Journal of Magnetism and Magnetic Materials 322 (2010) 3895–3901

Contents lists available at ScienceDirect

Journal of Magnetism and Magnetic Materials

0304-88

doi:10.1

n Corr

Ferdow

Tel.: +9

E-m

journal homepage: www.elsevier.com/locate/jmmm

Fabrication, characterization and measurement ofthermal conductivity of Fe3O4 nanofluids

Maryam Abareshi a, Elaheh K. Goharshadi a,b,n, Seyed Mojtaba Zebarjad b,c,Hassan Khandan Fadafan d, Abbas Youssefi e

a Department of Chemistry, Faculty of Sciences, Ferdowsi University of Mashhad, Mashhad 91775-1436, Iranb Center of Nano Research, Ferdowsi University of Mashhad, Mashhad 91775-1436, Iranc Department of Materials Science and Engineering, Engineering Faculty, Ferdowsi University of Mashhad, Mashhad 91775-1111, Irand Department of Physics, Faculty of Sciences, Golestan University, Gorgan, Irane Par-e-Tavous Research Institute, Mashhad, Iran

a r t i c l e i n f o

Article history:

Received 20 May 2010

Received in revised form

4 August 2010Available online 14 August 2010

Keywords:

Fe3O4 nanoparticle

Magnetic nanofluid

Thermal conductivity

53/$ - see front matter & 2010 Elsevier B.V. A

016/j.jmmm.2010.08.016

esponding author at: Department of Chem

si University of Mashhad, Mashhad 91775-14

8511 8797022; fax: +98511 8796416.

ail address: gohari@ferdowsi.um.ac.ir (E.K. Go

a b s t r a c t

Magnetite Fe3O4 nanoparticles were synthesized by a co-precipitation method at different pH values.

The products were characterized by X-ray diffraction, Fourier transform infrared spectroscopy, and

transmission electronic microscopy. Their magnetic properties were evaluated on a vibrating sample

magnetometer. The results show that the shape of the particles is cubic and they are superparamagnetic

at room temperature. Magnetic nanofluids were prepared by dispersing the Fe3O4 nanoparticles in

water as a base fluid in the presence of tetramethyl ammonium hydroxide as a dispersant. The thermal

conductivity of the nanofluids was measured as a function of volume fraction and temperature. The

results show that the thermal conductivity ratio of the nanofluids increases with increase in

temperature and volume fraction. The highest enhancement of thermal conductivity was 11.5% in

the nanofluid of 3 vol% of nanoparticles at 40 1C. The experimental results were also compared with the

theoretical models.

& 2010 Elsevier B.V. All rights reserved.

1. Introduction

Magnetic nanofluids, also called ferrofluids, are stable colloidalsolutions consisting of magnetic nanoparticles dispersed in abased fluid [1]. The magnetic nanofluid behaves as a smart orfunctional fluid due to some of its unique features. They havesome applications in a variety of fields such as electronic packing,mechanical engineering, aerospace, and bioengineering. Sincethe control and manipulation of the flow and energy transportprocesses in the magnetic nanofluids are possible using anexternal magnetic field, the promising potential of magneticfluids expanded into thermal engineering during the past decadebesides the above applications [2].

Water-based magnetic nanofluids are a special category of polarmagnetic nanofluids with particular features of particle interactionsand agglomerate formation processes [3]. The interest in water-based magnetic nanofluids in the selected bioengineering andbiomedical systems has been growing exponentially in the last

ll rights reserved.

istry, Faculty of Sciences,

36, Iran.

harshadi).

decades [4]. Surface coating of nanoparticles and colloidal stabilityof biocompatible water-based magnetic nanofluids are particularlyimportant for biomedical applications such as magnetic cellseparation, drug delivery, hyperthermia, and contrast enhancementin magnetic resonance imaging [3,5]. They have been extensivelyapplied to audio voice coil-damping, intertia-damping apparatuses,bearings, stepping motors, and vacuum seals [6].

