Nanofluids Paper Final Jl Nanofluids Sept 2012

8/12/2019 Nanofluids Paper Final Jl Nanofluids Sept 2012

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Viscosity and specific volume of TiO 2 /water nanofluid

Harinder Kaur Naina a , Ritu Gupta a , Hema Setia b and R.K. Wanchoo a *

aUniversity Institute of Chemical Engineering and Technology, Panjab University, Chandigarh

160014, India bUniversity Institute of Engineering and Technology, Panjab University, Chandigarh, 160014, India

* Corresponding Author: R.K.Wanchoo, University Institute of Chemical Engineering and Technology, Panjab

University, Chandigarh 160014, India, [email protected], Tel.: +91 172 2534933 ; +91 172 2779173

Abstract

Nanofluids are liquid suspensions containing nanometer-sized particles and have been found to

have great potential to deliver as effective heat transfer fluids. Interaction between nanoparticles in

nanofluids can induce structuring of the particles thereby modify the transport properties of base

fluid. In this study viscometric and volumetric behavior of anatase titanium dioxide (TiO 2)

nanoparticles dispersed in pure water have been investigated over a range of volumetric solids

concentrations ( = 0.5 -2.5%) and temperatures (T = 283.15- 313.15 K). Relative viscosity of the

nanofluid (nf / bf ) exhibited an exponential rise with and Arrhenius law was followed with rise in

temperature. The combined effect of and on relative viscosity of the nanofluid was very well

represented by = 2.924 0.136 . . A maximum of 50% rise in viscosity for2.5vol % TiO 2-water nanofluid was observed. Further, for TiO 2-water nanofluid, specific volume

data followed additive rule for dispersed liquids.

Keywords : nanoparticles, nanofluids, TiO 2, viscosity, specific volume, correlation.

1. Introduction

Nanofluids are a new promising class of heat transfer fluids synthesized by dispersing

nanoparticles into conventional heat transfer fluids such as water, oil and ethylene glycol resulting


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in increased thermal conductivity and higher heat transfer coefficients. To quantify the potential of

nanofluids for heat transfer applications, an evaluation of transport properties is essential.

Viscosity is as critical as thermal conductivity of heat transfer fluids used in heat

exchangers. Pumping power is proportional to the pressure drop, which in turn is related to fluid

viscosity. In laminar flow, the pressure drop is directly proportional to the viscosity. Hence, the

availability of reliable data on viscosity and specific volume of nanofluids is of paramount

importance.

Dispersing small amounts of nanoparticles in the conventional heat transfer fluids results in

an increased thermal conductivity and higher heat transfer coefficient of the resulting fluid which

can be advantageously used for the design of compact high performance heat exchangers. In order

to quantify the potential use of nanofluids for heat transfer applications, an evaluation of its thermo

physical properties such as density, viscosity, thermal conductivity are essential.

Though many researchers have experimentally investigated the thermo physical properties of

nanofluids, however, the experimental data on viscosity and specific volume of nanofluids are rare

compared to the available data on thermal conductivity. Further, discrepancies in the values of

viscosity of the same nanofluid reported by different authors are in variance [1,4,6,9].

Masuda et al. [1] experimentally determined the viscosity of TiO 2 (27nm)/water nanofluid.

They observed a 60% rise in viscosity of the base fluid for a TiO 2 nanoparticle volumetric loading

of 4.3%.

Pak and Cho [2] measured the viscosity of TiO 2 (27 nm)/water nanofluid at 25 oC in the shear

rate range 10-10 3 s-1 and volume percent range of 0.99% to 10 %. They observed a 12% rise in

viscosity over the base fluid for a 0.99 vol % TiO 2/ water nanofluid which was much higher than

that predicted by Batchelor [3].


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Murshed et al. [4] investigated the viscosity of TiO 2 (15 nm) in deionised water at room

temperature up to a 0.05 volume fraction. They reported a viscosity value of 1 .83 m Pa s for a 5 %

TiO 2/water nanofluid.

Tseng and Lin [5] also studied the rheological behaviour of anatase TiO 2 in water ( = 0.05 0.12) in the shear rate range of 10-1000s -1 . They suggested pseudo plastic flow behaviour up

to = 0.1 , above which the suspensions exhibited thixotropic behaviour. They proposed a

correlation for viscosity as a function of in the form = 13.47 . .

