Investigation of thermal conductivity, viscosity, and electrical conductivity ofgraphene based nanofluidsMadhusree Kole and T. K. Dey Citation: J. Appl. Phys. 113, 084307 (2013); doi: 10.1063/1.4793581 View online: http://dx.doi.org/10.1063/1.4793581 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v113/i8 Published by the American Institute of Physics. Related ArticlesGraphene hydrogenation by molecular hydrogen in the process of graphene oxide thermal reduction Appl. Phys. Lett. 102, 071910 (2013) Atomistic simulation study of brittle failure in nanocrystalline graphene under uniaxial tension Appl. Phys. Lett. 102, 071902 (2013) Hole doping of graphene supported on Ir(111) by AlBr3 Appl. Phys. Lett. 102, 061601 (2013) Barrier tunneling time of an electron in graphene J. Appl. Phys. 113, 043714 (2013) Eliminating defects from graphene monolayers during chemical exfoliation Appl. Phys. Lett. 102, 043102 (2013) Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors

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Investigation of thermal conductivity, viscosity, and electrical conductivityof graphene based nanofluids

Madhusree Kole and T. K. Deya)

Thermophysical Measurements Laboratory, Cryogenic Engineering Centre, Indian Institute of Technology,Kharagpur, West Bengal 721302, India

(Received 4 December 2012; accepted 12 February 2013; published online 27 February 2013)

Stable and well dispersed functionalized graphene–ethylene glycol (EG)þ distilled water nanofluids

having graphene nano-sheets (GnS) volume concentration between 0.041 and 0.395 vol. % are

prepared without any surfactant. Graphene nano-sheets are prepared from high purity graphite

powder by Hummers method followed by exfoliation and reduction by hydrogen gas. Thus, obtained

hydrogen exfoliated graphene (HEG) is then functionalized using acid. The graphene nano-sheets are

characterized using XRD, TEM, Raman spectroscopy, and FTIR spectroscopy. Thermal conductivity

and viscosity measurements are performed both as a function of graphene loading and temperature

between 10 and 70 �C. Thermal conductivity enhancement of �15% for a loading of 0.395 vol. %

f-HEG is observed at room temperature. The measured nanofluid’s thermal conductivity is explained

well in terms of the expression derived by Nan et al. (J. Appl. Phys. 81, 6692 (1997)), which

considers matrix-additive interface contact resistance of mis-oriented ellipsoidal particles. The

viscosity of the prepared f-HEG nanofluids and the base fluid (EGþ distilled water) displays

non-Newtonian behaviour with the appearance of shear thinning and nearly 100% enhancement

compared to the base fluid (EGþDI water) with f-HEG loading of 0.395 vol. %. Known theoretical

models for nanofluid’s viscosity fail to explain the observed f-HEG volume concentration

dependence of the nanofluid’s viscosity. Temperature dependence of the studied nanofluid between

10 and 70 �C is explained well by the correlations proposed earlier for nanofluids with spherical

nanoparticles. Electrical conductivity of the f-HEG nanofluids shows significant enhancement of

�8620% for 0.395 vol. % loading of f-HEG in a base fluid of 70:30 mixture of EG and distilled

water. VC 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4793581]

I. INTRODUCTION

Since the discovery of nanofluids by Choi,1 a large num-

ber of investigations have been reported on metallic and

metal oxide nanofluids, where the particles are spherical, and

also on carbon nanotube (CNT) based nanofluids, where the

particles are cylindrical in shape. However, till now, no de-

finitive conclusions could be arrived to suggest a better and

stable replacement to the existing coolants. Graphene, a

single-atom-thick sheet of hexagonally arrayed sp2-bonded

carbon atoms, has attracted much attention since its discov-

ery by Novoselov et al.2 in 2004. This two-dimensional (2D)

material, graphene, displays many unusual electrical, me-

chanical, and thermal behaviours, such as very high carrier

mobility,2 long-range ballistic transport at room tempera-

ture,3 quantum confinement in nanoscale ribbons,4 single-

molecule gas detection sensitivity,5 and high Young’s

modulus and fracture strength.6 In view of these unusual

properties, graphene is expected to be a potential material

for various new applications.7 Graphene is, however, a new

entrant in the area of nanofluids. Interestingly, the in-plane

thermal conductivity of a suspended single-layer graphene is

reported to be as high as 5200 W/mK.8 Further, as graphene

is a 2D material, the heat transfer properties are expected to

be much different from the zero dimensional nanoparticles

and one dimensional carbon nano-tube. Moreover, graphene

itself being an excellent thermal conductor, the graphene

based nanofluids are normally expected to display significant

thermal conductivity enhancement.