Thermal conductivity of traditional heat transfer fluids such aslubricants, engines coolants, and water is inherently low. Metalsand metal oxides in solid form have orders-of-magnitude ofhigher thermal conductivities than those of fluids. The thermalconductivity of fluids that contain suspended solid metallic andmetal oxides particles could be significantly higher than that ofconventional heat transfer fluids [7]. The exact mechanism ofthermal transport in nanofluids has not been known at thismoment, even if several potential mechanisms have beensuggested to describe the experimental results of thermalconductivity of nanofluids [8].

Although the magnetic properties of the magnetic nanofluidsare the subject of intense studies [9–11], there are few data inthe literature concerning their thermal properties [12–17].The investigation of heat transfer characteristics of magneticnanofluids is very interesting and important from the viewpointof fundamental study on their thermal behaviors and the

Table 1Synthesis conditions used in this work.

Sample pHinitial pHfinal

MN1 �1 10.5

MN2 1.5 10.5

MN3 �1 9.5

MN4 1.5 9.5

M. Abareshi et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3895–39013896

development of practical thermal devices of magnetic nanofluidsin a number of areas such as the new kind of heat exchangers,cooling loops, and energy conversion systems [2].

Hong et al. [12] prepared Fe nanofluids in ethylene glycol andshowed that the thermal conductivity of nanofluids increasesnonlinearly with the volume fraction of nanoparticles. Hong et al.[13] investigated the thermal conductivity of nanofluids contain-ing different volume fractions of Fe nanoparticles in ethyleneglycol. Zhu et al. [14] prepared Fe3O4 nanofluids in distilled waterand investigated the effect of volume fraction on the thermalconductivity of nanofluids. Philip et al. [15] observed theenhancement in the thermal conductivity of ethylene glycol withincrease in volume fraction of Fe3O4 nanoparticles. They alsomeasured the thermal conductivity of nanofluids in the presenceof external magnetic field. Philip et al. [16] prepared a stablecolloidal suspension of magnetite nanoparticles of averagediameter 6.7 nm, coated with oleic acid and dispersed inhexadecane, and measured their thermal conductivity. Theyindicated that the thermal conductivity of nanofluids increaseswith the volume fraction of nanoparticles. Yu et al. [17] appliedphase transfer method for preparing stable kerosene based Fe3O4

nanofluids. Their results showed that the enhancement of thethermal conductivity increases linearly with the volume fractionof Fe3O4 nanoparticles and the value is up to 34.0% for 1.0 vol.% ofnanofluid.

To the best of our knowledge, in spite of widespreadapplications of water-based Fe3O4 nanofluid, especially in biome-dical and bioengineering, there is only two reports in the literature[14,18] concerning the measurement of its thermal conductivityin different volume fractions. They did not try to investigate thetemperature dependence of thermal conductivity of Fe3O4 water-based nanofluids. Hence, the main goal of the present study is toinvestigate the effect of both temperature and volume fraction onthe thermal conductivity of Fe3O4-water nanofluids.

In this work, the magnetic Fe3O4 nanoparticles were synthe-sized by co-precipitation method at different pH values. The XRD,FTIR, and TEM techniques were used to characterize the structure,purity, and the size of the nanoparticles. The magnetic propertieswere evaluated by vibrating sample magnetometer. The Fe3O4

nanoparticles were dispersed into deionized water to obtain thedesired nanofluids. Tetramethyl ammonium hydroxide was usedas a dispersant. The thermal conductivity of Fe3O4 nanofluids wasmeasured as the function of temperature and volume fraction.The experimental results were compared with some knowntheoretical models.

2. Experimental details

2.1. Materials

The starting materials used in this work were ferric chloridehexahydrate (FeCl3 �6H2O), ferrous chloride tetrahydrate(FeCl2 �4H2O), aqueous ammonia, and tetramethyl ammoniumhydroxide (N(CH3)4OH). All chemicals were used as receivedwithout further purification.