Turgut et al. [6] measured the temperature dependent viscosity of TiO 2 nanoparticles (21 nm) in

deionized water up to a volume fraction of 0.03 in the temperature range of 13 to 55 oC. They

observed that with increase in temperature the viscosity of nanofluids decreases exponentially and

the relative viscosity is dependent on the volume fraction of nanoparticles in the base fluid.

Viscosity models given by Einstein [7], Nielsen (as quoted in [6]) and Krieger and Dougherty (K-

D)[8] underestimated their experimental data. However, the investigators have not presented any

model to represent their data on viscosity as a function of temperature and volume fraction.

Weerapun and Somchai [9] reported their experimental data on dynamic viscosity of TiO 2(21

nm)-water nanofluid covering the concentration range of 0.2 2 vol.% at 15 oC, 25 oC and 35 oC.

They observed that the measured viscosity of nanofluids was different compared to the values

obtained from the correlations and the data reported by others [1,2,4]. Further, they proposed a new

correlation for predicting the viscosity of TiO 2-water nanofluids as:

= ( + + ) (1)

where a,b and c are temperature dependent constants.

He et al [10] experimentally studied the rheological behaviour of water based TiO 2( 20 nm)

nanofluids at 22 oC. They carried out investigations on three particle size of TiO 2 in water (95nm,

145nm and 210nm) up to a concentration of 1.2 vol %. They suggested that water based titania

nanofluids are shear thinning over the shear rate range of 0.1 to 1000 s -1 . They observed that the %


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rise in viscosity increases with the size of the nanoparticles and with the concentration of

nanoparticles in the base fluid. Their measured values of viscosity were much higher than those

predicted by the Einstein model [7].

Hosseini and Ghader [11] presented a theoretical model based on the Eryings viscosity

model to predict the viscosity of nanofluids. However, the adjustable parameters reported by them

were system specific for Al 2O3 and CuO and cannot be used in general for any other system.

Most of the results reported on the effective viscosity of nanofluids [1,2,4,6,9] indicate the

anomalous increases in viscosity. Variations in data on the same nanofluid system reported by

different authors is also evident [1,4,6,9]. Further, with increase in the concentration of

nanoparticles in the base fluid ( ), available experimental data cannot be predicted by classical

models such as those given by Einstein [7], Krieger and Dougherty [8], Nielsen (as quoted in [6])

and Batchelor [3]. Hence, there is a need to generate more data on transport properties of

nanofluids and develop suitable correlations for predicting the transport properties through

parametric investigations on nanofluids.

Numbers of correlations are available in the literature to predict the viscosity of nanofluids.

However, these correlations seem to be system specific and fail to predict the data at higher

concentrations. No single correlation is available that can predict the available viscometric data on

nanofluids within reasonable accuracy. Some of the most widely used correlations are discussed

below.

Einstein [7], proposed an equation (Eq 2) for determining the viscosity of dilute suspension

of spherical particles.

= (1+ 2.5 ) (2)

were, nf is the viscosity of suspension, bf is the viscosity of base fluid and is the volume fraction

of particles in base fluid. Einstein's correlation is found to be valid for relatively low particle


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volume fractions, 0.02. Beyond this value, it underestimates the effective viscosity of the

suspension.

Brinkman [12] has extended Einstein's correlation for use with moderate particle concentrations, as

follows:

= . (3)

A semi-empirical equation was proposed by Krieger and Dougherty (KD)[8] and is expressed as

= 1 [ ]

(4)

Where, is particle volume fraction , m is the maximum packing fraction and [ ] is the intrinsic

viscosity ([ ] = 2 .5 for hard spheres). For randomly mono-dispersed spheres, the maximum close

packing fraction is approximately 0.64.[6]

Nielsen (as quoted in [6]) proposed a generalized equation for the relative elastic moduli of

composite materials, also widely used for relative viscosity, which is simplified for a suspension of

dispersed particles as

= (1+1.5 ) / ( ) (5)

where p and m are the volume fraction of particles and the maximum packing fraction,

respectively.

