an important role inenhancing the effective thermal conductivity of nanofluids.Despite the fact that nanofluids may be used under varioustemperatures, very few studies were performed to investi-gate the temperature effect on the effective thermal conduc-tivity of nanofluids. A summary of the published results ontemperature-dependent thermal conductivity of variousnanofluids is provided in Table 2.

Das et al. [9] experimentally investigated the effect oftemperature on the thermal conductivity of nanofluids con-taining Al2O3 (38.4 nm) and CuO (28.6 nm) nanoparticlesin water. A temperature oscillation technique, which deter-mines the thermal conductivity through measuring thethermal diffusivity of sample medium, was used in theirstudy. They reported a two- to four-fold increase in ther-mal conductivity enhancement for these nanofluids over atemperature range of 21–51 �C. It was also observed thatCuO/water-based nanofluids showed a higher enhance-ment with respect to temperature than that of Al2O3/water-based nanofluids. Nonetheless, their maximum mea-surement error was of the order of 7% at 50 �C. Das et al.suggested that the strong temperature dependence of ther-mal conductivity was due to the Brownian motion of nano-particles. Using the THW technique, the same group [23]performed experiments for water-based nanofluids contain-ing 10–20 nm sized Au particles. Nanofluids with citratestabilization showed thermal conductivity enhancementof 5–21% in a temperature range of 30–60 �C at a verylow volumetric loading of 0.00026%. They concluded thatchemical effects came into play in determining the extentof energy transfer in nanofluids.

By dispersing Al2O3 nanoparticles of 47 nm and 150 nmin water, Chon and Kihm [41] studied the effects of particlesize and fluid temperature on the thermal conductivity ofnanofluids. They observed a moderate enhancement ofthermal conductivity with respect to temperature. The ther-mal conductivity of Al2O3 (47 nm)/water-based nanofluidsincreased by 6–11% when the fluid temperature wasincreased from 31 �C to 51 �C. Chon and Kihm alsoshowed the inverse dependence of particle size on the ther-

Table 2Temperature-dependent thermal conductivity of nanofluids

Researchers Nanofluids [particle(size in nm)/base fluid]

Measurement technique Observed maximum enhancement of thermal conductivity (k) withtemperature

Das et al. [9] Al2O3(38.4)/water Temperature oscillationtechnique

For 4 vol%: 16% at 36 �C and 25% at 51 �CCuO (28.6)/water For 1 vol%: 22% at 36 �C and 30% at 51 �C

Patel et al. [23] Au (10–20)/water THW method For 0.00026 vol%: 5–21% at temperature range of 30–60 �CChon and Kihm

[41]Al2O3 (47)/water THW method 6% at 31 �C and 11% at 51 �CAl2O3 (150)/water 3% at 31 �C and 8.5% at 51 �C [for 1 vol%:]

Li and Peterson[12]

Al2O3 (36)/water Steady-state method For 2 vol%: 7% at 27.5 �C and 23% at 36 �C

Yang and Han[18]

Bi2Te3 (20 � 170)/FC72/oil 3x-Wire method For Bi2Te3/FC72 at 0.8 vol%: 8% at 10 �C and 7% at 40 �C

Venerus et al.[42]

Au (22)/water Al2O3 (30)/petroleum oil

Forced Rayleigh scattering No enhancement but slight decrease with the temperature in therange of 25–75 �C

Murshed et al.[35]

Al2O3 (80)/EG THW method 1 vol%: 11.4% at 60 �CAl2O3 (80)/DIW 1 vol%: 12.1% at 60 �CAl2O3 (150)/DIW 1 vol%: 10.3% at 60 �CAl (80)/EO 3 vol%: 37% at 60 �C


mal conductivity of nanofluids. They identified Brownianmotion of the nanoparticles as the possible mechanismfor increased thermal conductivity with fluid temperature.However, results obtained by Li and Peterson [12] demon-strated a surprising increase in the thermal conductivity ofnanofluids with a small increase of fluid temperature. Forexample, for Al2O3 (47)/water-based nanofluids at2 vol%, an increase in fluid temperature to 36 �C resultedin an enhancement of three times compared to the thermalconductivity at 27.5 �C.

Yang and Han [18] measured the thermal conductivityof suspensions of Bi2Te3 (20 � 170 nm) nanorods inFC72 and in oil (hexadecane) by using the 3x-wire method.Interestingly, they observed a slightly decrease in the ther-mal conductivity with increasing temperature, which is incontrast to the trend observed in nanofluids containingspherical nanoparticles. The contrary trend was claimedto be due mainly to the particle aspect ratio.

Venerus et al. [42] used the forced Rayleigh scatteringtechnique to measure the thermal conductivity of Au(22)/water and Al2O3 (30)/petroleum oil-based nanofluidsin the range of 25–75 �C. In contrast to all other reportedresults, they found that the level of thermal conductivityenhancement for these nanofluids is independent oftemperature.