2.2. Synthesis procedure

To synthesize Fe3O4 nanoparticles, FeCl3 �6H2O (1 M) andFeCl2 �4H2O (2 M) were prepared by dissolving iron salts inHCl (2 M) solution. Typically, 4 ml of FeCl3 and 1 ml of FeCl2

were mixed in a molar ratio of 2:1. Then, 50 ml of ammoniaaqueous solution was added into the solution with vigorousstirring at room temperature. A black precipitate was obtained.

The precipitate was separated by applying a magnet and washingwith deionized water several times. To find out the bestconditions for the formation of Fe3O4 nanoparticles, a series ofexperiments were conducted under different initial pH’s of theiron salts solutions and the final pH of the product. Differentconditions are summarized in Table 1.

Nanofluids containing different volume fractions of Fe3O4

nanoparticles were obtained by dispersing prepared Fe3O4

nanoparticles in a certain amount of deionized water. Tetramethylammonium hydroxide was used as a dispersant. The nanoparti-cles are coated with hydroxyl ions of the tetramethyl ammoniumhydroxide, which themselves attract a sheath of strong positiveions. This surface structure creates electrostatic interparticlerepulsion that can overcome coagulation forces of magnetic andvan der Waals attractions.

2.3. Characterization

X-ray diffraction measurements were carried out with aBruker/D8 ADVANCED diffractometer, using Cu Ka radiation(l¼0.15406 nm) in the range 2y¼25–701 by a step of 0.02. Thetransmission electron microscope instrument used was PHILIPSCM-120. The Fourier transform infrared spectra of the as-prepared products were recorded at room temperature with aKBr pellet on a Shimadzu 4300 spectrometer ranging from 400 to1500 cm�1. Vibrating sample magnetometer (VSM) was used formagnetization measurements. These measurements were takenfrom 0 to 760 kOe fields. The zeta potential of nanofluid wasmeasured by a particle size analyzer (Malvern, Nano Series, 3000,HS, UK).

2.4. Thermal conductivity measurement

In the present study, the thermal conductivity was measuredusing the KD2 Pro Thermal Properties Analyzer (Decagon Devises,USA), which is based on the transient hot wire method. The KD2Pro consists of a handheld controller and sensors that should beinserted into the medium. The single-needle sensor with 1.3 mmdiameter and 60 mm length was used (KS-1). The sensorintegrates in its interior a heating element and a thermo-resistorand it is connected to a microprocessor for controlling andconducting the measurements. The nanofluid sample was held ina cylindrical glass container with 40 mm diameter and 80 mmheight because a minimum of 1.5 cm of material parallel to thesensor in all directions is necessary. In addition to KD2 Prosystem, a thermostat bath (ThermoHaake K10 TT4310) was usedto maintain different temperatures of nanofluids during themeasurement process. In every measurement, the vessel contain-ing the nanofluid was placed in a thermostat bath. After thetemperature of the sample reached the bath temperature, thesample was kept at that temperature for further 30 min to ensuretemperature equilibrium before each measurement. At least fivemeasurements were taken for each concentration of the nanofluidat a given temperature to ensure the uncertainty of measure-ments within 5%.

MN2

MN4

MN1

MN3

584

4000 3000 2000 1500 1000 500Wave number (cm-1)

Inte

nsity

(a.u

)

Fig. 2. FTIR spectra of different samples.

