Received 3 Jun

Rec

24

Accepted 26 De

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549

. . . . . .

ns on t

ivity en

ivity en

onducti

. . . . .

stering

. . . . . .

ns on t

nd sim

Contents lists available at SciVerse ScienceDirect

journal homepage: www.e

Renewable and Sustain

Renewable and Sustainable Energy Reviews 21 (2013) 548561[16]. Magnetic nanouids (or ferrouids), which consist ofE-mail address: wangym@scut.edu.cn (Y. Wang).Dispersion of nano-sized particles of different materials(metals, metal oxides, etc.) in a carrier uid known as nanouidshas been a subject of intensive investigations over decades due totheir potential applications in heat transfer and electronic cooling

1364-0321/$ - see front matter & 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.rser.2012.12.039

n Corresponding author at: College of Materials Science and Engineering, South

China University of Technology, 510640 Guangzhou, China.

Tel.:/fax: 86 20 87114883.1. Introduction5. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558

5.1. Energy convention devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558

5.2. Thermomagnetic convection based cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558

5.3. Thermal conduction based and smart cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558

6. Concluding remarks and future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559Contents

1. Introduction . . . . . . . . . . . . . . . .

2. Preparation of MNF . . . . . . . . . .

3. Thermal conductivity of MNF . .

3.1. Experimental investigatio

3.1.1. Thermal conduct

3.1.2. Thermal conduct

3.2. Mechanisms of thermal c

3.2.1. Brownian motion

3.2.2. Nanoparticle clu

4. Thermomagnetic convection . . .

4.1. Experimental investigatio

4.2. Mathematical modeling a. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549

hermal conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550

hancement in the absence of magnetic elds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550

hancement in the presence of magnetic eld . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551

vity enhancement and theoretical models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554

hermomagnetic convection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554

ulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556Thermal conductivity enhancementKeywords:

Magnetic nanouids

Ferrouids

Heat transfer enhancement

Thermomagnetic convection

convection in devices using MNFs as heat transfer media.

& 2013 Elsevier Ltd. All rights reserved.cember 2012developments in this eld with the aim of identifying major affecting parameters and some novel

applications. This review emphasizes on thermal conductivity enhancement and thermomagneticeived in revised form

December 2012controlling its ow and heat transfer process via an external magnetic eld. This review presents recente 2011Magnetic nanouids (MNF) constitute a special class of nanouids that exhibit both magnetic and uid

properties. The interests in the use of MNF as a heat transfer medium stem from a possibility ofInnocent Nkurikiyimfura a,b, Yanmin Wang a,c,n, Zhidong Pan a,c

a College of Materials Science and Engineering, South China University of Technology, 510640 Guangzhou, Chinab Department of Applied Physics, Faculty of Applied Sciences, Kigali Institute of Science and Technology, PB 3900, Kigali, Rwandac Key Laboratory of Specially Functional Materials under Ministry of Education, 510640 Guangzhou, China

a r t i c l e i n f o

Article history:

a b s t r a c tHeat transfer enhancement by magnetic nanouidsA reviewlsevier.com/locate/rser

able Energy Reviews

oleic acid [1012], tetramethylammonium hydroxide [13], etc.A

vaptheappconcieeth

maximum particle size was determined by Odenbach [21] to be1/3

I. Nkurikiyimfura et al. / Renewable and Sustainable Energy Reviews 21 (2013) 548561 549metal materials (ferromagnetic materials) such as iron, cobalt,nickel as well as their oxides (ferrimagnetic materials) such asmagnetite (Fe3O4), spinel-type ferrites, etc.

MNF has been used as an advanced functional material to positionthe colloids at a certain part of devices by means of magnetic forces.For this reason, the main aspects for research involve the increase ofuid magnetization, the specic properties of free magnetic nanouidsurfaces in the presence of an external magnetic eld and themagnetoviscous and magnetorheological effects [15]. The use ofMNF as transfer media becomes of importance in applications[1618]. In particular, a possibility to induce and control the heattransfer process and uid ow bymeans of an external magnetic eldopened a window to a spectrum of promising applications includingmagnetically controlled thermosyphons for technological purposes,enhancement of heat transfer for cooling of high power electrictransformers, and magnetically controlled heat transfer in energyconversion systems [15]. The heat transfer enhancement usingMNF in the presence of magnetic eld can be classied as acompound heat transfer technique with the additives (i.e., magneticnanoparticles) and an external magnetic eld to increase the heattransfer process [19]. Compared to the conventional nanouids(nonmagnetic nanouids), the use of MNF affected by externalapplied magnetic eld for heat transfer enhancement offers thefollowing advantages [20]:

a) The possible absence of any moving parts necessary formaking the uid to ow in commonly energy conversion andcooling devices. The current of MNF is generated by tempera-ture difference and non-uniform magnetic eld, which can beformed by means of a permanent magnet system. The cong-uration of this system determines the direction and the type ofthe uid ow. As a result, the thermomagnetic convection isreadily handled;

b) The thermomagnetic convection is much more intensive thanthe gravitation one;

c) The possibility of tuning thermophysical properties (thermalconductivity and viscosity) of MNF using external magneticelds [21,22].

2. Preparation of MNF

MNF is prepared via the dispersion of nano-sized super-paramagnetic particles into a nonmagnetic carrier uid such aswater, ethylene glycol, hydrocarbon oil, etc. [23]. MNF used inheat transfer applications is subjected to a magnetic eld,apparemacosity, surface tension, temperature and oxidative stability,or pressure, stability in hostile environments [15]. However,choice of a carrier uid for MNF suitable for heat transferlications needs some additional requirements such as highductivity, high heat capacity, high thermal expansion coef-nt, etc. Conventional heat transfer uid (such as water, oils,ylene glycol, etc.) could be a superior option for advancedlications. Magnetic nanoparticles used in magnetic nanouidsusually prepared in different sizes and morphologies fromsiovisns [14]. Theoretically, it should be possible to produce disper-n in any liquid thereby being able to tailor the requirements ofnantiowide range of carrier uids are used, and some magneticouids are commercially available to satisfy different applica-colloidal mixtures of superparamagnetic nanoparticles suspendedin a nonmagnetic carrier uid, constitute a special class ofnanouids that exhibit both magnetic and uid properties[79]. To prevent the aggregation (due to London-van der Waalsinteraction and magnetic interaction between the particles), thesuspended nanoparticles are coated by a surfactant layer such asgnetic eld gradient and/or gravitational eld, which maydo(6kBT/m0M0pH) for MNF used in the presence of magneticeld and do(kBT/Drghp)1/3 for MNF in the presence of gravita-tional eld, where kB, T, M0, Dr, g, d, H and m0 denote theBoltzmann constant, temperature, spontaneous magnetization ofthe magnetic material, density difference between magneticparticle and the carrier uid, gravitational acceleration, the heightof the sample, the magnetic eld and the vacuum permeability,respectively. In addition, the aggregation of magnetic nanoparti-cles during the synthesis has to be avoided at all costs. Inprinciple, the aggregation of particles increases their activediameter and thus causes a destabilization of the suspension bysedimentation. The maximum particle diameter (d), in this case,was estimated as do 144kBT=m0M20

1=3corresponding to the

maximum interaction energy when two interacting particlescome into contact [21]. Recent efforts have been made tosynthesize metal and metal oxide magnetic nanoparticleswith the desired size/size distribution [24]. Metallic nanoparticlessuch as Ni, Fe and Co were prepared via the techniques likesimple reduction of metal-salts, gas-phase reduction of metalcomplexes, thermolysis of metalpolymer complexes, thermaldecomposition of metalcarbonyl complexes and submerged arcnanoparticle synthesis system (SANSS) [24,25]. Magnetic nano-particles of metal oxide such as Fe3O4, g-Fe2O3 and spinel-typeferrites of the formula MFe2O4 (with MMn, Co, Zn, Ni, etc.) aremostly used in MNF due to their chemical stability. Metal oxidemagnetic nanoparticles are usually prepared by chemical co-precipitation, micro-emulsion and recently phase transfer[14,24,26].