Batchelor [3] considered the effect due to the Brownian motion of particles on the bulk stress of an

approximately isotropic suspension of rigid and spherical particles and proposed Eq. (6) for

predicting the viscosity of nanofluids.

= (1+2.5 + 6.2 ) (6)

Maiga et al.[13] proposed a model for calculating the viscosity of nanofluids as

= (1+7.3 + 123 ) (7)

Yurong et al.[14] measured the thermal conductivity and viscosity of TiO 2 at 22 oC and developed

the following relation for calculating the viscosity of nanofluid


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= (199.21 + 4.62 + 1 ) (8)Massimo Corcione [15] derived an empirical correlation based on available data on dynamic

viscosity of nanofluids which can be expressed as

= . / . . (9)

where is the equivalent diameter of a base fluid molecule, given by = 0.1 /

in which

M is the molecular weight of the base fluid, N is the Avogadro number and is the mass density

of the base fluid at 293 K.

The correlations are based on experimental data and dont have a unified character, which could

be due to different physical state of the suspension including size and shape. These correlations

relate viscosity as a function of volume percentage of nano material only with no consideration for

temperature. Generally the viscosity of liquids decreases with an increase in temperature.

Present study reports the viscometric and volumetric behavior of anatase titanium dioxide

(TiO 2) nanoparticles dispersed in pure water over a range of volumetric solid concentrations ( =

0.5 -2.5%) and temperatures ( T = 283.15- 313.15 K).

Based on the observed data, a suitable correlation relating the viscosity of the nanofluid to the

vol% of TiO 2 in the nanofluid and the temperature has been developed.

2. Experimental

2.1. Nanofluid Synthesis

TiO 2 / water nanofluids were synthesized by two-step method. TiO 2 (Aeroxide (P25),

manufactured by Degussa Co.) nanoparticles, with an average primary particle size of 21nm were

dispersed in distilled water using different volumetric solids concentrations ( ) of TiO 2 (0.5, 0.75,

1.0, 1.5, 2.5 vol%). Data provided by the manufacturer includes, bulk density of anatase TiO 2 of

4175 kg/m 3 with a specific surface area of 5015 m 2/g, thermal conductivity 8.4 W/mK and

specific heat of 0.692 kJ/kg K. The density of distilled water used as base fluid is 997.6 kg/m 3 at


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25 oC. To obtain well dispersed nanofluids, pH of distilled water was first adjusted to~3 using

concentrated HNO 3. The mixture was sheared using a high speed homogenizer (Pro Scientific Inc,

USA, model No 01-02250 Pro 250) for 30 minutes. The mixture was then homogenized for 15

minutes using an ultrasonic processor (Hielscher, UP 100H). Stability of the mixture was observed

visually for any phase separation and any change in the density. The nanofluids, thus synthesized

were found to be stable for over a month.

2.2 Specific volume Measurement

Specific volume of the synthesized nanofluids was measured using Anton Paar DMA 48

density meter in the temperature range of 283.15- 313.15 K (0.1K) with an accuracy of 110 -

4gm/cm 3. In order to ascertain the accuracy of experimental results, the density meter was first

calibrated at each temperature with standard fluids of known density. The density of water was then

measured and compared with the literature value [16]. The density measurements were

reproducible to within 0.05%.

2.3 Viscosity Measurement

Ubbelhode viscometer was used to measure the viscosity of the synthesized nanofluids in

the temperature range 283.15- 313.15 K (0.1K). The viscometer was first calibrated using

standard liquids of known viscosity and density. The viscosity of base fluid- distilled water was

then measured. The measured values of base fluid were compared with the available literature

values [16]. The measurements were reproducible to within 0.08%.

3. Results and Discussion

3.1 Specific volume of nanofluids

Figure 1 shows the measured values of specific volume 1/ of nanofluid as a function

of temperature for various % volume fractions ( = 0.5 -2.5%) of TiO 2. Specific volumes were also

calculated by using the Pak and Cho [2] correlation, which is defined as:


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= + (1 ) (10)where is the density of the nanofluid, ( = / 100) is the volume fraction of nanoparticles,

is the density of the base fluid and is the density of the nanoparticles.

As is clear from Figure1, present experimental data is in good agreement with the specific volumes

predicted using equation (10) to within 1% for the entire concentration range studied.