Yu et al.9 first reported the thermal conductivity of gra-

phene oxide-ethylene glycol (EG) nanofluids. They observed

an enhancement of 61% for a loading of 5 vol. % of graphene

oxide nano-sheets at room temperature. Thermally exfoliated

graphene (TEG) based nanofluids with water and with EG has

been reported by Baby et al.10 They observed thermal con-

ductivity enhancement of �14% with only 0.056 vol. % of

graphene nano-sheets (GnS) dispersed in de-ionized (DI)

water at 25 �C, which increased to 64% at 50 �C. However, a

marginal enhancement �4% at 25 �C has been obtained for

EG based nanofluid with 0.05 vol. % of GnS. The same group

later11 reported an enhancement of �16% at 25 �C with

0.05 vol. % of functionalized GnS prepared by hydrogen exfo-

liation of graphite oxide (GO) sheets dispersed DI water.

Similar enhancement has also been observed by Gupta et al.12

It may be noted that thermal conductivity of EG based nano-

fluids did not display any significant enhancement for low

volume concentrations. Highest enhancement in thermal con-

ductivity (�86%) has been reported so far by Yu et al.13 for

5 vol. % of GnS dispersed in water at 30 �C prepared with so-

dium dodecyl-benzenesulfonate (SDBS) as surfactant.

It may be noted that for many applications, EG-water

mixture is generally used as the working coolant, while base

fluid used in most of the investigations on graphene

a)Author to whom correspondence should be addressed. Electronic mail:

tapasdey@hijli.iitkgp.ernet.in.

0021-8979/2013/113(8)/084307/8/$30.00 VC 2013 American Institute of Physics113, 084307-1

JOURNAL OF APPLIED PHYSICS 113, 084307 (2013)

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nanofluids is either pure water or pure EG. In view of the

above, in the present communication, we report our results

on the thermal conductivity, viscosity, and electrical conduc-

tivity of graphene nanofluids with 70:30 (by volume) mix-

ture of EG and distilled water as the base fluid. It may be

mentioned that this is the first report on the viscosity of gra-

phene based nanofluids. Results have been discussed to iden-

tify the mechanisms responsible for the observed thermal

conductivity and viscosity enhancement in graphene nano-

fluids prepared with 70:30 mixture of EG and distilled water.

II. NANOFLUIDS PREPARATIONAND CHARACTERIZATION

Graphite (99.99%, SP-1) is procured from Bay Carbon,

Inc., USA. All other materials like sulfuric acid, nitric acid,

sodium nitrate, potassium permanganate, hydrogen peroxide,

ethanol, and EG are of analytical grade and are procured

from M/S Loba Chemicals, India. Distilled water is used

throughout the experiment. Graphite oxide is prepared from

graphite using Hummers method.14 The dried GO thus

obtained is exfoliated and reduced by controlled flow of high

purity hydrogen gas11 in the presence of Argon atmosphere

at 200 �C. The hydrogen exfoliated graphene (HEG) is dark

black colour in appearance and is extremely light in weight.

The XRD pattern of graphite, GO, and HEG is shown in

Fig. 1. The intense crystalline peak (0 0 2) of graphite occurs

at �26.65�, which is the characteristic peak of hexagonal

graphite with a d-spacing of 0.34 nm. Upon oxidation of

graphite into GO, the peak position shifts to 11.14�. The inter-

planar spacing now increases to 0.79 nm. This increase in

d-spacing is due to the intercalation of –OH containing func-

tional groups in between the graphene layers. After exfolia-

tion of GO with hydrogen at �200 �C, the 11.14� peak

disappears and a broad peak appears, starting from �15� to

27�. The inter-planar spacing decreases to 0.39 nm. This indi-

cates a large extent removal of oxygen and water from the

interlayer during exfoliation. This broad peak also indicates

loss of the long range order in the prepared graphene. The

transmission electron micrograph of HEG is shown in Fig. 2,

which confirms the sheet-like morphology of the prepared

graphene (HEG).