The use of the required superparamagnetic particles in MNF isnot a denitive requirement of magnetic nanouid stability [8]. Asuspension with magnetic nanoparticles in carrier uids will notbe stable due to the presence of London-van der Waals andmagnetic forces, leading to the irreversible aggregation of theparticles and their subsequent sedimentation. Therefore, thepreparation of stable MNF requires an introduction of repulsiveforces between magnetic nanoparticles to counteract the London-van der Waals and the dipoledipole magnetic interactions. Therepulsive mechanism between the particles can be achieved,either by coating the particles with a polymer surfactant, whichproduces an entropic repulsion, and/or by charging the surfaceof the particles, producing a coulombian repulsion [8,14]. It isinteresting to note that the selection of the mechanism to be usedshould depend mainly on the properties of the carrier uids andthe particles. The dispersion process is usually performed in thepresence of a polymer surfactant by ultrasonic equipment and/ora high speed homogenizer.

3. Thermal conductivity of MNF

The original idea of using a suspension for heat transferapplication was a possibility of enhancing the thermal conductiv-ity of common heat transfer uids by the addition of nanoparti-cles with a higher thermal conductivity [4]. For this reason, someprevious investigations on thermal conductivity of nanouidswere dominated by nanouids prepared with metallic or metalliccontribute to the particle sedimentation in the uid. Since theinteraction range of magnetic nanoparticles in the applied elds isdirectly related to the particle size/size distribution of magneticnanoparticles [21], it is obvious that the later plays a vital role inthe particle sedimentation, thus affecting the stability of MNF.The stability against the particle sedimentation may be ensuredwhen the thermal energy of the particles becomes greater thanthat of magnetic and gravitational energies, respectively. theoxide nanoparticles such as TiO2, Al2O3, Cu, CuO, Ag, carbon

[69]g 0:003 Kp 2K 2jKpK

h i

I. Nkurikiyimfura et al. / Renewable and Sustainable Energy Reviews 21 (2013) 548561550Microconvection

model [71]1ARe Pr j f fKp 2KfjKpKf

Bruggeman

model [72]KKf 14 3j1

KpKf23j

h i Kf4

D

p

With D 3j12 KpKf 2

229j9j2 KpKf

Jeffrey model

[73]KKf 13jj2 3k2 3k34 9k

3

16a22a3

3k464

h iWith k a1a2 and a

KpKf

Rayleigh model

[74]

KKf Kf 3j KpKf2Kf Kpj13:939j2 KpKf =4Kf 3Kp KpKf

Murshed model

[75]K Kf QpoKpoKf 2g

31g3 1Kp 2oKf g31 Qpg3 o11

g31Kp 2oKf KpoKf Qp g31g3 1

n o Q6pg6Kf 3L2

3L2

4 9L

3

16

Kcp2Kf2Kcp3Kf

3L

4

26

" #( )

12rcpCpcpds

3kBT11:5g3Qp

2pcpg3r3p

s GT6prpds

" #( )Table 1Summary of frequently used models for thermal conductivity of MNF.

Model Expression

MaxwellGannet

model [70]

Kp 2Kf 2jKpKf Kp 2KfjKpKf

Modied

Maxwell

Gannet model

KiKf Kp 2Kf 2ji KpKf Kp 2Kfji KpKf nanotubes [4,2730]. These affected investigations on thermalconductivity of MNF since common magnetic materials used inMNF have a relatively low thermal conductivity, especially in theabsence of external magnetic eld. However, recent investiga-tions have proven that a solid material with a high thermalconductivity is not always an effective option for a suspensionto enhance the thermal conductivity of a carrier uid [31]. Thisnding as well as a possibility of controlling the thermal con-ductivity of MNF via an external magnetic eld could be plausiblereasons of recent great interests in the enhanced thermal con-ductivity of MNF. The thermal conductivity enhancement ischaracterized by a thermal conductivity ratio, which is denedas a quotient of the thermal conductivity of the (magnetic)nanouid (K) to that of the carrier uid (Kf).

3.1. Experimental investigations on thermal conductivity

Experimental investigations on thermal conductivity of MNFare mostly conducted at room temperature with the commonmethods for conventional (nonmagnetic) nanouids [32]. Themostly used techniques for MNF include the transient hot wire[13,3335] and thermal constants analyzer techniques [22,36,37].Paul et al. [32] gave the detailed information regarding these twotechniques as well as their advantages and disadvantages.

With g 1 trp , g1 1 t2rp , LKCpKfKCp 2Kf ,

KCp Klr 2KpKlr g3 Kp 2Klr

KlrKp g3 2Klr Kp , rCpand cpCp are density and specic h

complex particle, respectively, and they are given by rcp 1g3 rp3rppb3

2t22brptb2r2p 3rfpb3

22bb2brpbrp2btth(

Cpcp 1g3 Cpp 1 1g3

3Cpp

pb032t22b0rptb02r2p

3Cpf

pb03t222b0 b02b0rpb0rp2b0h(

wherep 3r2p3rptt2; b lnrprf

; b0 ln CppCpf

Description

Spherical particles with low volume fraction j

Spherical particles with volume fractionji; i x,y,z

A is a constant, Reand Prare Reynolds and Prandlt numbers

respectively, and gis a system dependent coefcient.Spherical particles, with high particle volume fraction j

High order terms represent pair interaction of randomly dispersed

particles

Suspensions of spherical particles with a regular particle distribution

Murshed model includes the effects of particle size, nanolayer, particle

movements, interactions, and surface chemistry of nanoparticles3.1.1. Thermal conductivity enhancement in the absence of magnetic

elds

Experimental investigations on the thermal conductivity ofMNF in the absence of magnetic elds show that the thermalconductivity enhancement is mainly affected by different para-meters, i.e., volume fraction of magnetic nanoparticles, particlesize/particle size distribution, chemical composition of magneticnanoparticles, temperature, particle coating layer, etc.

Some work on the effect of particle volume fraction showedthat the thermal conductivity of MNF increases with the particlevolume fraction [13,22,33,34,3740]. Abareshi et al. [13] mea-sured the thermal conductivity of a water based magnetitenanouid as a function of particle volume fraction at differenttemperatures. The thermal conductivity increased with theincrease of the particle volume fraction and temperature. Thehighest thermal conductivity ratio observed was 11.5% at aparticle volume fraction of 3% at 40 1C. Their experimental datashowed a fairly good agreement with the simulated results by theMurshed model (see Table 1). Li et al. investigated the effects ofparticle volume fraction, surfactants and magnetic eld on thetransport properties of a water based Fe magnetic nanouid [33].They observed a thermal conductivity enhancement of MNF withthe increase of particle volume fraction both with and withoutapplied magnetic elds. Their results also showed that theviscosity of MNF increased with the particle volume fraction

Cppand Cpf stand for the specic heat capacity at constant pressurefor nanoparticles and carrier uid, respectively. GT is the total potential

energy between two interacting colloidal nanoparticles.

eat of

1 1g3

i)

t2ti)

behavior was also explained by the presence of chain-likestructures in MNF with respect to the inuence of magnetic eld.

I. Nkurikiyimfura et al. / Renewable and Sustainable Energy Reviews 21 (2013) 548561 551of the suspended magnetic nanoparticles and the surfactants. Yuet al. [38] investigated the effects of particle volume fraction onthe thermal conductivity of a kerosene based Fe3O4 magneticnanouid prepared via a phase-transfer method. The thermalconductivity ratios obtained increased linearly with the increaseof volume fraction and temperature and the value was up to34.0% at 1 vol%. To further investigate the inuence of tempera-ture on thermal conductivity enhancement, the measurementswere performed in the temperature range from 10 to 60 1C. Theresults revealed that the absolute thermal conductivity increasedwith increasing temperature, while the thermal conductivity ratiowas almost constant and the thermal conductivities of the MNFtracked those of the carrier uid. Philip et al. [22,37] conducted awork on thermal conductivity of MNF prepared via the dispersionof magnetite nanoparticles in water, ethylene glycol and keroseneas carrier uids, respectively. Their results showed that thethermal conductivity ratio increased with the increase of particlevolume fraction, but there was no thermal conductivity enhance-ment for MNF at a volume fraction ofo1.71 vol%. The slope of thelinear region was 0.035 and the highest thermal conductivityratio observed was 23% at 7.8 vol%. Hong et al. [31] investigatedthe thermal conductivity enhancement of an ethylene glycol Febased magnetic nanouid. They found that the thermal conduc-tivity ratio increased nonlinearly with the increase of volumefraction. Hong et al. [39] investigated the thermal conductivity ofnanouids with different volume fractions of Fe nanoparticles inethylene glycol. Their results conrmed the intensication ofthermal conductivity with the particle volume fraction. In thecomparison of the copper and iron nanoparticles dispersed inethylene glycol, the thermal conductivity enhancement in iron-based nanouids was higher than that in copper-based nanouid.The observed thermal conductivity enhancement was attributedto the fact that the nanoparticles in the uids with high volumefractions formed clusters at a higher rate. Zhu et al. [41] prepareda distilled water based Fe3O4 magnetic nanouids and investi-gated the effect of volume fraction on the thermal conductivityenhancement of the MNF. Gutierrez [34] analyzed the thermalconductivity of water based spinel-type ferrite magnetic nano-uids prepared with magnetic nanoparticles of MnxZn(1x)Fe2O4(with x0, 0.3, 0.7, 1). The analysis of the volume fractiondependence on the thermal conductivity showed that the thermalconductivity ratio increased linearly with the increase of volumefraction. In addition, the investigations on the particle composi-tion effects revealed that the thermal conductivity ratio does notdepend on the chemical composition of magnetic nanoparticles.The enhancement of thermal conductivity was attributed to theeffects of the particle size and the volume fraction of magneticnanoparticles. The analysis of the carrier uid effects showed thatthe thermal conductivity ratio is higher for a carrier uid with alow thermal conductivity such as common hydrocarbon(K0.120.14 W/K m). However, the absolute thermal conduc-tivity of a MNF is higher for a carrier uid with a high thermalconductivity. For instance, the absolute thermal conductivity forwater based magnetic nanouid (K0.801 W/K m) reported wasthree times greater than that of oil based one (K0.255 W/K m)for the highest volumetric concentration of both uids. Holotescuet al. [42] reported on the utilization of the semi-empiricalequation for the effective thermal conductivity of the magneto-granulometric analysis to estimate the thermal conductivity oftransformer oil based magnetite magnetic nanouids. In theiranalysis, the semi-empirical equation for the effective thermalconductivity of the HolotescuStoian model [43] was applied,using the results obtained for the size distributions from themagnetogranulometry analysis, followed by a comparison withthe measured values of the effective thermal conductivity