M. Abareshi et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3895–3901 3897

3. Results and discussion

The phase and purity of the products were examined by XRDand the patterns of all samples prepared under differentconditions are shown in Fig. 1. All the reflection peaks in thepatterns can be indexed to the face center cubic phase ofmagnetite with lattice parameter of a¼8.374 A, which are inagreement with the standard values (JCPDS file no. 01–1111). Theexistence of any impurity compound other than magnetite is notobserved. The characteristic peaks of magnetite are (2 2 0), (3 1 1),(4 0 0), (4 2 2), (5 1 1), and (4 0 0). As the XRD patterns show theinitial pH of the iron salts solution and the final pH of product playimportant roles in the crystallinity of Fe3O4 nanoparticles.Although the crystal structure of Fe3O4 nanoparticles does notchange, the reflection peaks become sharper and narrower fromMN1 to MN4 samples, indicating that the crystallinity hasimproved. This suggests that changing the final pH (from 10.5to 9.5) and increasing the initial pH of the iron salts solution(from �1 to 1.5) improve remarkably the crystallinity of Fe3O4

nanoparticles.The average crystallite size of samples was calculated from the

XRD line broadening using the Scherrer formula:

dhkl ¼0:9lbcosy

ð1Þ

where dhkl is the microcrystalline dimension (nm), y is an angle ofincidence, l is the wavelength of X-ray (l¼0.15406 nm), and b isthe full width at half maximum. The crystalline sizes of differentsamples calculated according to (3 1 1) reflection using Scherrer’sformula were 8.4, 9.2, 10.3, and 10.9 nm for MN1, MN2, MN3, andMN4, respectively.

In order to further confirm the structure of the samples,FTIR spectrum was recorded at room temperature, shown in

2θ (degree)25 30 35 40 45 50 55 60 65

Inte

nsity

(a. u

.)

MN1

MN2

MN3

MN4220 400

311

440511

422

Fig. 1. X-ray diffraction patterns of the Fe3O4 nanoparticles at different conditions.

Fig. 2. A strong absorption band at 584 cm�1 is assigned to thevibrations of the Fe–O functional group. Two peaks at about 2480and 3400 cm�1 can be assigned to CO2 and H2O. The FTIR analysisreveals that the Fe3O4 nanocrystals are free of organic contami-nants. Fig. 3 shows the TEM image of Fe3O4 nanoparticles.Again, the TEM image confirms the cubic structure of Fe3O4

nanoparticles.Fig. 4 displays the magnetization curves of samples MN2 and

MN4 at room temperature. Two samples show superparamag-netic behavior with zero coercivity and remanence. This is relatedto the fine crystallite sizes of Fe3O4 particles, which are in thenanometer range. The saturation magnetization (Ms) values ofMN2 and MN4 were 26 and 56.36 emu g�1, respectively, whichare lower than that of the bulk Fe3O4 (92 emu g�1) [19,20]. It canbe seen that the Ms value of MN4 is higher than that of MN2.Combined with the XRD results of two samples, the Ms valueincreases with increase in the crystallinity. The well-crystallizedparticles have a thinner non-magnetic surface layer and lesssuperparamagnetic relaxation, which can be used to explain theincrease of saturation magnetization [21]. The particle sizeinfluences the magnetic properties of materials [22].The Ms valuedecreases with decrease in crystallite size for mono-domainparticles due to the surface spin canting (disorder) and thermalfluctuations. Therefore, the small saturation magnetization ofMN2 can also be attributed to the smaller size of the particlescompared with MN4. Similar observations were reported in theliterature [23,24].

The zeta potential (z) is a measure of the electric charge at thesurface of the particles, indicating the physical stability ofcolloidal systems. It has been reported that the nanoparticlesuspensions become stable dispersions with a high potentialvalue of zeta potential (z430 mV) [25]. In our work, the zeta

22 nm

15 nm

18 nm

Fig. 3. TEM image of Fe3O4 nanoparticles.

Magnetic field (kOe)

Mag

netiz

atio

n (e

mu

g-1)

Magnetic field (kOe)

Mag

netiz

atio

n (e

mu

g-1)

-60

-40

-20

0

20

40

60

-60

-40

-20

0

20

40

60

-6 -4 -2 0 2 4 6

-6 -4 -2 0 2 4 6

Fig. 4. Magnetization curves of (a) MN2 and (b) MN4 at room temperature.