The Raman spectra of pristine graphite, GO, and HEG is

shown in Fig. 3. For graphite, a highly intense G band occurs

at 1586 cm�1. This corresponds to the optically allowed E2g

phonons at the Brillouin zone centre.15 The absence of D

band in graphite suggests that graphite used is defect free.

The G band of GO is located at 1611 cm�1. The G band of

HEG is shifted back to 1591 cm�1, which is close the value

of pristine graphite indicating the reduction of GO during

hydrogen treatment. Moreover, a broadening of G band is

observed in GO and HEG and is attributed to an increase in

the disorder. The chemical treatment procedures to prepare

GO and its exfoliation to get HEG induce defects in the

FIG. 1. XRD pattern of graphite, graphite oxide, and hydrogen exfoliated

graphene.

FIG. 2. Transmission electron micrograph of hydrogen exfoliated graphene

nano-sheets.

FIG. 3. Raman spectra of pristine graphite (GR), GO, HEG, and functional-

ized graphene nano-sheets (f-HEG).

084307-2 M. Kole and T. K. Dey J. Appl. Phys. 113, 084307 (2013)

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graphitic structure. As a result, a broad D band with an inten-

sity comparable to that of the G band is obtained in GO and

HEG as well. The D and G bands denote the presence of sp3

and sp2 hybridized carbon atoms, respectively, in the sample.

Due to their hydrophobic nature, the as-prepared HEG does

not disperse in water and EG and requires functionalization,

which is done by treating HEG with (3:1) concentrated

H2SO4 and HNO3. The acid-HEG mixture is ultrasonicated

for 2 h at room temperature and is then washed several times

with distilled water until pH becomes neutral. The solution is

then centrifuged and dried in a vacuum oven to get function-

alized graphene. Figure 3 also includes the Raman spectra of

f-HEG. In HEG, the G and D bands occur at 1591 cm�1 and

1355 cm�1, respectively. In the case of f-HEG, both the band

positions are shifted to higher wave number side and also

broadened with respect to HEG. The G band has a broad

peak centred around 1596 cm�1 and D band has a peak cen-

tred around 1366 cm�1. The ratio of the D band intensity to

G-band intensity in f-HEG is higher than that of HEG. This

increase in the relative intensity of the disordered mode is

attributed to the increased number of structural defects.9,16,17

After acid functionalization, hexagonal carbon order gets dis-

rupted, i.e., the carbon atoms get sp3 hybridized. The effect

of acid treatment and attachment of functional groups of the

synthesized f-HEG are further confirmed from FTIR studies

(Fig. 4). It may be observed that for f-HEG, the peaks at

around 3446 and 1620 cm�1 are due to -OH functional

groups. A small doublet peak of -CH2 (2933 and 2866 cm�1)

and -CH at 1363 cm�1 is present both in HEG and f-HEG.

The peaks at 1710 and 1380 cm�1 can be assigned to the

C¼O and C-O stretching vibrations of -COOH. These func-

tional groups help the graphene sheets to disperse in water-

EG mixture.

Functionalized graphene–EGþ distilled water (70:30)

nanofluids with various volume concentrations of GnS (viz.,

0.041, 0.124, 0.207, and 0.395 vol. %) are prepared by

intense ultrasonication for 45 min. No surfactant is used in

the preparation of the present nanofluids. It may be noted

that constancy in thermal conductivity of the nanofluid with

time reflects the stability of the nanofluids.9 Therefore, the

suspension stability of the prepared nanofluids is verified by

measuring periodically for several months, the thermal

conductivity of the stationary nanofluid maintained at 30 �C.

The result (Fig. 5) shows that the thermal conductivity of the

nanofluids does not display any worthwhile degradation and

is constant for �150 days (5 months). The constant thermal

conductivity clearly reflects high stability of the garphene-

(EG-DI water) nanofluids.