obtained by a hot ball method. It was revealed that the use ofPhilip et al. [22,37] reported a dramatic enhancement of thethermal conductivity up to K/Kf4.0 (300%) in magnetite-basednanouid, under the inuence of an applied magnetic eld alongthe direction of heat ow. The reported thermal conductivityenhancement was within the predicted value for parallel modeconduction. The decrease in K observed after the critical value ofmagnetic eld was explained by the zippering of chains. Theyargued that the cluster morphology and distribution both couldthe magnetogranulometric approximation of the magnetite nano-particle size distribution could evaluate the thermal conductivitymore efciently, compared to the use of the classical Maxwellequation. They also ascertained the importance of the dataregarding the analysis of the lognormal distribution by eithernumber or volume, as well as the fact that the results werestrongly dependent on the experimental method and theassociated model.

3.1.2. Thermal conductivity enhancement in the presence of

magnetic eld

Recent work on the control of the thermal conductivity of MNFhas received a particular interest because the anomalousthermal conductivity observed under the inuence of an externalmagnetic eld. In the presence of magnetic elds, besides theaforementioned parameters affecting the thermal conductivity ofMNF without magnetic elds, the thermal conductivity of MNFcan be affected by the orientation and the intensity of the appliedmagnetic eld [15,33]. Measurements of thermal conductivity inthe presence of magnetic eld are usually performed at roomtemperature using the same techniques as those used in theabsence of magnetic elds. The magnetic eld is generated byeither electromagnets or permanent magnets. Richler et al. [44]investigated the effect of magnetically driven structure formationon heat ux in MNFs on the basis of thermal conductivitymeasurements in variation of an external magnetic eld. For thispurpose, they developed an improved measuring device based onthe plane heat source instead of the standard hot wire method isused to enable both parallel and perpendicular orientations ofmagnetic eld and heat ux. Thermal conductivity measurementswere carried out in variation of strength and direction of anexternal magnetic eld relative to heat ux. It was concluded thatunlike former experimental investigations, for the rst time theresults showed qualitative consistency with theoretical predic-tions for both orientations.

Li et al. [33] reported on the inuence of magnetic eldstrength and direction on the transport properties of MNF. Theyfound that an external magnetic eld had remarkable effects onthe both thermal conductivity and viscosity of the MNF. Littlechange in the thermal conductivity of the MNF was found in themagnetic eld perpendicular to the temperature gradient, irre-spective of the applied magnetic eld strength and the volumefraction of particles. The thermal conductivity of the MNFincreased with the strength of the applied magnetic eld beingparallel to the temperature gradient. The reason for this enhance-ment was the change of microstructures induced by the externalmagnetic eld in the MNF. They further explained that when themagnetic eld was parallel to the temperature gradient, theformed particle chains provided the more effectively bridges forenergy transport inside the MNF along the direction of tempera-ture gradient and enhanced the thermal process in the MNF.It was revealed that the viscosity rstly increased with themagnetic eld and nally approached a constant as the magne-tization of the magnetic uid achieved a saturation state. Thishave impacts on thermal conductivity enhancement and support

I. Nkurikiyimfura et al. / Renewable and Sustainable Energy Reviews 21 (2013) 548561552the transport of heat through the aggregates. In their report, amagnetically polarizable nanouid (magnetic nanouid) could beused as a reversible switchable thermal uid, i.e., insulation tohigh thermal conducting uid and vice versa, by changing themagnetic eld. Wright et al. [45] reported an innovative conceptof integrating magnetically sensitive metal or metal oxides in auid with carbon-nanotubes in order to increase the thermalconductivity of the uid. It was shown that the MNF with Nicoated single wall nanotubes was signicantly enhanced in thepresence of magnetic eld. The thermal conductivity enhance-ment observed was attributed to the inuence of magnetic eldon the microstructure of the uid. It was indicated that under theapplied magnetic eld, the Ni coated nanotubes could formaligned chains that favored to connect the nanotubes, resultingin the improved contacts. Wensel et al. [46] investigated thethermal conductivity of nanouids with metal oxides nanoparti-cles (Fe3O4 and MgO) and carbon nanotubes in the presence ofmagnetic eld. They observed that a maximum thermal conduc-tivity could be increased by up to 10% at a rather low particleweight fraction of 0.02 wt%. The possible explanation to theseinteresting results was the aggregation of metal oxide particles onthe surface of nanotubes by electrostatic attraction and theformation of the chain-structure along the nanotubes. It wassuggested that the investigated nanouids could be used forcoolant applications since their viscosity was similar to that ofwater. Nkurikiyimfura et al. [36] investigated the inuences ofparticle size and particle volume fraction on the thermal con-ductivity enhancement of an engine oil based magnetite magneticnanouid in a magnetic eld. It was shown that the thermalconductivity could be enhanced with the smaller magnetiteparticles used in the nanouids at a greater particle volumefraction. In addition, the thermal conductivity enhancement wasfound to be related to magnetic eld parallel to temperaturegradient. They analyzed that the increase of thermal conductivityratio was due to the chain-like structures formed in MNF underthe inuence of magnetic eld. The thermal conductivityenhancement observed for the smaller particles was explainedby the super-paramagnetic behavior of the smaller particles andtheir effect on the aggregates formation. Though the magneticeld parallel to temperature gradient exhibited a positive effecton the thermal conductivity of the MNF, a high magnetic eld hada negative effect on other thermophysical properties of the uidsuch as rheological properties and thermal conductivity itself[22,36,37]. This is due, especially, to the undesirable clumpingand zippering of chains under the inuence of high magneticelds. This restriction calls for the simultaneous treatment ofthermal conductivity enhancement with other transport proper-ties, especially, the viscosity (Z). When the thermal conductivityand magnetoviscous effects were considered, the enhancementcould be characterized by a ratio of the thermal conductivity tothe viscosity. Philip et al. [47] addressed this issue and suggestedthe tuning of the K/Z-ratio rather than the thermal conductivityalone. Their report devoted to the determination and character-ization of the viscosity and thermal conductivity enhancement ina stable magnetic nanouid with the particles size less than10 nm as a function of volume fraction, shear rate, magnetic eldand time. Their results revealed that, without any magnetic eld,the increase of MNF viscosity was much greater than the thermalconductivity enhancement. They also noted that the K/Z-ratio ofMNF at 0.078 vol% could be tunable from 0.725 to 2.35 bycontrolling the applied eld. The MNF with tunable K/Z-ratiocould be used as multifunctional smart materials for miniaturecooling with damping applications. Gavili et al. [48] conductedexperimental investigation on the thermal conductivity of waterbased MNF under magnetic eld created by the Helmholtz coils.