Very recently, the effect of temperature on the enhance-ment of effective thermal conductivity of various nanofl-uids was investigated by Murshed et al. [35] fortemperatures from 20 to 60 �C. At 60 �C, the effective ther-mal conductivity of Al2O3 (80 nm)/EG-based nanofluidsincreases by about 9% and 12% (compared to that of thebase fluid) for nanoparticle volumetric loadings of 0.5%and 1%, respectively. The enhancement of effective thermalconductivity of Al (80 nm)/EO nanofluids are 20% and37% for volumetric loadings of 1% and 3% nanoparticlesin the base fluid, respectively. Their results for Al2O3

(80 nm)/DIW-based nanofluids at 1% volumetric loadingwere found to be consistent with the experimental data of

Das et al. [9] and Chon and Kihm [41] although the sizeof their Al2O3 nanoparticles is much larger. For the samesize (150 nm) of Al2O3 nanoparticles, Murshed et al.’sresults of thermal conductivity are slightly higher thanthose reported by Chon and Kihm [41]. The observed dif-ferences could be due to the addition of surfactant to nano-fluids and the different measurement methods.

Other than the studies of Yang and Han [18] and Vene-rus et al. [42], all published results demonstrate that thethermal conductivity of nanofluids increases significantlywith the fluid temperature. However, there is a clear lackof consistency among the reported results of differentresearch groups.

4. Studies on thermal diffusivity of nanofluids

While the determination and prediction of the effectivethermal conductivity of nanofluids have attracted muchattention in recent years, very little work has been per-formed on the effective thermal diffusivity of nanofluids,which is especially important in convective heat transferapplications. Xuan and Roetzel [43] discussed the effectivethermal diffusivity tensor for flowing fluids under both lam-inar and turbulent flow conditions. However, neitherexperimental nor theoretical result for the effective thermaldiffusivity of nanofluids was provided in their paper. Wanget al. [44] measured the thermal conductivity and specificheat of some nanofluids and thereby calculated their effec-tive thermal diffusivity. Their calculated results were alsofound to fluctuate severely with volume fraction.

Murshed et al. [45] studied the effective thermal diffusiv-ity of several types of nanofluids at different volume per-centages (1–5%) of titanium dioxide (TiO2), aluminumoxide (Al2O3) and aluminum (Al) nanoparticles in ethyleneglycol and engine oil. The thermal diffusivities of thesenanofluids measured directly by a novel transient doublehot-wire technique were found to increase substantiallywith increased volume fraction of nanoparticles in base flu-

Particle volume fraction0.01 0.02 0.03 0.04 0.05

Rel

ativ

e vi

scos

ity (

η nf/

η f)

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4TiO2 /DIW

Masuda et al. [48] (TiO2 /water)

Al2 O3 /DIW

Wang et al. [7] (Al2 O3 /water)

K-D [55] model (TiO2 /DIW)

Nielsen's [56] model (TiO2 /DIW)

Fig. 4. Relative viscosities of nanofluids with nanoparticle volumefraction.


ids. For example, for maximum 5% volumetric loading ofTiO2 nanoparticles of 15 nm and 10 � 40 nm in ethyleneglycol, the maximum increase in effective thermal diffusiv-ity was observed to be 25% and 29%, respectively. Nanofl-uids with aluminum nanoparticles in ethylene glycol andengine oil showed substantial enhancement of thermal dif-fusivity i.e. maximum 49% and 36%, respectively comparedto their base fluids. The effects of particle shape and basefluid were also observed in their study.

5. Studies on viscosity of nanofluids

Although some review articles [39,46,47] emphasized thesignificance of investigating the viscosity of nanofluids,very few studies on effective viscosity were reported. It isbelieved that viscosity is as critical as thermal conductivityin engineering systems that employ fluid flow. Pumpingpower is proportional to the pressure drop, which in turnis related to fluid viscosity. In laminar flow, the pressuredrop is directly proportional to the viscosity.

Masuda et al. [48] measured the viscosity of suspensionsof dispersed ultra-fine particles in water. They found thatTiO2 (27 nm) particles at a volumetric loading of 4.3%increased the viscosity of water by 60%. Wang et al. [7]observed that the effective viscosity of Al2O3 (28 nm)/DIW-based nanofluids was increased by about 86% for a5 vol% of nanoparticles. In their case, a mechanical blend-ing technique was used for dispersion of Al2O3 nanoparti-cles in distilled water. They also found an increase of about40% in viscosity of ethylene glycol at a volumetric loadingof 3.5% of Al2O3 nanoparticles. Their results indicate thatthe viscosity of nanofluids depends on dispersion methods.In contrast, Pak and Cho [49] found that at 10 vol% con-centration of nanoparticles, the viscosities of Al2O3

(13 nm)/water and TiO2 (27 nm)/water-based nanofluidsare several times greater than that of water. This large dis-crepancy could be due to differences in dispersion tech-nique and size of particles. Pak and Cho also usedadjusted pH values and employed an electrostatic repulsiontechnique. As expected, the viscosity of nanofluids dependson the methods used to disperse and stabilize the nanopar-ticle suspension. Their [49] viscosity results were signifi-cantly larger than the predictions from the classicaltheory of suspension rheology such as Einstein’s model[50].

Das et al. [51] and Putra et al. [52] measured the viscos-ity of Al2O3/water and CuO/water-based nanofluids as afunction of shear rate and showed Newtonian behaviorof the nanofluids for a range of volume percentage between1% and 4%. For Al2O3/water-based nanofluids, Das et al.[51] also observed an increase in viscosity with an increaseof particle volume fraction.

At a given shear rate, Ding et al. [53] observed that theviscosity of nanofluids increased with an increasing CNTconcentration and decreasing temperature. A clear shearthinning was observed at all concentrations. This suggeststhat nanofluids can offer better fluid flow performance

due to the higher shear rate at the wall, which results inlow viscosity.