3.2 Viscosity of nanofluids

The measured viscosities of nanofluids with volume fraction of TiO 2 in water over a range

of volumetric solids concentrations ( = 0.5 -2.5%) and temperatures (T = 283.15- 313.15 K) are

given in Figure 2. Viscosity of nanofluid increases exponentially with increase in volume

percentage of TiO 2 in water ( ) . The variation in viscosity with temperature for all concentrations

of nanofluids are similar, the viscosity decreases with an increase in the temperature and obeys

Arrhenius law.

Present experimental data was fitted to a model equation of the form (Eq.11) and model

parameters a, b and c were determined using non-linear regression technique by minimizing the

sum of squares of errors between experimental and predicted values.

= exp (11)

The model parameters thus obtained are: a = 2.924, b = 0.136 and c = 316.06.

The final form of the eq. (11) can be expressed as:

= 2.924 . . (12)where nf is the viscosity of the nanofluid Pa-s , bf is the viscosity of the base fluid Pa-s, is the %

volume fraction of the nanoparticles in the base fluid and T is temperature in Kelvin. Present

viscometric data is predicted by Eq. (12) very well to within an accuracy of 5 %.

Present viscosity data was compared with the predicted viscosity values using various

models available in the literature. Table 1 lists the statistical deviation parameters for these models.


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As is evident from Table 1, present correlation (Eq.12) predicts our data better than any of other

models with a minimum MRQE of 0.035.

In Figure 3, viscosity predicted by proposed correlation (Eq.12) is compared with some of the the

recent available data on TiO 2 / water nanofluid [6,9].

Equation (12) predicts the available data of Turgut et al [6] and Weerapun and Somchai [9] to

within 10%.

In order to extend the proposed correlation for nanofluids the viscosity predicted by Eq. 12 was

also compared with the available data [16,17] on viscosity for Al 2O3 /water, CuO/water and SiO 2

/water nanofluids (Figure 4). The proposed correlation predicts the available data reasonably well

within an error of 12% for 2.5 % .4. Conclusions

Present study reports the experimental data on specific volume and viscosity of TiO 2-water (0.5-

2.5 vol%) nanofluid in the temperature range of 283.15 313.15 K. The measured specific volume

of the nanofluid was found to follow additive rule for dispersed liquids. It was observed that at a

fixed temperature, the viscosity of the nanofluid increased exponentially with an increase in

volumetric concentration of TiO 2 in the nanofluid. A maximum of 50% rise in viscosity for 2.5

vol% TiO 2-water nanofluid was observed. With an increase in temperature, the viscosity of

nanofluid followed an Arrhenius type equation. A new correlation for predicting the viscosity of

nanofluid as a function of concentration of the nanoparticles in the base fluid and the temperature

has been proposed. The proposed correlation (Eq. 12) predicts the available experimental viscosity

of TiO 2/water system within accuracy of 10%. The proposed correlation (Eq. 12) also predicts the

experimental data on viscosities for other nanofluid systems to within an error 12%.


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References

[1] H. Masuda, A. Ebata, K. Teramae, N. Hishinuma, Netsu Bussei. 4, 227 (1993) (in Japanese).

[2] B.C. Pak, Y.I. Cho, Experimental Heat Trans. 11, 151 (1998).

[3] G.K.Batchelor, J Fluid Mech . 83, 97 (1977).

[4] S.M.S. Murshed, K.C. Leong, C. Yang, Int J Therm Sci . 44, 367 (2005).

[5] Wenjea J. Tseng, Kuang-Chih Lin, Mater Sci and Eng A . 355, 186 (2003).

[6] A. Turgut I. Tavman M. Chirtoc H. P. Schuchmann C. Sauter S. Tavman, Int J

Thermophy. 30, 1213 (2009).

[7] A.Einstein, Annalen der Physik, Leipzig. 19, 289 (1906).

[8] I.M. Krieger, T.J. Dougherty, Trans Soc Rheol . 3, 137 (1959).

[9] Weerapun Duangthongsuk and Somchai Wongwises, Exp Therm Fluid Sci . 33, 706 (2009).

[10] Yurong He, Yi Jin, Haisheng Chen, Yulong Ding, Daqiang Cang, Huilin Lu, Int J Heat

Mass Transfer . 50, 2272 (2007).