The magnetic eld strength was controlled by an electric current.The saturation time and the reversibility of thermal conductivitywere also examined after the magnetic eld was turned off. Theobtained results showed that the MNFs with 5.0% volume fractionof nanoparticles with an average diameter of 10 nm enhanced thethermal conductivity more than 200% at maximum value.Furthermore, the variation of thermal conductivity with tempera-ture was also shown.

3.2. Mechanisms of thermal conductivity enhancement and

theoretical models

Though the thermal conductivity of MNF has been a subject ofsome investigations, the mechanisms for interpreting experimen-tal data both in the absence and presence of applied magneticeld are still needed. Among the mechanisms proposed forconventional nanouids, the Brownian motion and particle clus-tering/structure are the two much-debated mechanisms [37,49].

3.2.1. Brownian motion

The Brownian motion refers to the seemingly random move-ment of particles suspended in liquid or gas, and the motion isdue to collision with base uid molecules, which makes particlesundergo a random walk motion [3,50,51]. The Brownian motioncould contribute to the thermal conductivity enhancement in twoways, namely, the direct contribution due to motion of nanopar-ticles that transports heat (diffusion of nanoparticles) and theindirect contribution due to the so called micro-convection of uidsurrounding individual nanoparticles [5,51,52]. It is hypothesizedthat the later effect could set up a current of heat transferbetween nanoparticles and the carrier uid, hence enhancingthe thermal conductivity of the nanouid. Recent studies rejectedthis hypothesis, suggesting that the thermal conductivityenhancement of MNF could be explained by the particle cluster-ing [22,37,53]. Philip et al. [22] showed that the microconvectionof the uid medium around randomly moving nanoparticles didnot affect the thermal conductivity of a nanouid and themicroconvection model overestimated the thermal conductivityvalues. They analyzed the modest thermal conductivity enhance-ment in the well-dispersed particles. The diffusion of magneticnanoparticles plays an important role at a low volume fraction(jo2%), which could be explained by the effective medium(Maxwell) theory rather than the effects associated with theBrownian motion induced hydrodynamics. Their explanation tothe conductivity enhancement in MNF at a high volumefraction (j42%) was due to the presence of dimmers or trimmersin the uid. These results were in a reasonable agreementwith the Maxwell-Gannet model, especially at higher volumefractions.

Tsai et al. [54,55] reported the effect of viscosity on thethermal conductivity of magnetite based nanouids. They notedthat the measured thermal conductivity of nanouids graduallyapproached a value predicted by the Maxwell equation withincreasing the viscosity. Their results provided an evidence ofthe viscosity of MNF did affect the thermal conductivity. Thediffusion of magnetic nanoparticles could be an important factorthat enhanced the thermal conductivity. It was suggested that thethermal conductivity of MNF in the absence of magnetic eldscould be predicted by combined models [5660] where theconduction part could be obtained from the prediction by theMaxwell equations

3.2.2. Nanoparticle clustering

Aggregation of particles into sparse clusters, or ideally intolinear chains and its inuence on the nanouids properties have

received a particular interest recently, and it is expected to be a

I. Nkurikiyimfura et al. / Renewable and Sustainable Energy Reviews 21 (2013) 548561 553main mechanism of thermal conductivity of the nanouids[1,2,51,6064]. The presence of particle clusters in a nanouidleads to extended and highly conductive paths for the heat owand thus to a quick heat transport along long distances since heatcan be conducted much faster by solid particles if compared to acarrier uid [60]. Bishop et al. [65] reviewed different interactionsoccurring in magnetic nanoparticles self-assembly as well as theirscales. It was shown that even without the effect of externalmagnetic eld; the magnetic-interaction-induced self-assembledaggregation could occur in MNF. The aggregation structure ofmagnetic particles controls the heat conduction in the MNF. In theabsence of an external magnetic eld, the distribution of particlesin the MNF is disordered and the thermal conductivity of MNF isisotropic. When magnetic nanoparticles self-assemble, they tendto align their magnetic moments in the direction of the localmagnetic eld due to the neighboring particles or the appliedelds [21,66,67]. This gives rise to the anisotropy of interactionenabling magnetic nanoparticles to form micron-sized, one-dimensional chains/wires, rings, two-dimensional aggregates oreven three-dimensional super-lattices. The understanding of theaggregate formation mechanisms, their distribution/distributionmorphology and their manipulation with an external magneticeld are prerequisite to understand the mechanisms of thermalconduction in MNF. Hong et al. [39] investigated the effect ofmagnetic nanoparticles clustering for an ethylene glycol based Femagnetic nanouids without magnetic elds. The thermal con-ductivity was determined as a function of the duration of theapplication of the ultrasonic vibration, which varied from 0 min(i.e. no vibration applied) to 70 min. It was indicated that thermalconductivity ratio increased with increasing vibration time, andthe rate of this increase became smaller for longer vibration time.Furthermore, the variation of thermal conductivity with timeafter the application of vibration was investigated, and it wasfound that thermal conductivity decreased with time. Variation ofaverage size of clusters was also determined as a function of timeafter the application of vibration, and the cluster size increasedwith time. As a result, the size of the clusters formed by thenanoparticles had a major inuence on the thermal conductivity.The effect of particle clustering on the thermal conductivity wasalso claimed by Zhu et al. [41]. They found that the clustering andnanoparticle alignment was mainly responsible for the anoma-lous thermal conductivity enhancement. Jiang et al. [68] prepareda MNF by one step phase transfer, and investigated the aggrega-tion effect on thermal conductivity enhancement of the preparedMNF. The microstructure of the MNF was analyzed by a dynamiclight scattering method, which unveiled the variation of aggre-gated congurations with particle concentration and time. Theobserved wave-like structure of the measured thermal conduc-tivity as a function of particle concentration was explained as themanifestation of the aggregation-structure variation. The analysisfor the possible mechanism of aggregate formation in MNF in zeromagnetic elds revealed that the particle coating layers were alsoof importance in the cluster formation. They concluded that thethermal conductivity of MNF could be manipulated for somenanouids by changing a stabilizer used and thus controlling thestructure of the aggregates. Philip et al. [22] performed anexperiment to prove the enhanced thermal conduction throughpercolating structures in MNF. They stated that the maximumenhancement was observed when the chains like aggregateswere well-dispersed without clumping. The MNF could be usedas a reversible switchable thermal uid, i.e., insulation to highthermal conductivity and vice versa, via the change of themagnetic eld.

Some attentions have been paid to theoretical and mathema-tical modeling of the thermal conductivity enhancement of MNF

both in the absence and presence of magnetic elds. Table 1summarizes the commonly used models to validate experimentalresults.

Fang et al. [69] attempted to model the thermal conductivityof MNF in the presence of magnetic eld. Their model consisted ofthe modied Maxwell-Gannet model by the introduction of ananisotropic constant that accounted for the microstructure of theuid under an applied magnetic eld.

The obtained model was given as

KxKf

Kp2Kf 2jx KpKf

Kp2Kfjx KpKf 1

With jx(1Cx)jwhere Cx is the anisotropic structure para-meter in the x direction expressed as

Cx 1N

XNi 1

Xj4 i

Cxij 2

Cxij n!

xU e!

ij

214

d

rij

33

where subscripts i and j are particle numbers, d is the diameter ofthe particle, rijrirj, rij 9 r!ij9, e!ij r!ij=rij, ri is the position ofthe ith particle, n

!x is the unit vector along the x direction. From

Eqs. (2) and (3), the higher particle volume fraction, the shorterdistance between two particles rij 9 r!ij9, the greater value of theanisotropic structure parameter Cx could be obtained. When thechain like structure along the x direction becomes more obvious,the value of the anisotropic structure parameter Cx becomesgreater. The anisotropic structure parameter Cx well characterizesthe distribution of particles along the x direction. Note that thesame method can be used to calculate the thermal conductivity ofMNF along the y and z directions. The anisotropic thermalconductivity of MNF calculated by the modied Maxwell-Gannet formula is in agreement with those computed by thenumerical methods.

Fu et al. [70] conducted theoretical investigation on theeffective thermal conductivity tensor for MNFs using a two-stephomogenization method. The differential effective medium the-ory was used to determine the equivalent thermal conductivity ofmagnetizable nanoparticle chains and then, the theory wasgeneralized to self-consistent anisotropic effective medium the-ory to investigate the effective thermal conductivity tensors ofmagnetic nanouids. The numerical results showed that theaspect ratio of chain-like aggregated clusters plays an importantrole in enhancement of anisotropic thermal conductivity. Inaddition, the theoretical results on the elements of thermalconductivity parallel to the elds and perpendicular to the eldswere in good agreement with the experimental data. Their resultsfurther conrmed the non-monotonic dependence of effectivethermal conductivity on magnetic eld strength, in accordancewith experimental reports.