III. EXPERIMENTAL DETAILS

A. Thermal conductivity

A transient hot-wire (THW) method is used for thermal

conductivity measurements. Since the THW measurement

lasts for a period of the order of seconds, the problems asso-

ciated with convection can be eliminated. According to the

principle presented by Nagasaka and Nagashima,18 the ther-

mal conductivities of measured fluids ðkÞ can be determined

from

k ¼ q

4p

�dT

d ln t

� �: (1)

As the thermal conductivity of the liquid is inversely propor-

tional to the slope of the temperature–time response of the

wire, it is calculated by measuring the slope of the straight

line represented by Eq. (1). The experimental uncertainty of

thermal conductivity measurements is estimated to be within

61%. The hot-wire cell is calibrated using ethylene glycol

and distilled water. The measured thermal conductivity of

ethylene glycol and water is found to be within 1% of the

reported values.

B. Viscosity

The viscosity of the nanofluids is measured by a

Brookfield programmable viscometer (model: LV DV-II-Pro)

appropriately connected to a PC controlled Julabo tempera-

ture controlled bath to vary the fluid temperature between

10 and 70 �C. Basically, the viscometer drives a spindle

immersed in nanofluids. Due to rotation of the spindle, a vis-

cous drag of the fluid against the spindle is developed, which

is measured by the deflection of the calibrated spring. The

temperature of the fluid is measured by a Pt-100 temperature

FIG. 4. FTIR spectra of HEG and f-HEG.

FIG. 5. Thermal conductivity versus number of days of the prepared nano-

fluids (containing 0.395 vol. % f-HEG) confirming the stability of the

suspension.

084307-3 M. Kole and T. K. Dey J. Appl. Phys. 113, 084307 (2013)

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sensor. By choosing the most appropriate spindle, data are

taken when the applied torque is between 10% and 100%.

The operation of the viscometer and data collection (namely,

viscosity, shear stress, shear strain rate, RPM, torque, and

temperature) is done using the WINGATHERVR

software. All the

measurements are performed under steady-state conditions

and the calibration of the viscometer was checked with

the standard fluid provided by Brookfield Engineering

Laboratories. The estimated maximum uncertainty in the vis-

cosity measurement is �3%.

C. Electrical conductivity

Electrical conductivity of the GnS–(EGþ distilled water)

nanofluids both as functions of f-HEG loading and fluid tem-

perature between 10 and 70 �C are measured using a M/S

EUTECH Instruments, Bench Conductivity/TDS meter

(model CON510). The conductivity meter has a measuring

range between 0.2 and 200 000 lS/cm and a resolution of

0.1%. Prior to the measurements, the meter is calibrated using

the buffer solutions of known electrical conductivities.

Measurements are performed using �40 ml of the nanofluid

sample in a cylindrical glass tube, with the conductivity probe

immersed in it. This entire assembly is placed in a tempera-

ture controlled bath (60.01 �C). At each temperature, the

measurements are repeated for 5 times, and the average value

is taken. The estimated uncertainty in the measurement of

electrical conductivity of the nanofluid is within 65%.

IV. RESULTS AND DISCUSSION

A. Thermal conductivity

Experiments are performed both as a function of func-

tionalized GnS concentration (0.041-0.395 vol. %) and fluid

temperature between 10 and 70 �C. The thermal conductivity

ratio ðknf =kbf Þ of the prepared nanofluids measured at 30 �Cis shown in Fig. 6 as a function of f-HEG concentration.

Thermal conductivity of the prepared nanofluids increases

nearly linear with graphene concentration. Thermal conduc-

tivity shows a maximum enhancement of �15% for a load-

ing of 0.395 vol. % f-HEG at 30 �C. Figure 6 also includes

the thermal conductivity enhancement of pure water and

pure EG based graphene nanofluids reported by others.11,12

It may be seen that our results are close to that reported by

Gupta et al.12 for chemically reduced graphene-water nano-

fluids. It is important to note from Fig. 6 that the thermal

conductivity enhancement obtained in the present case falls

in between, which reported for f-HEG dispersed in pure DI

water and pure EG, respectively.11 This is expected in view

of the fact that the base fluid in the present case is 70:30 (by

volume) mixture of EG and distilled water.