Prasher et al. [54] reported the viscosity results of alu-mina-based nanofluids for various shear rates, tempera-ture, and particle volume fraction. Their datademonstrate that viscosity is independent of shear rate,proving that the nanofluids are Newtonian in nature. Italso shows that with increasing nanoparticle volume frac-tion, the viscosity also increases. On the other hand, theyfound that viscosity is independent of temperature. Thisis contrary to the normal dependence of liquid viscosityon temperature.

For TiO2 (34 nm)/water-based nanofluids, Wen andDing [32] found about 20% increase in the effective viscos-ity for a concentration of 2.4 weight %. However, a muchhigher viscosity increase was observed under low share rateconditions i.e. 25–100 s�1.

As shown in Fig. 4, Murshed et al. [35] measured the vis-cosity of TiO2 (15 nm)/DIW-based nanofluids. Theirresults were higher than those of Masuda et al. [48] whoshowed that TiO2 (27 nm) particles at a volume fractionof 4.3% increased the viscosity of water by 60%. However,viscosities of Al2O3 (80 nm)/DIW-based nanofluids werefound to increase by nearly 82% for the maximum volumet-ric loading of nanoparticles 5%. A similar increment (86%)of the effective viscosity of the same nanofluids was alsoobserved by Wang et al. [7]. Comparisons between theresults obtained by Murshed et al. [35] and the predictionsby Krieger and Dougherty’s [55] and Nielsen’s [56] modelsshowed that these models severely under-predict the viscos-ity of nanofluids (Fig. 4).

All reported results show that the viscosity of nanofluidsis increased anomalously and cannot be predicted by clas-sical models such as by Einstein [50], Krieger and Dough-erty [55], Nielsen [56], and Batchelor [57]. No firmconclusion can be drawn from the above fluctuating dataof several nanofluids. Thus, more thorough investigations


should be carried out on the effective viscosity ofnanofluids.

6. Theoretical studies on nanofluids

6.1. Underlying mechanisms for the enhanced thermal

conductivity of nanofluids

The classical models which were developed from theeffective medium theory for the effective thermal conductiv-ity of composites have been verified by experimental datafor mixtures with low concentrations of milli- or microme-ter-sized particles. Experiments have shown that nanofluidsexhibit anomalously high thermal conductivity, which can-not be predicted accurately by the classical models. Toexplain the observed enhanced thermal conductivity ofnanofluids, Wang et al. [7] and Keblinski et al. [37] pro-posed various mechanisms, which were not considered byclassical models. Wang et al. [7] suggested that the micro-scopic motion of nanoparticles, the surface properties,and the structural effects might cause enhanced thermalconductivity of nanofluids. In nanofluids, the microscopicmotion of the nanoparticles due to Brownian motion,van der Waals force, and electrostatic force can be signifi-cant. Wang et al. however, showed that Brownian motiondoes not contribute significantly to the heat energy trans-port in nanofluids. They indicated that the electric doublelayer and van der Waals force could have strong electroki-netic effects on the nanoparticles. The surface propertiesand structural effects were not confirmed as potentialmechanisms in their study.

Keblinski et al. [37] later elucidated four possible mech-anisms for the anomalous increase in nanofluids heat trans-fer, and these mechanisms are (i) Brownian motion of thenanoparticles, (ii) liquid layering at the liquid/particleinterface, (iii) nature of the heat transport in the nanopar-ticles, and (iv) the effect of nanoparticle clustering.

Brownian motion is caused by the random bombard-ment of liquid molecules. Due to the Brownian motion,particles randomly move through the liquid, therebyenabling stronger transport of heat (compared to sole heatconduction), which can increase the effective thermal con-ductivity. For Brownian motion to be a significant contrib-utor to the thermal conductivity, it would have to be amore efficient mechanism than thermal diffusion in thefluid. However, by a simple analysis, Keblinski et al. [37]showed that the thermal diffusion is much faster thanBrownian diffusion, even within the limits of extremelysmall particles.

When the size of the nanoparticles in a nanofluidbecomes less than the phonon mean-free path, phononsno longer diffuse across the nanoparticle but move ballisti-cally without any scattering. However, it is difficult to envi-sion how ballistic phonon transport could be more effectivethan a very-fast diffusion phonon transport, particularly tothe extent of explaining anomalously high thermal conduc-tivity of nanofluids. No further work or analysis has been

reported on the ballistic heat transport nature of nanopar-ticles. Instead, the continuum approach was adopted in allreported works [17,29,35,38].

Liquid layering around the particle (i.e. nanolayer) wasproposed as another responsible mechanism accountingfor higher thermal properties of nanofluids. The basic ideais that liquid molecules can form a layer around the solid par-ticles and thereby enhance the local ordering of the atomicstructure at the interface region. Hence, the atomic structureof such liquid layer is significantly more ordered than that ofthe bulk liquid. Given that solids, which have much orderedatomic structure, exhibit much higher thermal conductivitythan liquids, the liquid layer at the interface would reason-ably have a higher thermal conductivity than the bulk liquid.Thus the nanolayer is considered as an important factorenhancing the thermal conductivity of nanofluids.