Nkurikiyimfura et al. [71] investigated the effect of chain-likemagnetic nanoparticles aggregates on the thermal conductivity ofmagnetic nanouids (MNFs) in magnetic eld via a proposedmodel of thermal conductivity of MNFs. The anisotropic feature ofthermal conductivity ratio was predicted based on the eldinduced chain-like magnetic nanoparticles aggregates in MNFs.It was indicated that for a magnetic eld parallel to temperaturegradient, the thermal conductivity component along the magneticeld was signicantly enhanced due to the magnetic eld inducedchain-like magnetic nanoparticles aggregates. The experimentaldata of thermal conductivity enhancement along the magneticeld direction were similar to those predicted by the proposed

model.

I. Nkurikiyimfura et al. / Renewable and Sustainable Energy Reviews 21 (2013) 5485615544. Thermomagnetic convection

Thermomagnetic convection refers to a convective heat trans-fer that makes use of the spatial gradient in the magneticsusceptibility of MNF that is produced in the presence of atemperature gradient [7274]. When a MNF is exposed to anon-uniform magnetic eld in the presence of a temperatureeld, besides the conventional gravitational body force, thevarying susceptibilities result in a non-uniform magnetic body

force on the MNF (Kelvin body force), given as f!

m m0M!

Ur! B!,where m0 stands for the magnetic permeability of the vacuum,

and M!

the magnetization and B!

the magnetic induction [75,76].When the approximation of equilibrium magnetization withmagnetic susceptibility is dependent solely on the local value ofapplied magnetic eld and the density, magnetic and gravita-tional forces both are potential. The Kelvin body force creates astatic pressure eld in the ow that is symmetric about theapplied magnetic eld producing an irrotational force eld. Such asymmetric eld does not alter the velocity prole and theconvection inside the uid cannot arise [9]. The non-potentialityof the bulk forces (gravitational and magnetic forces) appearsonly if a uid possesses a spatial non-uniformity of the density r

and magnetization M!

due to their dependences on temperatureor on the particle concentration j [77]. The later condition issatised for non-isothermal systems with an asymmetric (orbiased) temperature distribution about the imposed magneticeld. The resultant Kelvin body force, which is also asymmetric inthis case, creates a eld force, which leads to the self-organizedadjective motion of the MNF across isotherms. The condition forthe free convection to develop is calculated as follows [77]:

r! f! r!T bTr0 g!7m0bm w0H2 rH2

a0 4

where f!

denotes the vector sum of the Kelvin body force and thegravitational body force; the sign77denotes the parallel andanti-parallel orientation of the magnetic eld gradient with

respect to the gravitational force, bm is relative pyromagneticcoefcient of the uid, and bT is the relative volumetric expansioncoefcient.

The heat transfer intensity is determined by the Rayleighnumber Ra, which consists of thermomagnetic and thermogravi-tational parts:

Ra RaTRam rcpl4

ZKdT

dzbTrgm0bmM

dH

dz

5

According to the numerical analysis, even in lab-scale experi-ments, thermal (RaT) and magnetic (Ram) Rayleigh numbers bothare greater; they can exceed the values of 105106, showing thatthe problem of convective heat transfer may be theoreticallyconsidered in the framework of a boundary layer approximation[77]. From the expression of the Rayleigh number, it is clear thatthe intensity of thermomagnetic convection and therefore theefciency of devices using MNF as heat transfer media is providednot only by the magnetic eld and the temperature distributionselds but also by the properties of MNF with the thermophysicalproperties and the pyromagnetic coefcient, i.e., the degree ofdependence of magnetization on temperature. In general, thepyromagnetic coefcient of a MNF is given by [78]

b bTM@M

@m

dm

dT

@M@T

6

with

bT 1 dr

r dTwhere r and bT denote the density of magnetic liquid and itsthermal expansion coefcient, respectively. In high magneticelds, when magnetization of liquid is close to saturation, thepyromagnetic coefcient can be simplied as

bM bTbm 7

where bm(1/m)(dm/dt) denotes the relative pyromagnetic coef-cient of dispersed material. Under these conditions, the value ofpyromagnetic coefcient increases with increasing the sumb(9dm/dT9bT) in the required temperature range for the sameMNF. This condition suggests that the choice of magnetic materialshould depend on the thermal expansion of the carrier uid. Forliquids with small thermal expansion, this coefcient of (dm/dT) ismore important. In low magnetic elds, the linear law of magne-tization can be assumed and the value of pyromagnetic coefcientis expressed as

bM 1TbT2bm

8

It is clear that under low magnetic elds, the share of dispersedmaterial in pyromagnetic coefcient becomes more signicant [78].Recent efforts have been made to synthesize MNF suitable for heattransfer application. A special aspect is to prepare magnetic nano-particles with a greater pyromagnetic coefcient, i.e., at the Curietemperature being close to the operating range (considering theboiling point of the carrier and the stability of the uid at elevatedtemperature). The most used magnetic materials are the Zn-substituted spinel-type ferrites because Zn substitution alters theirmagnetic parameters in a wide range of values [7981]. This allows toobtain ferrite particles with different thermomagnetic coefcients.Mn0.5Zn0.5Fe2O4 based magnetic nanouids are widely used amongstdue to their low Neel temperature (100 1C), and thus higher thermo-magnetic coefcients (see Table 2).

4.1. Experimental investigations on thermomagnetic convection

Shuchia et al. [82] investigated the effect of magnetic eldposition on heat transfer and driving force characteristics of amixture of MNF with an organic uid introduced in a heattransport device. Their results indicated that the heat transfercapability and the magnetic driving force were improved bymagnetic elds when the magnetic eld was applied on theentrance of the heated region. Blums et al. [77] investigated theheat transfer from a nonmagnetic cylinder to a MnxZn(1x)Fe2O4tetradecane temperature sensitive magnetic nanouid, under theinuence of transverse laminar free convection in the presence ofuniform and non-uniform magnetic elds directed transversally tothe axis of the cylinder. Their results conrmed the additive actionof thermo-gravitation and thermomagnetic body forces on the heattransfer intensity in ferrouids. The heat transfer enhancementwas attributed to the properties of MNF and the magnetic eldgradient. They explained that it was possible to use temperaturesensitive magnetic nanouids to achieve a magnetic Rayleighnumber (Ram) that exceeds the thermo-gravitational Rayleighnumber (RaT). They also found that a greater magnetic Rayleighnumber and a higher heat transfer could be achieved when themagnetic eld gradient was increased. Zablockis et al. [83] con-ducted experimental and numerical investigations of thermomag-netic convection in a heated cylinder under the magnetic eld in asolenoid. They found that the heat transfer under a magnetic eldcould be increased. However, the solenoid used showed to beimpractical, especially for generating sufciently strong magneticelds. Yamaguchi et al. [84] conducted an investigation on a MnZn ferrite alkyl-naphthalene based magnetic nanouid in a cubiccavity. The magnetic eld and magnetization were affected by

temperature, and the greater magnetization and magnetic forces

on.

F

alen

n

alen

n

e alk

I. Nkurikiyimfura et al. / Renewable and Sustainable Energy Reviews 21 (2013) 548561 555Table 2Summary of theoretical and numerical investigations on thermomagnetic convecti

Author Geometry andDimension

Magnetic eld MNF

Zablockis

et al. [89]

Cylindrical

domain

dimensions

2 6 cm

Non-uniform constant magnetic

eld of a Solenoid placed in a

hollow area inside the domain

Temperature

sensitive MN

Yamaguchi

et al. [91]

Square cavity Uniform magnetic eld generated

by vertical electromagnetic

Alkyl-naphth

based MnZ

ferrite MNF

Yamaguchi

et al.