Hamilton and Crosser19 stated that the particle shape has

a substantial effect on the effective thermal conductivity of

the suspension when the particle-to-liquid thermal conductiv-

ity ratio is above 100. Gao et al.20 theoretically explained the

large enhancement of the effective thermal conductivity of

nanofluids by adjusting the shape of nanoparticles. Graphene

is a two-dimensional solid and has a very high aspect ratio. In

addition, graphene has the largest surface area compared to

nano-tubes and other nanoparticles; consequently, graphene

nano-sheets will have significantly larger contact area/inter-

face with the base fluid. Therefore, the thermal contact resist-

ance (Kapitza resistance) at the graphene–fluid interface is

reduced profoundly. This should help to improve the effective

thermal conductivity of the nanofluid.

A benchmark study21 performed by researchers from

over 30 organizations worldwide on the thermal conductivity

of nanofluids demonstrated that the experimental data were

in good agreement with the effective medium theory devel-

oped for dispersed particles by Maxwell22 and generalized

by Nan et al.23 considering the matrix-additive interface con-

tact resistance. The effective thermal conductivity expression

as suggested by Nan et al.23 for composite with completely

mis-oriented ellipsoidal particles is

knf ¼ kbf3þ /½2b11ð1� L11Þ þ b33ð1� L33Þ�

3� /ð2b11L11 þ b33L33Þ; (2)

where Lii is the geometrical factor. bii is defined as

bii ¼kp � kbf

kbf þ Liiðkp � kbf Þ(3)

with kp: the thermal conductivity of the ellipsoid particles.

For graphene, the aspect ratio is very high, so, L11 ¼ 0 and

L33 ¼ 1.13 It may be seen from Fig. 7 that the effective ther-

mal conductivity proposed by Nan et al.23 fairly well explains

the measured data. Using least square fitting of the experi-

ment data, the in-plane thermal conductivity of functionalized

HEG (f-HEG) is obtained as: 10.9 6 1.08 W/mK. It is seen

that the thermal conductivity of graphene estimated from the

effective-medium approximation is much lower than the

intrinsic thermal conductivity of suspended graphene sheet.8

This is possible because of the fact that the hydrogen exfoli-

ated graphene contains various structural defects caused by

strong oxidization of graphite. Using Nan et al.23 model,

Yu et al.13 also estimated the in-plane thermal conductivity

of chemically reduced graphene to be 6.8 6 0.8 W/mK.

Similarly, the thermal conductivity of reduced graphene

FIG. 6. Thermal conductivity ratio ðknf =kbf Þ of the prepared nanofluids as a

function of nano-sheet concentration at room temperature. Comparison with

the thermal conductivity results on graphene nanofluids of others.11,12

084307-4 M. Kole and T. K. Dey J. Appl. Phys. 113, 084307 (2013)

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oxide measured by Schwamb et al.24 was reported to be

between 0.14 and 2.87 W/mK. Such a low value for thermal

conductivity of graphene was thought to be due to significant

amount of lattice defects introduced during the chemical oxi-

dation of graphite to GO. Moreover, theoretical calculation25

demonstrated that the thermal conductivity of graphene is

also dependent on the size, the edge roughness, and the defect

density.

Figure 8 shows the temperature dependence of the ther-

mal conductivity of the base fluid (70 vol. % EGþ 30 vol. %

distilled water), as well as that of nanofluids containing vari-

ous volume concentrations of f-HEG. Temperature variation

of the thermal conductivity of both the base fluid and the

prepared nanofluids is qualitatively similar and increases lin-

early with increase in temperature. The enhancement ratios

are 4.3% and 13.4% for the nanofluids with f-HEG concen-

trations 0.041 and 0.395 vol. % at 10 �C, respectively.