The effective volume of a cluster is considered much lar-ger than the volume of the particles due to the lower pack-ing fraction (ratio of the volume of the solid particles in thecluster to the total volume of the cluster) of the cluster.Since heat can be transferred rapidly within such clusters,the volume fraction of the highly conductive phase (cluster)is larger than the volume of solid, thus increasing its ther-mal conductivity [11,37]. It is however noted that in gen-eral, clustering may also exert a negative effect on heattransfer enhancement, particularly at a low volume frac-tion by settling small particles out of the liquid and creatinga large regions of ‘‘particle free” liquid with a high thermalresistance [37].

Besides these mechanisms, it is the authors’ believe thatthe effects of particle surface chemistry and particles inter-action for nanometer-sized particles could be significant inenhancing the thermal conductivity of nanofluids.

6.2. Models for the effective thermal conductivity

To predict the effective thermal conductivity of solidparticle suspensions, several models were developed sincethe treatise by Maxwell [1]. As mentioned previously, theseclassical models such as those attributed to Maxwell [1],Hamilton–Crosser [58], Bruggeman (Hui et al. [59]), andWasp (Xuan and Li [8]) were developed for predictingthe effective thermal conductivity of a continuum mediumwith well-dispersed solid particles.

The Maxwell model [1] was developed to determine theeffective electrical or thermal conductivity of liquid–solidsuspensions for low volumetric loading of spherical parti-cles. This model is applicable to statistically homogeneousand low volume fraction liquid–solid suspensions with ran-domly dispersed and uniformly sized spherical particles.Hamilton and Crosser [58] modified Maxwell’s model todetermine the effective thermal conductivity of nonspheri-cal particles by applying a shape factor. For spherical par-ticles, the Hamilton and Crosser (HC) model reduces to theMaxwell model. The Bruggeman model (BGM) [59] isanother well-known model for determining the effectivethermal conductivity of mixture and composites. In this


model, the mean field approach is used to analyze the inter-actions among the randomly distributed particles. TheWasp model is the same as the Maxwell model althoughit is not specified for any particular shape of particles.

The classical models were found to be unable to predictthe anomalously high thermal conductivity of nanofluids.This is because these models do not include the effects ofparticle size, interfacial layer at the particle/liquid interface,and Brownian motion of particles, which are considered asimportant factors for enhancing thermal conductivity ofnanofluids [7,37–40,60]. Recently, many theoretical studieshave been carried out to predict the anomalously increasedthermal conductivity of nanofluids. Several models havebeen proposed to include various mechanisms. A detailed

Table 3Summary of models for the effective thermal conductivity of nanofluids

Researchers Classical models/equations

Maxwell [1] keff=kf ¼ kpþ2kfþ2/ðkp�kf Þkpþ2kf�/ðkp�kf Þ

Hamilton andCrosser (HC)[58]

keff=kf ¼ kpþðn�1Þkf�ðn�1Þ/ðkf�kpÞkpþðn�1Þkfþ/ðkf�kpÞ

h i

Bruggeman (Huiet al. [59])

keff ¼ 14 ½ð3/� 1Þkp þ ð2� 3/Þkf � þ kf

4

ffiffiffiffiDp

whereD = [(3/ � 1)2(kp/kf)

2 + (2 � 3/)2 + 2(2 + 9/ � 9/2)(kp

kf)]Wasp (Xuan and

Li [8])keff=kf ¼ kpþ2kf�2/ðkf�kpÞ

kpþ2kfþ/ðkf�kpÞ

Researchers Models/Expressions for nanofluids

Wang et al. [17] keff

kf¼ð1�/Þþ3/

R 10

kcl ðrÞnðrÞkcl ðrÞþ2kf

dr

ð1�/Þþ3/R 1

0

kf nðrÞkcl ðrÞþ2kf

dr

Xue [60] 9 1� vk

� � keff�kf

2keffþkfþ v

kkeff�kc;x

keffþB2;xðkc;x�keff Þ þ 4keff�kc;y

2keffþð1�B2;xÞðkc;y�keff Þ

h i

Yu and Choi[38,61]

(1) keff=kf ¼ kpeþ2kfþ2/ðkpe�kf Þð1þbÞ3

kpeþ2kf�/ðkp�kf Þð1þbÞ3

(2) keff=kf ¼ 1þ n/eff A1�/eff A, where A ¼ 1

3

Pj¼a;b;c

kpj�kf

kpjþðn�1Þkf

Xuan et al. [62] keff=kf ¼ kpþ2kf�2/ðkf�kpÞkpþ2kfþ/ðkf�kpÞ þ

/qpcp

2kf

ffiffiffiffiffiffiffiffiKBT3prcg

q

Kumar et al. [24] keff=kf ¼ 1þ c 2KBTpgd2

p

/rf

kf ð1�/Þrp

Jang and Choi [40] keff=kf ¼ 1þ c df

dpkf/Re2

dpPr

Prasher et al. [63] keff=kf ¼ ð1þ A/RemPr0:333Þ ð1þ2aÞþ2/ð1�aÞð1þ2aÞ�/ð1�aÞ where af = 2Rb

dp

Koo andKleinstreuer [64]