[104]

Partitioned

rectangular box

Alkyl-naphth

based MnZ

ferrite MNF

Yamaguchi Cubic cavity Uniform magnetic eld generated Mn-Zn ferritwere observed in the regions near the upper wall and center insidethe cavity rather than in the region near the bottom and side walls.The analysis of the uid ow showed a weak ow roll inside cavityunder the magnetic force, which brought the lower temperatureuid downward in the center region, and streamed the highertemperature uid upward along the regions near the side walls.They also found that, with the magnetic eld imposed, the heattransfer inside the cavity was increased, compared to that withoutthe magnetic eld, and the heat transfer increased further withincreasing the strength of the magnetic eld. Yamaguchi et al. [85]also performed the numerical and experimental investigations onheat transfer characteristics of a temperature sensitive magneticnanouid lled in a cubic container with a heat generating squarecylinder stick inside. Their results showed that, regardless of theheat generating object sizes, the heat transfer characteristic of the

et al. [90] by permanent magnets naphthalene bas

MNF

Mukhopad-

hyay

et al. [82]

Two-

dimensional

enclosure

Magnetic eld created by a line

dipole

Zablotsky

et al. [96]

Rectangular cell Permanent magnet attached to the

cell

Tetradecane

temperature

sensitive MnZn

based MNF

dimensions:

100 15mmheight: 150mm

Jafar et al.

[105]

Cylinder Kerosene based

MNF

Dimensions:

3:5 75mm

Jue [106] 2-D square cavity

Dimensions:

w 0:05,a 3:475mm,b 3:475mm,L 5:5mm

Strek and

Joseph

[107]

Channel between

two parallel

plates

Dipole located below the channel

Dimensions:

h 0:02m;L 0:2m

Jafar et al

[102]

Cylindrical

geometry

Xuan et al.

[108]

Micro-channel Model Remarks

Lattice

Boltzmann

model

The HTC increased up to sevenfold within the studied range

of parameters

e Lattice

Boltzmann

model

The HTC increased with the magnetic eld strength

e Single model Heat transfer enhancement is affected by improving heat

transfer characteristics at higher Rayleigh number when a

strong magnetic eld is imposed

yl- Lattice Heat transfer characteristic of the used MNF was enhancedMNF was enhanced when the magnetic eld was applied. How-ever, the heat transfer process became poor as the size of the insideheat generating object increased. This poor heat transfer processwas due to the decrease of the space where the uid owed withthe increase of the heat generating object size. The experimentaldata were predicted by the numerical result, disclosing the moreow details of the natural convection of the MNF inside cavity.

Some previous work focused on the synergy between themagnetic eld and temperature gradient and thermomagneticconvection was analyzed irrespective to the effect of magneticeld on the thermophysical properties of the used MNF. However,recent studies have shown that the thermomagnetic convectioncan be strongly affected by the externally applied magnetic eldthrough the thermophysical properties of the uid [86,87]. Engleret al. [86] investigated the magnetoviscous effect on the

ed Boltzmann

model

when the magnetic eld was applied

Single phase

model

(scaling

analysis)

The Nusselt number scales with Ra0:25m and thermomagnetic

heat transfer increases when the length scale decreases

Single phase

model

Thermomagnetic convection exceeds the thermo-

gravitational convection;

and a higher enhancement is obtained when the magnet is

placed near the warmer source

Mixture

(two-phase)

model

The heat transfer enhancement is function of magnetic

strength and direction. The heat transfer enhancement

decreases with the increase of particle size

Single phase

model

The magnetic nanouid ow and heat transfer are adjusted

not only by the magnet strength but also by a proper choice

of its position

Single model

(COSMOL

codes)

External magnetic eld has inuence on both on ow and

heat transfer and the convection process is similar to the

thermo- gravitational convection

Mixture

model

The magnetic soret effect can be higher than the

conventional one and its strength depends on the magnetic

eld magnitude

Lattice

Boltzmann

model

The heat transfer enhancement is related to the orientation

magnetic eld and a higher enhancement is obtained when

the magnetic eld gradient is parallel with the incoming

stream.

themaThprecontovaffinveconin[88neufortraeheproun

4.2

difrec[90geonecomcat

mithenaexpanthema

I. Nkurikiyimfura et al. / Renewable and Sustainable Energy Reviews 21 (2013) 548561556ture of magnetic nanoparticles and carrier uid. However, dueto the restricted magnetic nanoparticle size, the assumptionsof thermal equilibrium conditions and negligible motion slipbetween particles, MNF is usually considered as a conventionalsingle phase uid with average physical properties of individualphase that exhibit magnetic behavior. In this case, the conven-tional hydrodynamic equations can be modied to account forthe Kelvin body force, the so called ferro-hydrodynamic equations,and coupled with magnetization equation and Maxwellsequations used to model and characterize the uid ow andheat transfer processes. Mahmoudi et al. [92] analyzed thenatural convection for a two-dimensional triangular enclosurewith partially heated from below and cold inclined wall lledwith nanouid in presence of magnetic eld. The governingequations were solved by a nite volume method. The owpattern, isotherms and average Nusselt number were presentedfor 0oHao100, 104oRao107, 0ojo0.05 and six cases thatwere made by location of heat sources. The results showed that inpresence of magnetic eld the ow eld was suppressed and heattransfer decreased. Furthermore, it was observed that a maximumreduction of average Nusselt number in a high value of Haoccurred when Ra106. It was found that the nanoparticles weremore effective when Ra104 where conduction was more pro-nounced. Sheikholeslami et al. [93] investigated the naturalconvection in a concentric annulus between a cold outer squareand heated inner circular cylinders in the presence of static radialmagnetic eld using the lattice Boltzmann method. The inner andouter cylinders were maintained at constant uniform tempera-tures, and it was assumed that all walls could insulate themagnetic eld. The numerical investigation was carried out fordifferent governing parameters, i.e., the Hartmann number, nano-particles volume fraction and the Rayleigh number. The effective1.rmomagnetic convection. Under certain circumstances, thegnetoviscous effect can affect the thermomagnetic convection.e increase of magnetoviscous effect was attributed to thesence of coarse particles in the studied samples. It wascluded that for the thermomagnetic convection, the magne-iscous effect could be increased in the MNF, which wouldect the experimental results of the threshold of convection. Theuence of magnetoviscous effects on the thermomagnetic con-tion was also conrmed in a recent theoretical investigationthe onset of BernardMangaroni thermomagnetic convectiona horizontal magnetic nanouid layer by Nanjundappa et al.]. Also, Lajvardi et al. [89] addressed the forced thermomag-tic convection heat transfer of a water based magnetic nano-id with nanoparticles of Fe3O4 (10-nm) in a heated copper tubelaminar ow. They observed a signicant enhancement in heatnsfer coefcient under the inuence of an applied magneticld and magnetic nanoparticle volume fraction. The observedat transfer enhancement was attributed to the thermophysicalperties of MNF such as thermal conductivity or heat capacityder the applied magnetic eld.

. Mathematical modeling and simulation

Several numerical investigations have been conducted onferent geometries such as the RayleighBernard conguration,tangular enclosure, cylinder, cube, partitioned cavity, etc.,91]. The heat transfer processes and uid ow in thesemetries have been simulated in the presence of static mag-tic eld and more recently in modulated magnetic elds. Themonly used mathematic models can be summarized in two

egories:

Single phase (homogeneous) model. MNF is a multiphase mix-thermal conductivity and viscosity of nanouids were calculated anlker et al. [100]. Aminfar et al. [101] used the two phasexture model and the control volume technique to investigatehydro-thermal characteristics of water based magnetite

nouid contained in a vertical rectangular duct. The duct wasosed to a non-uniform transverse magnetic eld generated byelectric current going through a wire located parallelly underduct. The results showed that the use of the aforementionedgnetic eld increases the Nusselt number and friction factorVousing the Maxwell-Garnetts (M-G) and Brinkman models, respec-tively. Also, the multi-distribution-function (MDF) model wasused for the uniform magnetic eld effects simulation. The resultsrevealed that the average Nusselt number was an increasingfunction of nanoparticle volume fraction as well as the Rayleighnumber, while it was a decreasing function of the Hartmannnumber.

2. Mixture model (two-phase model). The mixture model uses asingle uid approach, and it is an intermediate between thesingle phase approximation and full set of equations governingthe dynamic of multiphase ow [94]. For this reason, somefactors such as friction between magnetic nanoparticles andthe carrier uid, the Brownian diffusion, sedimentation anddispersion are included in the model. The inclusion of the laterfactors in the model provides a possibility of understandingthe function of each phase in the heat transfer process and theproblem related to the stability of MNF under both magneticand gravitational forces [95,96].

Mousavi [97] used CFD techniques to investigate the effects ofsingle phase approximation and mixture model on the owbehavior and heat transfer of a kerosene based magnetic nano-uid in a cylindrical geometry. It was found that at a great particlevolume fraction, the mixture model approach is more effectivethan single phase approach, and the former approach is conve-nient to study the effects of aggregation and particle size onhydrodynamics of the system. Using the mixture model, theyobtained that with coarse magnetic particles, the heat transfercould decrease and the Rayleigh rolls would not be observed.