Table 2Thermal conductivity of pure water.

T (1C) k (W m�1 K�1)

Literature [26] Our work

10 0.580 0.583

20 0.598 0.595

30 0.615 0.632

40 0.630 0.679

M. Abareshi et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3895–39013898

potential of nanofluid (j¼2%) was �41.7 mV at pH¼12.8, whichsuggests that the Fe3O4 nanofluids have good dispersion andstability.

To verify the accuracy of our measurements, the thermalconductivity of water was measured at different temperaturesand compared with the literature data [26], see Table 2. Fig. 5shows the thermal conductivity ratio (k/kf) of nanofluid as afunction of volume fraction of Fe3O4 nanoparticles at 30 1C. k andkf represent thermal conductivity of nanofluid and base fluid,respectively. The results show that the thermal conductivity ratioof nanofluids increases with increasing volume fraction in therange of measurements. The highest enhancement of thermalconductivity was 11.4% in the nanofluid of 3 vol% of nanoparticles.

The effect of temperature on the enhancement of thermalconductivity of nanofluids is also investigated by measuring thethermal conductivity of nanofluids for different temperaturesranging from 10 to 40 1C. As it is observed in Fig. 6, the thermalconductivity of Fe3O4 nanofluid (j¼3%) increases by about 11.5%at 40 1C. The thermal conductivity of different nanofluidsincreases significantly with temperature. This is because at hightemperatures the Brownian motion of nanoparticles intensifies.

As it is evident from the experimental results of manyresearchers, it is known that the thermal conductivity ofnanofluids depends on different parameters including the thermalconductivities of the base fluid and the nanoparticles, the volumefraction, surface area, size and shape of the nanoparticles, and thetemperature of the medium. There is no satisfactory theoryavailable to predict the thermal conductivity of nanofluids.

However, there exist several semi-empirical correlationsto calculate the apparent conductivity of two-phase mixtures.Some of the well-known classical models are Maxwell [27],Bruggeman [28], Jeffrey [29], and Rayleigh [30]. The experimentalresults have been compared with these models and are shownin Fig. 7.

The Maxwell [27] model, an existing traditional modelfor thermal conductivity, was proposed for solid–liquid mixtures.The effective thermal conductivity, keff, according to this model isgiven by

keff , Maxwell ¼kpþ2kbþ2ðkp�kbÞfkpþ2kb�ðkp�kbÞf

kb ð2Þ

where kp is the thermal conductivity of the nanoparticle, kb is thethermal conductivity of the base fluid, and f is the particlevolume fraction of the suspension. Maxwell’s formula shows thatthe effective thermal conductivity of nanofluids relies on thethermal conductivity of the spherical particles, the base fluid, andthe volume fraction of the solid particles.

The Bruggeman model [28] is another well-known model fordetermining the effective thermal conductivity of mixture and it

Temperature (°C)5

The

rmal

con

duct

ivity

rat

io (k

/kf)

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

1.18ϕ = 1%

2% 3%

10 15 20 25 30 35 40 45

Fig. 6. The thermal conductivity ratio (k/kf) as a function of temperature at

different volume fractions of Fe3O4.

Volume fraction (%)

The

rmal

con

duct

ivity

rat

io (k

/kf)

0.98

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16Present workMaxwell model [27]Jeffrey model [29]Bruggemen model [28]Reyleight model [30]

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Fig. 7. Comparison between experimental data for Fe3O4 nanofluids and those

calculated by conventional models.

Volume fraction (%)

Ther

mal

con

duct

ivity

rat

io (k

/kf)

1.04

1.06

1.08

1.10

1.12

1.14

T= 30 K

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Fig. 5. The thermal conductivity ratio (k/kf) as a function of volume fraction at 30 1C.