keff=kf ¼ kMG

kfþ 1

kf5� 104b/qpcp

ffiffiffiffiffiffiffiKBTqpD

qf ðT ;/Þ

Xie et al. [65] keff=kf ¼ 1þ 3H/þ 2H2/2

1�H/

Gao and Zhou [66] 1� / ¼ kf

keff

� �3AkfþB1

keffþB1

� �3C1 kfþB2

keffþB2

� �3C2

Leong et al. [67] keff ¼ðkp�klrÞ/pklr½2c3

1�c3þ1�þðkpþ2klrÞc3

1½/pc3ðklr�kf Þþkf �

c31ðkpþ2klrÞ�ðkp�klrÞ/p ½c3

1þc3�1�

Murshed et al. [29] keff ¼kf 1þ0:27/4=3

pkpkf�1

� �h i1þ 0:52/p

1�/1=3p

kpkf�1

� ��

1þ/4=3p

kpkf�1

� �0:52

1�/1=3p

þ0:27/1=3p þ0:27

Murshed et al. [35] keff ¼ðkp�klrÞ/pklr½c2

1�c2þ1�þðkpþklrÞc2

1½/pc2ðklr�kf Þþkf �

c21ðkpþklrÞ�ðkp�klrÞ/p ½c2

1þc2�1�

Notation: k is the thermal conductivity, d is the particle diameter, and / is tparticle, base fluid, layer, and cluster, respectively.

summary of all classical and recently developed modelsfor the prediction of the effective thermal conductivity ofnanofluids is provided in Table 3.

Yu and Choi [38,61] modified the Maxwell and Hamil-ton–Crosser models to account for the effect of the interfa-cial layer. They replaced the thermal conductivity andvolume fraction of nanoparticles with the thermal conduc-tivity and volume fraction of equivalent particles (i.e. par-ticle with a nanolayer), respectively. The thermalconductivity of an equivalent particle is considered to bethe same as the thermal conductivity of particle. This isnot realistic because the interfacial layer is formed by theliquid molecules wrapping over the particle surface andthe concentration of these adsorbed molecules in the inter-

Remarks

Depends on the thermal conductivities of both phases and volumefraction of solidValid for both the spherical and cylindrical particles and n = 3/wwhere w is the particle sphericity

Valid for spherical particles and considered interaction betweenparticles/

Same as Maxwell model

Remarks

Based on effective medium approximation (EMA) and fractal theory

¼ 0 Based on the Maxwell theory and average polarization theory withthe interfacial shell effect

Considered interfacial layer where (1) modified Maxwell model and(2) modified HC model with n = 3w�a

Second term of the equation has wrong units while first term is theMaxwell modelBased on kinetic theory and Fourier’s law

Based on convection and conduction heat transport

kf/ Included the effect of convection near the particle and interfacialresistance with unknown parameters A, m, Rb

Assumed randomly moving nanoparticles with surrounding liquidmotion having unknown parameters of b and f

Considered the presence of a nanolayer

Based on EMA and for spherical particles, it reduces to BruggemanmodelConsidered interfacial layer as separate component and for sphericalshape particle

Based on homogeneous distribution of nanoparticles

For cylindrically shaped particles in base fluid

he particle volume fraction. Subscripts eff, p, f, l, and c, denote effective,


facial layer is lower than that of the solid particle. Hence,the interfacial layer thermal conductivity should be lowerthan that of the solid particles but higher than that of theliquid. Apart from the dimension and thermal conductivityof nanolayer, the particle shape factor is also unknown intheir model [61].

Xue [60] proposed a model for calculating the effectivethermal conductivity of nanofluids. His model is basedon the Maxwell theory and average polarization theory,which includes the interfacial shell effect. In validatingXue’s [60] model with the experimental data of Choiet al. [19], two incorrect parameters (semi-axis and depolar-ization factor) were used. By using the two correctedparameters, Yu and Choi [61] later showed that Xue’smodel gave far higher values of thermal conductivity (e.g.knf = 32kf for 1 vol%) than those given in his paper [60].Thus, the validity and accuracy of Xue’s model are yet tobe established.

Based on the fractal theory for the clustering andpolarization of nanoparticles, Wang et al. [17] modifiedthe Maxwell model. Their model, however, requires thethermal conductivity of particle cluster and their radiusdistribution to be determined numerically. In addition,this model is yet to be validated with more experimentalresults.

Xie et al. [65] deduced a model for the prediction of theeffective thermal conductivity of nanofluids by consideringthe impact of interfacial layer. However, similar to Yu andChoi [38,61] and Xue [60] models, this empirical model hasto be fitted with experimental data by adjusting two fittingparameters. This model also does not consider anydynamic mechanism. By taking into account geometricand physical anisotropy, Gao and Zhou [66] proposed adifferential effective medium model based on the Brugg-eman model. For spherical particles, their model reducesto the Bruggeman model. By considering the uniformityand geometrical structures (e.g. body centered cubic) ofhomogenously dispersed nanoparticles in base fluids, amodel was developed by Murshed et al. [29] for the effectivethermal conductivity of nanofluids which shows a nonlin-ear nature. However, for Al2O3/DIW-based nanofluids,this model yields much higher thermal conductivity valuesthan those of experimental data.

All the existing models can be categorized into two gen-eral groups, which are

(i) static models which assume stationary nanoparticlesin the base fluid in which the thermal transport prop-erties are predicted by conduction-based models suchas those of Maxwell and Hamilton–Crosser, and

(ii) dynamic models which are based on the premise thatnanoparticles have lateral, random motion in thefluid. The particle motion is believed to be responsi-ble for energy transport directly through collisionbetween nanoparticles or indirectly through microliq-uid convection that enhances the thermal energytransfer.