Xuan et al. [98] investigated the ow and thermal processes ofMNF owing through a micro-channel. By altering the orientationand magnitude of an external magnetic eld, they could controlthe ow and thermal processes of MNF. They also found that theeffect of the external magnetic eld intensity was dependentupon its magnitude, its synergistic relation with the ow direc-tion of the main stream, the temperature gradient, and gravity inthe gravitational eld. They concluded that for the purpose ofheat transfer enhancement, the most remarkable effect could beachieved when the orientation of the magnetic eld gradient isparallel with the incoming stream. They analyzed that a magneticeld gradient opposite to the main stream would suppress a heatexchange between the MNF and the solid surface. Jafari et al. [99]used the mixture model to simulate the heat transfer phenomenain a kerosene based magnetic nanouid owing in a cylindricalgeometry. It was indicated that the increase of magnetic nano-particle size could cause the generation of colloids in the system,which had a detrimental effect on the heat transfer of the system.Jafari et al. [96] investigated the parameter effects on thethermomagnetic convection using the Taguchi technique. Thethermomagnetic convection in a cylindrical geometry dependedon some parameters like the particle diameter, particle volumefraction, temperature difference in the magnetic nanouid layer,the magnetic eld magnitude parallel to temperature gradientand the aspect ratio of the geometry as well. They reported thatthe magnetic soret effect could be greater than the conventionalone and its strength depended on the magnetic eld strength.Their results were in agreement with the experimental data byd also creates a pair of vortices that enhances heat transfer and

avity

e

nsfe

I. Nkurikiyimfura et al. / Renewable and Sustainable Energy Reviews 21 (2013) 548561 557prevents sedimentation of nano-particles. Furthermore, unlikethe axial non-uniform magnetic eld, the increase of the Nusseltnumber for the transverse magnetic eld was considerable in alllengths along the duct, and it was also concluded that withincreasing the Reynolds number, the effect of the transversenon-uniform magnetic eld on the Nusselt number was morethan that of the axial non-uniform magnetic eld. Suslov [91]investigated the linear stability of MNF between two verticaldifferentially heated plates placed in a uniform external magneticeld perpendicular to the plates and presented a completestability diagram for two and three-dimensional disturbances.It was shown that the thermogravitational and magnetic effectswere the two mechanisms of appearance of three stability modes.A work with the later modes showed that, depending on thegoverning parameters, the instability patterns were vertical sta-tionary magneto- convection rolls and/or vertical or obliquelycounter-propagating thermogravitational or thermomagneticwaves [102]. Suslov et al. [102] used the disturbance energyanalysis to highlight the physical mechanisms driving convectionin MNF. They found that the increase of magnetic effect wasmanifested by the existence of thermomagnetic waves, whichgradually replaced thermogravitational buoyance-driven waves.Krakov et al. [103] investigated the inuence of porous media anduniform magnetic eld on the thermal convection in magneticuid. In porous square cavity, the competition between gravityconvection and thermomagnetic convection mechanisms couldlead to a complicated dependence of the heat ux through thecavity in magnetic eld. The increase of magnetic eld couldenhance and depress heat transfer. It was also indicated that thedependence of the Nuselt number on the Rayleigh number couldbe complicated, leading to a hysteresis in some cases. Ashouriet al. [104] analyzed the thermomagnetic convection heat transferin a two-dimensional square cavity by a semi-implicit nitevolume method. In their investigation, the side walls of the cavitywere heated at different temperatures, the top and bottom wallswere isolated, and a permanent magnet was located near thebottom wall. They noted that in the absence of magnetic eld, theheat transfer was only affected by conduction. However, theconvective ow and heat transfer increased with increasing

Table 3Existing thermomagnetic convection heat transfer correlations.

Reference Geometry

Ashouri et al. [113] Square cavity

Mukhopadhyay [82] Rectangular c

Moraveji and Hejazian [114] Horizontal tub

Nu: Nuselt number, Nu: overall Nuselt number, h: the heat tramagnetic eld intensity when a magnetic eld was applied. Basedon the numerical analysis, they introduced a general correlationfor the overall Nusselt number on the side walls in a wide rangeof effective parameters, viz. 1oPro103, 2106oRamo1011,0oMao102, 0oZo102, 0oTro0.3, 0.25oL*o1.0, 0oW*o0.1, 0.02oG*o0.1, where Pr is the Prandlt number, Ram themagnetic Rayleigh number, Ma the thermomagnetic number, Zthe viscosity, Tr the rational temperature, G* the gap between thesurface of permanent magnet and cavity in dimensionless form,L*, W* denote the length and width of the permanent magnet indimensionless form respectively (see Table 3). The maximumerror produced via this correlation was approximately 6%. Mor-aveji et al. [105] presented the computational uid dynamics(CFD) method, with a single phase approach, to determine theeffects of nanoparticle concentration and ow rate on the con-vective heat transfer and friction factor of water based magnetitenanouid owing through a plain copper tube in turbulentregime with different Reynolds numbers (3000oReo22000).Magnetite nanoparticles with the average diameter of 36 nm,suspended in water as a base uid with four particle concentra-tions of 0.02, 0.1, 0.6 vol% were used. Applying the modelingresults, they found two relations to estimate the Nusselt numberand friction factor, based on the dimensionless numbers. Theresults showed that the modeling data were in good agreementwith the experimental data. The maximum error was around 10%.

Recent studies analyzed the thermomagnetic convection in thepresence of modulated magnetic eld [106108]. Kaloni et al.[107] performed a theoretical investigation of the convectiveinstability problem in the thin horizontal layer of a MNF heatedfrom below and under alternating magnetic elds. Lange et al.[106] considered the thermomagnetic convection in a horizontallayer of magnetic eld subjected to a vertical temperaturegradient and a spatially modulated magnetic eld. Their investi-gations revealed that, in contrast to the purely thermal drivensystem, the nonzero ow eld of the initial state was character-ized by a 2-vortex structure. They also stated that the later statewas unknown in the classical RayleighBenard conguration, andshowed a potential of spatial modulations of the external drivingto open new horizons in the eld of pattern formation with softmagnetic substances. Engler et al. [109] conducted theoreticaland experimental investigations on the onset of convection underthe inuence of time-modulated magnetic eld. The shift in theonset of convection depended on the frequency of the externalmagnetic eld. Matura et al. [108] investigated the inuence of atime-periodic and spatially homogeneous magnetic eld on thelinear stability properties and on the nonlinear response of aferrouid layer heated from below and above. They observed thatthe stability of the conductive state and particularly the type ofresponse, which can be harmonic or sub-harmonic, was deter-mined by the system parameters. The stability boundary of theconductive state in the high-frequency limit coincided with thestationary stability boundary when a mean magnetic Rayleighnumber was used. The stability boundary for low-frequency

Correlations

Nu 0:03064 Gn0:1101Wn0:58681 2:314W*11:570Ln 0:8480Ln2 T

0:2278r

Pr0:01818=Pr0:5a1a2Za3 1a4ZRaa5m

Nu hDK DdT Ra0:25m

Nu 0:00248Re1:03Pr0:51j47:5

r coefcient (HTC), a1 and a2 are the constants.modulation was shifted in a way that the conductive state gotstabilized. They noted that sub-harmonic response was nottypical for ferrouids because of their high Prandtl numbers.However, in low-Prandtl number simulations, they found non-linear relaxed sub-harmonic convective states as predicted by thelinear analysis. They further investigated the nonlinear responsefor heating from below and above for a large span of modulationfrequencies. For a high-frequency modulation, the dynamics wasnearly averaged, and the order parameters approach the values,which have a driving with the corresponding mean magneticRayleigh number. In the case of heating from above, a change inthe sense of rotation of the convection rolls was observed.They also noted that, for a low-frequency modulation, thenumerical noise could affect the pattern selection. This was the

thermal applications of MNF. As mentioned above, the application

in a case if the heat source was located into the region of a

Re

I. Nkurikiyimfura et al. / Renewable and Sustainable Energy Reviews 21 (2013) 548561558of an external magnetic eld on a MNF with varying susceptibil-ities gives a non-uniform magnetic body force (i.e., Kelvin bodyforce), which leads to the thermomagnetic convection. Since mostof MNFs exhibit a superparamagnetic behavior, they do not obeythe CurieWeiss law, thus becoming less magnetic at highertemperatures. Recent development of thermomagnetic coolingcase when the convection amplitudes cannot be below the noiselevel, depending on the numerical accuracy, in the under-criticalphase of driving. The simulations showed that for rather lowmodulation frequencies the oscillation proles approach thestationary curves.