However, the values are enlarged up to only 5.6% and 17%,

respectively, when the temperature is raised to 70 �C. The

above results demonstrate that temperature does not have a

strong influence on the thermal conductivity enhancement of

the present nanofluids. It may be noted that for graphene-

pure EG nanofluids nearly temperature independent behav-

iour of thermal conductivity enhancement has been reported

earlier.10,11,13 On the contrary, the thermal conductivity

enhancement of graphene-water nanofluids displays signifi-

cant temperature dependence. In view of the above, for the

present (70:30) mixture of EG and distilled water based gra-

phene nanofluids, the observed marginal influence of tem-

perature on the thermal conductivity enhancement may be

expected.

B. Viscosity

In the absence of any prior data on the viscosity of both

base fluid (70 vol. % EGþ 30 vol. % distilled water) and the

functionalized graphene nanofluids, it is important to confirm

whether they display Newtonian or non-Newtonian behav-

iour as a function of both fluid temperature and graphene

concentration. The viscosity of the base fluid measured as a

function of shear strain rate between 10 and 70 �C is shown

in Fig. 9. It may be seen that over the measured temperature

range, viscosity of the base fluid decreases with the shear

strain rate, indicating non-Newtonian behaviour. With

increasing GnS loading in the base fluid, this non-Newtonian

feature of the base fluid becomes more prominent (Fig. 10).

Shear stress vs. shear strain rate plot for both base fluid and

the prepared nanofluids at 30 �C are shown in Fig. 11. It is

seen that for all the studied nanofluids, the shear stress varies

FIG. 7. Estimation of thermal conductivity of the prepared nanofluids by

Nan et al.23 model.

FIG. 8. Temperature dependence of thermal conductivity of both base fluid

and the prepared nanofluids.

FIG. 9. Viscosity vs. shear strain rate of EG-distilled water mixture at differ-

ent temperatures.

FIG. 10. Viscosity vs. shear strain rate of the prepared nanofluid containing

0.395 vol. % f-HEG within the measured temperature range (10–70 �C).

084307-5 M. Kole and T. K. Dey J. Appl. Phys. 113, 084307 (2013)

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nonlinearly with shear strain rate, indicating the “shear

thinning” behaviour, which is consistent with the observed

decrease in viscosity with increasing shear strain rate for all

the studied nanofluids. Relative viscosity ðlnf =lbf Þ of GnS–

(EG þdistilled water) nanofluids increases with increasing

f-HEG loading at 30 �C as is shown in Fig. 12. Viscosity of

the nanofluid enhances nearly by �100% that of the base

fluid, at a loading of 0.395 vol. % of f-HEG. It may be noted

that though the percentage enhancement in viscosity is large,

the absolute value of the nanofluid viscosity is very nominal

(�12.1 cP) and is almost similar to that of ethylene glycol at

room temperature. Volume concentration dependence of vis-

cosity of the f-HEG-EGþ distilled water nanofluids at room

temperature are estimated on the basis of the several existing

and widely used models26–31 and is compared with the meas-

ured data (Fig. 12). We confirm that none of these models

viz., Einstein,26 Brinkman,27 Krieger and Dougherty,28

Batchelor,29 Neilson,30 and Kitano et al.31 could provide an

acceptable estimate of the measured viscosity of the gra-

phene nanofluids. Temperature dependence of viscosity of

the nanofluids containing different volume concentrations of

f-HEG is shown in Fig. 13. The viscosity decreases rapidly

with rise in temperature and displays an asymptotic

behaviour. The decrease in nanofluid viscosity with increase

in temperature is expected due to the weakening of the inter-

particle and inter-molecular adhesion forces and similar

trends have also been observed in almost all other varieties

of nanofluids.32–34 Unfortunately, theoretical formulations to

predict the temperature dependence of viscosity of nano-

fluids are practically absent. A few empirical correlations for

temperature dependence of nanofluid viscosity were, how-

ever, suggested by a few authors32,34–36 mainly to explain

their own set of viscosity data. These correlations were tested

to fit the present set of data on the temperature dependence

viscosity of GnS–(EGþ distilled water) nanofluids. It may

be noted that all the four correlations referred above follow

equally well the measured temperature dependence of vis-

cosity of the graphene–EGþ distilled water nanofluids with

average R2 value between 0.97728 and 0.98763.