Researchers in the first group [17,34,35,38,40,60,61,65,67–70] used the concept of a liquid/solid interfaciallayer to develop models and to explain the anomalousimprovement of the thermal conductivity in nanofluids.Approaches adopted in these studies can be classified underthe static model category. Except for Leong et al.’s [67]model, most of these models were developed by directlymodifying the Maxwell model, Hamilton–Crosser model,or Bruggeman model through the particle volume fraction.The layer dimension and properties are assumed to bemuch higher in order to fit the experimental data. Recently,Sabbaghzadeh and Ebrahimi [69] presented a model forcylindrically shaped particles by combining the approachesof Jang and Choi [40], Ren et al. [70] and Xie et al. [65].Their model takes into account the effect of the nanolayerin exactly the same way as Ren et al. and Xie et al.

Other groups of researchers emphasized on the contri-bution of dynamic part related to particle Brownianmotion. Although Wang et al. [7] and Keblinski et al.[37] showed that the contribution of Brownian motion toenergy transport in nanofluids is not significant, otherresearchers [62,24] held contrary views. Considering aggre-gation and Brownian motion of nanoparticles, Xuan et al.,[62] deduced a model for the effective thermal conductivityof nanofluids. However, their proposed model [Eq. (13) intheir paper] yields the wrong units. Kumar et al. [24] devel-oped a model based on Fourier’s law of diffusion andapplied the kinetic theory to consider Brownian motionof the nanoparticles. However, they postulated that themean-free path of a nanoparticle in fluid is of the orderof 1 cm, which is physically unrealistic. Moreover, theirmodel predicts an inverse cubic dependency on the particlediameter ð1=d3

pÞ as opposed to a simple inverse dependency(1/dp).

Jang and Choi [40] postulated that Brownian motioncontributes to microconvection. They deduced a theoreticalmodel that accounts for the role of dynamic nanoparticlesin nanofluids. Koo and Kleinstreuer [64] and Prasher et al.[63] considered the importance of Brownian-motion-drivenconvection in the fluid, rather than its direct contributionto the thermal conductivity of the particle motion itself.The models proposed by these researchers include the con-tribution of Brownian motion, and were derived from thekinetic theory. It is noted that the kinetic theory is notdirectly applicable to nanofluids without making significantcorrections. The arguments presented by Jang and Choi[40] are neither consistent nor convincing. Macroscale con-vection behavior was assumed at the nanoscale by invokingmacroscale correlations for flow around a solid sphere.Since the mean-free path of liquid is independent of theparticle diameter, it can be found [from Eqs. (11) and(12) in their paper] that their Reynolds number becomesindependent of particle size, which is not a justified conclu-sion. The correlation for flow past a sphere, however,assumes that the Reynolds number is linearly dependenton the sphere diameter. In Prasher et al.’s [63] model, the


effective thermal conductivity of nanofluids varies substan-tially with unknown parameters (especially constant m),which could only be determined by matching the experi-mental data. Similar to Jang and Choi [40], the Reynoldsnumber defined in Prasher et al.’s model also needs to bejustified.

Recently, Eapen et al. [71] defined a possible mechanismof thermal transport in dilute nanofluids. By calculating theheat flux from a nonequilibrium molecular dynamics simu-lation (NEMD) they showed that there are three modes,which are (i) the kinetic, (ii) the potential, and (iii) thecollisions.

Most recently, an improved model was developed byLeong et al. [72] to predict the effective thermal conductiv-ity of nanofluids containing spherically shaped nanoparti-cles. Compared to existing models, their model showsbetter agreement with experimental results. This was attrib-uted to the inclusion of both static and dynamic mecha-nisms such as particle size, nanolayer, particle movement,particle surface chemistry and interaction potential.

7. Electrokinetic phenomena of nanofluids

Electrochemical effects certainly influence the thermalconductivity of nanofluids through stability and particleinteractions. For example, the electrostatic repulsive force,which is described by the zeta potential, is important toavoiding agglomeration and thus sedimentation of nano-particles. Although some review articles [39,73] pro-nounced that the surface chemistry of nanoparticles couldbe an important factor influencing the thermal conductivityof nanofluids, there are very few reported studies whichinvestigate its effect on the enhanced thermal conductivityof nanofluids. Xie et al. [74] showed that simple acid treat-ment of carbon nanotubes enhanced the suspension stabil-ity of carbon nanotubes in water. It was attributed tohydrophobic-to-hydrophilic conversion of the surface nat-ure due to the generation of a hydroxyl group. Patel et al.[23] reported that 4 nm gold nanoparticles with a coating ofa covalent chain in toluene were about 50 times less effec-tive for heat transport than uncoated 10–20 nm gold parti-

Table 4Summary of forced convection heat transfer experimental studies of nanofluid

Researchers Geometry/flow nature Nanofluids Fin

Pak and Cho[49]

Tube/turbulent Al2O3 (13 nm), TiO2

(27 nm)/waterAt 3pur

Xuan and Li[22]

Tube/turbulent Cu (<100 nm)/water A la(Re

Wen andDing [77]

Tube/laminar Al2O3 (13 nm)/water Incr

Ding et al.[53]

Tube/laminar CNT/water At 0

Heris et al.[78]

Circular tube/laminar Al2O3 (20 nm), CuO (50–60 nm)/water

h in

Lai et al. [79] Tube/laminar Al2O3 (20 nm)/DIW Nu

Jung et al. [80] Rectangularmicrochannel/laminar

Al2O3 (20 nm)/water h in

cles in water. This is contrary to the findings of thenanoparticle size effect on the effective thermal conductivityof nanofluids [24,40].