5. Applications

MNF can be used as a coolant (thermal management applica-tions) and/or a heat transfer medium in energy conversionsystems. The later application is in the embryonic stage. The useof MNF in thermal management is currently used in somecommercial applications such as loud speakers cooling [21]. Themost recently developed applications will be reviewed as follows.

5.1. Energy convention devices

Shimada [110] analyzed the ow and heat transfer characteristicsin a parallel duct-type energy conversion device with a MNF under anon-uniform magnetic eld using the theoretical equations based onthe heat conduction theory. The results showed that the heatconduction model was capable of predicting the temperature andpressure distributions quantitatively for the performance of varioustypes of magnetic eld. Lian et al. [111] established a mathematicalmodel for the prediction of ow and heat transport features of thetemperature-sensitive magnetic uid and the design of an automaticenergy transport device based on the thermomagnetic effect. Theirresults revealed that a stable circulation ow could be maintained ina loop-shape channel in the presence of a proper external magneticeld and temperature gradient of the magnetic uid. In addition,some studies on the factors affecting the device performance, themagnetic eld strength and the uid temperature difference betweenthe heating section and cooling section were preponderant. It wasindicated that the developed device was not sufciently adequate tobe used for heat-to-power energy conversion, and it could be ratherused as an automatically-cooling. The developedmodel was validatedwith the experimental data. The established model could be used tosimulate the performance of devices exploiting the thermomagneticeffect for the design and evaluation purposes. Lian et al. [112]reported the performance of automatic energy transport in coolingdevices based on the thermomagnetic effect of a temperaturesensitive magnetic nanouid. The investigated devices consisted ofordered loop of permanent magnets, heat sources, heat sinks andtemperature sensitive magnetic uid assembled into an automaticenergy transport device. By adjusting the external magnetic eldand/or temperature gradient eld inside the magnetic nanouid, theycould control the energy transport process of designed devices. Inaddition, the constructed device showed a self regulating feature thatthe ow velocity of the MNF increased with the increase of the heatload and vice versa. Their results also showed that the performance ofautomatic energy transport systems was related to the structure ofconstructed loop.

5.2. Thermomagnetic convection based cooling

The thermomagnetic convection based on cooling is one of thedevices is mainly motivated by their great potential applicationimmersed in MNF. Philip et al. [53] developed a multifunctionaldevice that used MNF with tunable thermal conductivity toviscosity ratio to remove heat and arrested vibrations (damper),simultaneously. They concerned that the development of suchdevices could have applications in micro-uidic devices, micro-and nano-electromechanical systems (MEMS and NEMS) andother miniature devices. However, these thermal conductivitybased cooling devices are still in their embryonic stage and need afurther development for practical applications.

6. Concluding remarks and future directions

This paper reviewed recent development on MNF for heattransfer applications. Recent studies have dominated the ther-momagnetic convection and the development of devices bymeans of thermomagnetic effects. Some researchers initiatedthe investigations on other aspects of heat transfer such as theenhancement and control of thermal conductivity of MNF in thethamepreese ndings, developed at the India Gandhi Center of Atomicsearch, were used in development of smart cooling devicest took advantage of the large thermal conductivity enhance-nt and the conduction to remove the heat from a hot deviceMNThmaximal magnetic eld intensity, when the efciency of powergeneration cycle reached its maximum. A high intensication ofthe heat transfer observed when the magnet was placed inproximity of the warmer source was in agreement with theprevious studies by Rosensweig [113] and Jue [114]. Li et al.[115] reported the operating characteristics of a miniature auto-matic cooling device at different parameters. They found that forthe design of a cooling device with a MNF as a coolant, thefollowing points should be concerned:

i. To select a suitable magnetic uid with a greater pyromagneticcoefcient, a lower Curie point, a higher saturation magnetiza-tion, a lower viscosity and a higher boiling point;

ii. To exert a stronger intensity of the external magnetic eldand/or the eld gradient, if possible; in order to maintain asynergy between the magnetic eld and the temperaturegradient eld.

Xuan et al. [116] reported the practical design of a liquidcooling device based on the thermomagnetic effect for electroniccooling, in which the waste heat generated from the electronicelements was used as a useful power to drive the magnetic uidow and to transport the waste heat to a distant radiator. Theyfound that the thermomagnetic cooler with a magnet locatednearby the heat source could realize a better cooling performanceand a steadier start-up procedure. They also emphasized on theadvantages and disadvantages of thermomagnetic cooling forelectronic cooling applications.

5.3. Thermal conduction based and smart cooling

A recent work demonstrated that the thermal conductivity ofF could be tuned by an externally applied magnetic eld [22].for small scale cooling devices such as in miniature micro-scaleelectronic devices.

Zablotsky et al. [90] investigated a possibility of technicalapplication of surface cooling based on thermomagnetic convec-tion. They found that the cooling effect of 75 W/cm2 reached intheir setup could meet only low technical demands. Their resultsalso conrmed that that a signicant augment of the coolingintensity by thermomagnetic convection could be obtained onlysence of an external magnetic eld. The use of MNF in heat

clustering, clusters morphology and distribution;

application of the thermal conductivity tuning in energyconversion systems and heat exchangers.

Naand

[

I. Nkurikiyimfura et al. / Renewable and Sustainable Energy Reviews 21 (2013) 548561 559transfer applications appears promising. However, the develop-ment of this area is still challenged by many aspects rangingfrom the preparation and characterization of MNF to practicalapplications through the understanding of the mechanismsresponsible for the observed heat transfer enhancement. In orderto design systems with enhanced heat transfer and/or heattransfer effectiveness (heat transfer coefcient) using a MNF asa heat transfer uid, the understanding of the mechanisms andthe physical phenomena is needed. The problems of hydrody-namics and heat/mass transfer have been dealt with. However,some problems related to the stability of MNF in the presence ofmagnetic and gravitational elds, heat transfer mechanisms andthe inuence of formulation methods on the thermophysicalproperties are still needed to be solved.

Recent studies on MNF preparation mainly focused on thepreparation of temperature sensitive super-paramagnetic nano-particles and their dispersion in appropriate carrier uids. In anideal MNF, each particle appears superparamagnetic with themagnetic moment m

!. However, a real MNF, as used in some

experiments, is a poly-dispersed system and may contain asmall fraction of single- and/or multi-domain ferro-/ferri-mag-netic nanoparticles. The presence of these coarser particlescould lead to a poor stability of MNF and have severe effectson the thermophysical properties of the uid and the heattransfer effectiveness of systems as well. In addition, thecoarser particles in the MNF samples in the presence ofmagnetic eld lead to the formation of long and irreversiblechain-like clusters, which have detrimental effects on thethermophysical properties (such as thermal conductivity andviscosity) of the uid. A higher thermal conductivity could beexpected for MNF prepared with the smaller particles. It wasinteresting to note that the polydispersity of magnetic nanopar-ticles could also affect directly the current of thermomagneticconvection. Future investigations on the preparation of MNF shouldfocus on the control of size/size distribution of magnetic nanoparti-cles. Another aspect for further development is the particle morphol-ogy control during the preparation. It is well known that themagnetic properties of magnetic nanoparticles and hence the clusterformation in magnetic nanouids could be affected by the particlemorphology. The control of particle size/size distribution togetherwith the particle morphology may lead to the preparation of well-engineered MNF with desired properties and long-term stability andfurther on the development of devices using MNF for practicalapplications.

Some studies have shown that the thermal conductivityincreased with the particle volume fraction in the absence ofmagnetic eld. It is clear that the intensive investigations areneeded to understand the mechanisms and the inuence ofother parameters (such as surfactant layer, particle morphology,temperature, etc.) on the thermal conductivity of MNF in zeromagnetic elds.

The investigations on thermal conduction in the presence ofmagnetic eld have shown a promising and potential applicationin various elds such as smart cooling. The anomalous thermalconductivity observed was explained by the formation of chain-like structures in MNF under the magnetic eld. The under-standing of these structures and their manipulation by anexternal magnetic eld becomes the main challenge ofthe future investigation on thermal conductivity enhancementin MNF. The control of the self-assembly processes requires theunderstanding of the relationship between the magnetic proper-ties and other particle characteristics such as particle size/sizedistribution, particle morphology as well as the applied mag-netic eld. The future investigations on thermal conductivityenhancement in the presence of magnetic eld should focus on

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