M. Abareshi et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3895–3901 3899

is given by

keff , Bruggeman ¼1

4ð3f�1Þkpþð2�3fÞkb

� �þ

kb

4

ffiffiffiffiDp

ð3Þ

where D is given by

D¼ ð3f�1Þ2 kp=kb

� �2þð2�3fÞ2þ2 2þ9f�9f2

� �kp=kb

� �h ið4Þ

The Jeffrey model [28,29] for the effective thermal conductiv-ity of suspensions is given by

keff

kb¼ 1þ3bþ 3b2

þ3b3

4þ

9b3

16

aþ2

2aþ3þ

3b4

64þ � � �

!f2

ð5Þ

where

b¼a�1

aþ2ð6Þ

and

a¼kp

kbð7Þ

For a mixture with a regular particle distribution, the Rayleighmodel [29] has the following form:

keff ¼ kbþ3fkp�kb

2kbþkp�f 1þ3:939f73ðkp�kbÞ=ð4kbþ3kpÞ

n oðkp�kbÞ

kb

ð8Þ

As Fig. 7 shows the enhanced thermal conductivity ofnanofluids cannot be explained by these classical models. This isbecause these classical models do not include the effects ofparticle size and size distribution, interfacial layer at the particle/liquid interface, movement of nanoparticles, and temperature,which may be considered as important factors for enhancing thethermal conductivity of nanofluids [30,31]. Thus, new models ofthe effective thermal conductivity for nanofluids will be needed tobe proposed.

Recently, Murshed et al. [32] have developed a new andimproved theoretical model to predict the observed thermalconductivity of nanofluids. The effective thermal conductivity ofnanofluids in this model considering the static and dynamicmechanisms is given by

keff , Murshed

¼ kf

Qpoðkp�okf Þ 2g31�g3þ1

� �þðkpþ2okf Þg3

1 Qpg3ðo�1Þþ1� �

g31ðkpþ2okf Þ�ðkp�okf ÞQp g3

1�g3þ1� �

( )

þ Q2p g

6kf 3L2þ

3L2

4þ

9L3

16

kcpþ2kf

2kcpþ3kfþ

3L4

26

!( )

þ1

2rcpCp�cpds

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3KBTð1�1:5g3QpÞ

2pcpg3r3p

sþ

GT

6prpds

" #( )ð9Þ

where g¼1+(t/rp) and g1¼1+(t/2rp). t stands for interfaciallayer thickness and it is equal to t¼

ffiffiffiffiffiffi2pp

s (s is a parametercharacterizing the diffuseness of the interfacial boundaryand the typical value of s is in the range 0.3–0.6 nm). o is anempirical parameter (o41) that depends on the order of fluidmolecules in the interface, nature, and surface chemistry ofnanoparticles.

L is defined as

L¼kcp�kf

kcpþ2kfð10Þ

where kcp is the thermal conductivity of a complex particle, whichcan be obtained by

kcp ¼ klr2ðkp�klrÞþg3ðkpþ2klrÞ

ðklr�kpÞþg3ðkpþ2klrÞð11Þ

Volume fraction (%)0.0

The

rmal

con

duct

ivity

rat

io (k

/kf)

1.0

1.1

1.2

1.3

1.4Presente work6.1 nm Fe3O4/water [18]9.8 nm Fe3O4/water [14]

0.5 1.0 1.5 2.0 2.5 3.0 3.5

Fig. 9. Comparison between the present data and the measured data from other

researchers.