[11] Marziehsadat Hosseini, Sattar Ghader, J Mol Liq. 153, 139 (2010).

[12] H.C.Brinkman, J Chem Phys. 20, 571 (1952).

[13] Sidi El Becaye Maiga, Cong Tam Nguyen, Nicolas Galanis, Gilles Roy, Superllatices and

Microstructures . 35, 543 (2004).

[14] Yurong He, Yubin Men, Yunhua Zhao, Huilin Lu, Yulong Ding, Numerical investigation

into the convective heat transfer of TiO 2 nanofluids flowing through a straight tube under

laminar flow conditions, Appl Thermal Eng . 29, 1965 (2009).

[15] Massimo Corcione, Energy Conversion and Management . 52, 789 (2011).

[16] K. Raznjevic, In: Handbook of Thermodynamic Tables and Charts , Hemisphere Publishing

Corporation, London (1976)

[17] C.T. Nguyen, F. Desgranges, G. Roy, N. Galanis, T. Mare, S. Boucher, H.A.Mintsa, Int J

Heat Fluid Flow . 28, 1492 (2007).


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[18] I. Tavman, A.Turgut, M. Chirtoc, H.P.Schuchmann, S.Tavman, Archives Mat Sci Eng. 34

(2), 99 (2008).


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Harinder Kaur Naina , Ritu Gupta , Hema Setia and R.K. Wanchoo *

FIG.1 . Measured specific volume of TiO 2 /water nanofluid at different temperatures as a function

of % volume fraction( ).

0.9

0.93

0.96

0.99

1.02

1.05

275.15 285.15 295.15 305.15 315.15

S p e c

i f i c v o

l u m e

1 0 - 3

, m

3 / k g

Temperature, K

Water 0.5% TiO 0.75% TiO 1% TiO 1.5% TiO 2.5% TiO

Pak and Cho [2]

2 2 2 2 2


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Harinder Kaur Naina, Ritu Gupta , Hema Setia and R.K. Wanchoo *

FIG.2 . Variation in measured viscosity of TiO 2-water nanofluids with volumetric solids

concentrations ( ) at different temperatures.

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0 0.5 1 1.5 2 2.5 3

E x p e r i m e n

t a l v

i s c o s

i t y ,

m P a s

Concentration , %

283.15 K 288.15 K 293.15 K 298.15 K 308.15 K 313.15 K


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FIG. 3. Parity plot between the available experimental viscosity of TiO 2 / water nanofluid

and the viscosity predicted by Eq.12.

0.4

0.8

1.2

1.6

2

0.4 0.8 1.2 1.6 2.0

P r e

d i c t e d v

i s c o s

i t y ,

m P a s

Experimental viscosity, mPa s

present study [Eq 12]

Turgut et al [6]

Weerapun and Somchai[9]

+10%

-10%


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FIG. 4. Parity plot between the available experimental viscosity of Al 2O3, CuO, SiO 2, TiO 2 in

water nanofluids and the viscosity predicted using Eq.12.

0

0.4

0.8

1.2

1.6

2

0 0.4 0.8 1.2 1.6 2

P r e

d i c t e d v

i s c o s

i t y ,

m P a s

Experimental viscosity, mPa s

Al O Nguy en et al.[ 16]

CuO Nguyen et al [16]

SiO Tavman et al [17]

present study

Weerapun and Somchai [9]

Turgut et al [6]

2 3

2

+12%

-12%


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Table 1. Statistical deviation parameters

Model MRQE % ARE SQE

Einstein [7] 0.126 8.491 0.141

Brinkman [12] 0.126 8.453 0.140

Batchelor [3] 0.125 8.436 0.140

K-D [8] 0.126 8.446 0.140

Neilsen (as quoted in [6]) 0.111 7.361 0.123

Maiga et al.[13] 0.072 4.586 0.075

Yurong et al. [14] 0.081 5.523 0.085

Weerapun and Somchai [9] y 0.135 8.704 0.152

Massimo [15] 0.106 7.030 0.116

Present model (Eq 12) 0.035 2.914 0.034

y Constants at different temperatures were interpolated from the given data at 15 oC, 25 oC, 35 0C

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Nanofluids Paper Final Jl Nanofluids Sept 2012