C. Electrical conductivity

Though important, the electrical conductivity of nano-

fluids has not yet been widely studied compared to their

thermal conductivity. The electrical conductivity of a sus-

pension can either increase or decrease depending on the

FIG. 11. Shear stress vs. shear strain rate plots of various GnS-EGþ distilled

water nanofluids at room temperature.

FIG. 12. Relative viscosity ðlnf

lbfÞ of GnS-EGþ distilled water nanofluids at

30 �C as a function of functionalized GnS concentration. The solid lines are

the relative viscosity predicted by various classical models.26–31

FIG. 13. Temperature dependence of the viscosity of the prepared nanofluids

between 10 and 70 �C for various f-HEG volume concentrations.

FIG. 14. Electrical conductivity as a function of f-HEG concentration at

room temperature. Line is a guide to the eye.

084307-6 M. Kole and T. K. Dey J. Appl. Phys. 113, 084307 (2013)

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background electrolyte, the particle size,37,38 the particle

loading,39 and the charge of the particle.40 An analytical

model was proposed38 to explain the particle size and con-

centration effects on nanofluid electrical conductivity.

Electrical conductivity of the present f-HEG–EGþ distilled

water nanofluids increases linearly with volume concentra-

tion of functionalized HEG as shown in Fig. 14. The electri-

cal conductivity of the base fluid increases from 1 lS/cm to

�87.2 lS/cm for a loading of 0.395 vol. % f-HEG at 30 �C,

which corresponds to an anomalous enhancement of 8620%.

Fig. 15 shows the temperature dependence of electrical con-

ductivity of both the base fluid and prepared nanofluids. It is

seen that the electrical conductivity increases linearly with

temperature for all cases; however, the rate of enhancement

is higher for nanofluids with higher loading of functional-

ized graphene. Baby et al.11 observed an enhancement in

electrical conductivity by 1400% for f-HEG loading of

0.03 vol. % in DI water at 25 �C. But in case of pure EG as

base fluid, the increment was only 220%. In both cases, the

electrical conductivity increased with increasing volume

concentration as well as increasing fluid temperature.

V. CONCLUSIONS

Summarizing, hydrogen exfoliated graphene nano-sheets

are prepared and functionalized. Surfactant free graphene–

EGþ distilled water nanofluid prepared by ultrasonication are

found to be stable for greater than 5 months. Thermal conduc-

tivity, viscosity, and electrical conductivity of the nanofluids

are measured both as a function of f-HEG concentration and

fluid temperature between 10 and 70 �C. Thermal conductivity

results show a maximum enhancement of �15% for a loading

of 0.395 vol. % f-HEG at 30 �C, and the thermal conductivity

of f-HEG is estimated to be 10.9 6 1.08 W/mK. Thermal con-

ductivity of both the base fluid and the prepared nanofluids

increases linearly with temperature. However, the thermal

conductivity ratios are nearly temperature independent.

Viscosity measurements confirm that both the base fluid and

prepared nanofluids are non-Newtonian in nature throughout

the measured temperature range. Viscosity enhances by

�100% that of base fluid at room temperature for nanofluid

containing 0.395 vol. % f-HEG. Though the percentage

enhancement in viscosity is large, its absolute value is, how-

ever, very nominal (12.1 cP), nearly same as EG at room tem-

perature. None of the classical models succeed in explaining

the observed viscosity enhancement with f-HEG loading at

room temperature. Temperature dependence of viscosity of

the prepared nanofluids is well explained by some of the exist-

ing empirical correlations. Electrical conductivity of the nano-

fluids increases linearly both with f-HEG concentration and

the base fluid temperature. Enhancement of electrical conduc-

tivity by �87 times that of the base fluid is obtained for nano-

fluid with 0.395 vol. % of f-HEG at 30 �C. The above results

indicate that the graphene–(EGþwater) nanofluids could pos-

sibly be a useful candidate for coolant applications.

ACKNOWLEDGMENTS

One of the authors (T.K.D.) acknowledges the financial

help received from Department of Science & Technology

(DST), New Delhi, in the form of a research Grant. Award

of a CSIR Senior Research Fellowship is also gratefully

acknowledged by Miss Madhusree Kole.

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