M. Abareshi et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3895–39013900

where klr is the thermal conductivity of nanolayer and it can bewritten as klr¼okf.

rcp and cp�cp are density and specific heat of complex particle,respectively, and they are given by

rcp ¼1

g3rpþ 1�

1

g3

3rp

pb32t2þ2brptþb2r2

p

� ��

�3rf

pb3t2ð2þ2bþb2Þþbrpðbrpþ2btþ2tÞ� ��

ð12Þ

Cp�cp ¼1

g3Cp�pþ 1�

1

g3

3Cp�p

pb032t2þ2burptþb

02r2p

� ��

�3Cp�f

pb03t2ð2þ2buþb

02Þþburpðburpþ2butþ2tÞ� ��

ð13Þ

where p¼ ð3r2pþ3rptþt2Þ, b¼ lnðrp=rf Þ, and b0 ¼ ln(Cp�p/Cp�f).

Cp�p and Cp� f stand for the specific heat capacity at constantpressure for nanoparticles and base fluid, respectively.

GT is the total potential energy between two interactingcolloidal nanoparticles and is defined as

GT ¼�A

6

2r2cp

d2s þ4rcpds

þ2r2

cp

d2s þ4rcpdsþ4r2

cp

þ lnd2

s þ4rcpd

d2s þ4rcpdsþ4r2

cp

!" #

þ2preorcpz2 expð�kdsÞ ð14Þ

where rcp¼rp+t, ds ¼ 0:893rcpQ�1=3cp , e0, er, and z are the radius of

complex particle, particle surface to surface distance, dielectricconstants for vacuum, dielectric constants for medium, and zetapotential, respectively.

The prediction made by the Murshed model was comparedwith the experimental results in Fig. 8. The Murshed model givesbetter prediction of the thermal conductivity of these nanofluidscompared with the classical models. This is because this modelincludes the effects of particle size, nanolayer, particle move-ments, interactions, and surface chemistry of nanoparticles, whichmay be responsible for the enhanced thermal conductivity ofnanofluids. It is obvious that the prediction of this modeloverestimates the experimental results especially at highervolume fractions (j42%), which could be likely attributed tothe difference in the quality of the interactions that has beenviewed in the model and Brownian motion for this material; thisshould be considered in the dynamic part of the model as amodification [31].

Volume fraction (%)

The

rmal

con

duct

ivity

rat

io (k

/kf)

1.04

1.06

1.08

1.10

1.12

1.14

1.16

1.18Experimental Murshed model

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Fig. 8. Comparison between experimental data for Fe3O4 nanofluids and those

calculated by Murshed model [32] at 30 1C.

A comparison between our work and the previous data [14,18]from other researchers is shown in Fig. 9. It is clear that the dataobserved by other researchers are quite different from those ofthe present study. The main reason for this contrast is not clear. Itmay be caused by several factors such as difference in the particlesize, particle preparation, or even the measurement technique.

4. Conclusions

Superparamagnetic Fe3O4 nanoparticles were successfullysynthesized by a simple and cost-effective co-precipitationmethod in different conditions. The XRD, TEM, FTIR, and VSMtechniques were used to characterize the structure, size, purity,and magnetic properties of the nanoparticles. The best crystal-linity was observed for MN4 sample (pH initial¼1.5 and pHfinal¼9.5). The results reveal that the Ms value increases withincrease in the crystallinity and particle size.

Fe3O4 nanofluids were prepared by dispersing Fe3O4 nanopar-ticles in distilled water as the base fluid. Tetramethyl ammoniumhydroxide was used to improve the dispersion of Fe3O4 in distilledwater. Measurement of zeta potential of nanofluids shows thatFe3O4 nanoparticles have good dispersion in water.

The effective thermal conductivity of Fe3O4 nanofluids withdifferent volume fractions was investigated experimentally at, 10,20, 30, and 40 1C. Thermal conductivity of Fe3O4 nanofluidsincreases up to 11.5% as the volume fraction of nanoparticlesincreases up to 3 vol% at 40 1C. From the thermal conductivitymeasurement, the results show that the relative thermalconductivity of nanofluids increases with increase in volumefraction and temperature.

The experimental results were also compared with somedifferent theoretical models. Among the models, the Murshedmodel gives better predictions of the thermal conductivity ofthese nanofluids compared with these classical models.

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