Lee et al. [75] investigated the effect of zeta potential andparticle hydrodynamic size (i.e. the mobility equivalent size)on the thermal conductivity of nanofluids. The hydrody-namic diameter of CuO nanoparticles and thermal conduc-tivity of the nanofluids at different pH values were measuredin their study. Their results demonstrated that the pH valueaffects the thermal performance of the nanofluids. As thesolution pH value departs from the iso-electric point of par-ticles, the colloidal particles become more stable and even-tually alter the thermal conductivity of the fluid. Theyidentified that the surface charge state is primarily responsi-ble for the enhancement of thermal conductivity of thenanofluids. However, no further research was reported.

Prasher et al. [76] studied the effect of aggregation on theeffective thermal conductivity of nanofluids. They claimedthat the observed thermal conductivity of nanofluids canbe explained by the aggregation kinetics. It was alsoreported that the colloidal chemistry plays a significant rolein deciding the thermal conductivity of nanofluids.

8. Convective heat transfer studies of nanofluids

Compared to the reported research on thermal conduc-tivity, investigations on convective heat transfer of nanofl-uids are scarce. A summary of previous studies on forcedconvection heat transfer of nanofluids is given in Table 4.

Pak and Cho [49] performed experiments on convectiveheat transfer of two types of nanofluids i.e. c-Al2O3 andTiO2 dispersed in water, under turbulent flow conditions.Even though the Nusselt number (Nu) was found toincrease with the particle volume fraction and the Reynoldsnumber, the heat transfer coefficient (h) actually decreasedby 3–12%. On the other hand, Eastman et al. [81] showedthat with less than 1 vol% of CuO nanoparticles, the con-vective heat transfer coefficient of water under dynamicflow conditions was increased more than 15%.

The experimental results of Xuan and Li [22] illustratedthat the convective heat transfer coefficient of Cu/water-

s

dings

vol%, the convective heat transfer coefficient (h) was 12% smaller thane water for a given average fluid velocityrger enhancement of h with volume fraction (/) and Reynolds number

) was observedeased h with / and Reynolds number was observed

.5 wt.%, h increased by more than 350% at Re = 800

crease with / and Pe. Al2O3 shows higher enhancement than that of CuO

increased 8% for / = 0.01 and Re = 270creased 15% for / = 0.018


based nanofluids varied significantly with the flow velocityand the volumetric loading of particles. For example, for2 vol% of Cu nanoparticles in water, the Nusselt numberincreased by about 60% which is higher than that predictedby the Dittus–Boelter [82] equation.

Wen and Ding [77] presented the convective heat transfercharacteristics of nanofluids at the tube entrance regionunder laminar flow conditions. The experiments were con-ducted for 600 < Re < 2200. Their results illustrate thatthe local heat transfer coefficient varies with / and Re.For example, for / = 0.016 and at x/D � 63, the local h

was 41% higher for Re = 1050, and 47% higher forRe = 1600, compared with the results for pure water. Theenhancement was particularly significant in the entranceregion and decreased with axial distance. The same researchgroup [53] later conducted convective heat transfer experi-ments for CNT-based nanofluids in laminar flow and con-stant wall heat flux conditions. Surprisingly, the maximumincrease in the convective heat transfer coefficient was morethan 350% at Re = 800 and at 0.5 weight % of CNT.

Heris et al. [78] investigated convective heat transfer ofCuO and Al2O3/water-based nanofluids under laminarflow conditions through an annular copper tube. In theirstudy, the heat transfer coefficient was found to increasewith increasing particle volume fraction as well as Pecletnumber. Al2O3/water-based nanofluids showed higherenhancement of heat transfer coefficient compared toCuO/water-based nanofluids.

Lai et al. [79] studied Al2O3 (20 nm)/DIW-based nanofl-uids flowing through 1 mm sized stainless steel test tubeand subjected to constant wall heat flux and low Reynoldsnumber (Re < 270). Compared to the base fluid, the Nus-selt number of this nanofluid had a maximum enhancementof 8% for 1 vol% nanoparticle at Re = 270.

Jung et al. [80] conducted convective heat transfer exper-iments for Al2O3/water-based nanofluid in a rectangularmicrochannel (50 lm � 50 lm) under laminar flow condi-tions. The convective heat transfer coefficient increasedby more than 32% for 1.8 vol% of nanoparticles in base flu-ids. The Nusselt number increases with increasing Rey-nolds number in the laminar flow regime (5 < Re < 300).Based on the results, they proposed a new convective heattransfer correlation for nanofluids in microchannels.

The above review shows that the results reported by var-ious groups vary widely and most of the studies lack phys-ical explanation for their observed results. Therefore,further research on convective heat transfer of nanofluidsis needed.

9. Computational studies on heat transport of nanofluids

Xue et al. [83] were the first to use molecular dynamicssimulation (MDS) to identify the effect of liquid layeringat the liquid–solid interface on thermal transport in nano-fluids. Interestingly, their results demonstrate that layeringof the liquid atoms at the liquid–solid interface does nothave any significant effect on the thermal properties of

nanofluids. It is noted that their simulations were per-formed for the specific model system consisting of simplemono-atomic liquid. Thus their finding may not apply tocomplex fluids. In fact, there is no reported study whichconfirmed their conclusion.

Bhattacharya et al. [84] developed a technique to com-pute the effective thermal conductivity of a nanofluidusing the Brownian dynamics simulation. By comparingthe results of their simulations with available experimentaldata, they showed that their technique predicts the ther-mal conductivity of nanofluids to a good level of accu-racy. No other research group has reported any workusing the same computational technique although Bhat-tacharya et al. claimed it is less expensive than MDS.Xuan et al. [85] proposed a Lattice Boltzmann modelfor simulating flow and energy transport processes insidenanofluids. They considered the external and internalforces acting on the suspended nanoparticles and interac-tions among the nanoparticles and fluid particles. The dis-tributions of suspended nanoparticles inside nanofluidswere also calculated. Based on the simulation results, theyinferred that the fluctuation of Nusselt number of nanofl-uids along the main flow direction is due to the unstabledistribution of nanoparticles. No further development ismade in exploring the use of the Lattice Boltzmannmethod to explain the anomalous thermal conductivityof nanofluids.

Several preliminary numerical studies on the convectiveheat transport of nanofluids were conducted by a researchgroup led by Nguyen and co-workers [87–89]. They showedthat nanofluids can considerably enhance heat removal inboth tube flow [87] and radial flow between two disks[87,88]. The hydrodynamic and thermal fields of Al2O3/water-based nanofluids in a radial laminar flow systemwere numerically studied by Roy et al. [86]. Their resultsshowed a twofold increase in heat transfer for 10 vol% ofnanoparticles in water. They also observed that the wallshear stress increased with an increase in particle volumefraction. For Al2O3/water/ethylene glycol-based nanofl-uids, numerical results of Maı̈ga et al. [87] showed thatthe heat transfer coefficient increases with an increase ofthe particle concentration. However, the presence of suchparticles has also induced drastic effects on the wall shearstress that increases appreciably with the particle loading.

Palm et al. [88] performed numerical investigation forthe laminar forced convection flow of nanofluids with tem-perature-dependent properties. They found that Al2O3/water-based nanofluids with a volume fraction of 4% canproduce a 25% increase in the average wall heat transfercoefficient compared to water alone. Significant differenceswere also found when using constant property nanofluids(temperature independent) versus nanofluids with tempera-ture-dependent properties. The use of temperature-depen-dent properties resulted in larger heat transfer predictionswith corresponding decrease in wall shear stresses whencompared to predictions using constant properties nanofl-uids. With an increase in wall heat flux, Palm et al. found


that the average heat transfer coefficient increases whilstthe wall shear stress decreases.

Based on Khanafer et al.’s [89] model and taking intoaccount particle dispersion, Jou and Tzeng [90] numericallyinvestigated heat transfer performance of nanofluids insidetwo dimensional rectangular enclosures. Their results dem-onstrate that increasing volume fraction and buoyancyparameter can cause an increase in average heat transfercoefficient.

10. Summary and future work

From the above review, it can be summarized thatnanofluids exhibit enhanced thermal conductivity, whichincreases with increasing volumetric loading of nanoparti-cles. Review of experimental studies clearly showed a lackof consistency in the reported results of various researchgroups. The effects of several important factors such asparticle size and shapes, clustering of particles, tempera-ture of the fluid, and dissociation of surfactant on theeffective thermal conductivity of nanofluids were notinvestigated adequately. It is imperative to conduct moreinvestigations in order to confirm the effects of these fac-tors on the thermal conductivity of wide range ofnanofluids.

It is implicitly found that existing classical models can-not explain the observed enhanced thermal conductivityof nanofluids. However, most of the recently developedmodels only include one or two postulated mechanismsof nanofluids heat transfer. Moreover, these models werenot validated with a wide range of experimental data.There is, therefore a need to develop more comprehensivemodels, which are based on the first principle, and canexplicitly explain the enhanced thermal conductivity ofnanofluids. Particles size, particle dispersions and cluster-ing should be taken into account in the model developmentfor nanofluids.

Although thermal diffusivity is important, very littlework has been reported on the determination of the effec-tive thermal diffusivity of nanofluids. No model is availableto precisely predict the effective thermal diffusivity of nano-fluids. The existing classical models are also found to beunable to predict the viscosity of nanofluids. Therefore,analytical studies on the development of theoretical modelsfor the thermal diffusivity and viscosity of nanofluids arehighly desirable. In addition, studies on characterizationof viscosity, electrokinetic properties and convective heattransfer of nanofluids are rather scarce.

Although a significant number of studies have beenperformed on the heat transfer characteristics of nanofl-uids, there has been very little agreement in the datafrom different research groups. Hence, proper samplepreparation and repeatable and more systematic experi-mental studies on thermophysical properties, particularlythermal conductivity, thermal diffusivity, convective heattransfer coefficients and viscosity of nanofluids areworthwhile.

Research efforts which are focused on the application ofnanofluids in advanced cooling techniques for more effi-cient cooling of electronics and microelectromechanicalsystems (MEMS), and investigations on spray coolingand microchannel flow of nanofluids will also be of greatinterest.

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Documents

Thermophysical and electrokinetic properties of nanofluids – A critical review