Electrical and Rheological Behavior Of Stabilized

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Electrical and Rheological Behavior Of Stabilized Al2O3 Nanofluids Alina Adriana Minea* Facultatea Stiinta Si Ingineria Materialelor, Universitatea Technica Gheorghe Asachi, Iasi, Romania Abstract: -Al2O3 nanoparticles were dispersed in 20 % wt. aqueous solution to prepare four types of non-Newtonian nanofluids. Rheological characteristics of the base fluid and nanofluids with various nanoparticle volume concentrations were measured. Results show that all nanofluids as well as the base fluid exhibit pseudoplastic (shear thinning) behavior. The rheological characteristics of nanofluids and those of the base fluid are functions of particle concentrations. Electrical conductivity show polynomial behavior at a temperature of 25°C for different concentration fluids. The flow characteristics show rheopectic behavior according to concentration of Al2O3 with highly non-Newtonian characteristics at lower shear stresses. Rheological characteristics suggest that at room temperature viscosity is higher for higher concentration nanofluids.

Keywords: Electrical conductivity, experimental, non-newtonian, power law, rheological behavior. 1. INTRODUCTION Numerous high-tech industries such as microelectronics, transportation, manufacturing, and metallurgy are often faced with the technical challenges of having higher heating and cooling performance. Usual methods to enhance heat transfer rates such as active and passive techniques [1, 2] have the disadvantage to increase the required pumping power of the cooling fluid. The development of advanced fluids with improved electrical and thermal characteristics is of dominant importance to achieve higher flux densities. Electrical and thermal conductivities of solids may be orders of magnitude greater than that of fluids and it is therefore expected that dispersion of solid particles will significantly improve the thermal and electrical behavior of fluids. Nanofluid is a new dimensional thermo fluid term emerged after the pioneering work by Choi [3]. Nanofluid is a solid–liquid mixture which consists of nanoparticles and a base liquid. Due to very small sizes and large specific surface areas of the nanoparticles, nanofluids have superior properties like high thermal conductivity, minimal clogging in flow passages, long-term stability, and homogeneity [3]. Many investigators have studied the various characteristics of fluid flow and heat transfer behavior of nanofluids over the past 15 years [4-6] and found that enhanced heat transfer coefficients were obtained with nanofluids. However, it is important that the enhanced heat characteristics of these new fluids are not counteracted by additional pumping power to circulate these fluids in the process. It is therefore necessary to also examine the rheological behavior of these fluids. There have been few researches on the characteristics of dispersion and rheological properties of nanofluids [7-15]. Since the rheological properties provide the knowledge on the microstructure under both static and dynamic conditions, the study on the rheological characteristics of nanofluid can reveal the route to understand the mechanism of heat transfer enhancement, and hence the optimum design conditions. Towards this, the effect of nanoparticle diameter, particle volume fraction, and temperature on the viscosity of the nanofluid and thermal conductivity has been critically analyzed and presented. All of the rheological studies showed that viscosity of nanofluids was larger than that of the base fluid and increased with an *Address correspondence to this author at the Facultatea Stiinta Si Ingineria Materialelor, Universitatea Technica Gheorghe Asachi, Iasi, Romania, IASI, STR. C.NGRI NR.62, SC.A, AP.2, COD 700070; Tel: 0040723455071; E-mail: [email protected] 1573-4137/13 $58.00+.00

increase in the nanoparticle concentration. For all these investigations, different types of base fluids were used but they were all Newtonian fluids. Based on the available data in the literature, the resulting dispersion of nanoparticles in Newtonian base fluids resulted in nanofluids exhibited Newtonian behavior [9, 14, 15], while many other nanofluids exhibited non-Newtonian, mainly shear-thinning, behavior [9-13, 15]. The viscosity of nanofluids decreased with an increase in the nanoparticle size [13, 16]. Xinfang et al. [17] have studied the viscosity of Cu/water nanofluids, and their results showed that viscosity of nanofluids is independent of nanoparticle concentration. Tseng and Tzeng [18] have shown that aqueous nanofluids containing indium tin oxide nanoparticles over shear rate range of 10 to ~500 s-1 exhibited Newtonian behavior, but as shear rate increased their rheological behavior change into shear thinning flow. Similar results were obtained by Alphonse et al. [19]. The rheological behavior of nanofluids has often been modeled using the power law model with its two fitting parameters: the power law index and the consistency index. The power law index of nanofluids normally increases with an increase in temperature whereas the consistency index of nanofluids decreases with temperature. It can be noted here that most of the above-mentioned studies have typically investigated the mechanism for augmentation of heat transfer by nanofluids, the stability of the suspensions and their superior thermal performance over the conventional heat transfer medium. The major focus of the research work, so far, has been on the estimation of thermophysical properties, primarily on the effective thermal conductivity. Despite the vast scientific and technological importance of electrical conductivity characteristics of nanoparticle suspensions, studies concerning the issue of the effective electrical conductivities of nanofluids have largely been ignored. Also, there is very few data published when it comes to the electrical properties of nanofluids. On the other hand, among the transport properties, electrical conductivity might bring information on the state of dispersion and stability of the particulate suspension. Although some preliminary studies with similar objective have been reported [20–23], a systematic study addressing this extremely significant issue is yet to be found in the literature. In this context, the present work has been undertaken to explore the electrical transport property of nanofluids. One of the objectives of the present study is to investigate the effective electrical conductivity of water-based alumina (Al2O3) nanofluids. This is accomplished by conducting experiments at © 2013 Bentham Science Publishers

2 Current Nanoscience, 2013, Vol. 9, No. 1

Alina Adriana Minea

different volume fractions of nanofluids. In this paper, the rheological behavior of suspensions of nanoparticles in a non-Newtonian fluid was experimentally studied, too. 2. THEORETICAL MODELS 2.1. Electrical Conductivity The Maxwell model [24] was the first model developed to determine the effective electrical or thermal conductivity of liquid– solid suspensions. This model is applicable to statistically homogeneous and low volume fraction liquid–solid suspensions with randomly dispersed, uniformly sized and noninteracting spherical particles. The Maxwell equation predicts that the effective conductivity of the suspension (eff), is a function of the conductivity of the particles (p), conductivity of the base fluid (bf) and the volume fraction () of the particles, and is given by:

eff bf

.

= 1+

3( 1) ( + 2 ) ( 1)

(1)

where =p/bf, is the conductivity ratio of the two phases. Generalization of the Maxwell's model leads to the following cases depending on the conducting nature of the particles and the base fluid [25] a)

b)

c)

eff bf eff bf

eff bf

3 = 1 , for pbf (insulating particles) 2

= 1+ 3 , for pbf (highly conducting particles)

= 1+ 2.5

μbf

(2)

=

1

(1 )

(3)

2.5

With increasing particle volume concentration, the flow around a particle is influenced by the neighboring particles. The KriegerDougherty model [29] is based on the assumption that equilibrium exist between individual spherical particles and dumbbells that continuously form and dissociate as Eq. (4):

μnf μbf

= 1 a m

[ ] m

(4)

where m is the maximum concentration at which flow can occur, a the effective volume fraction of aggregates and [] is the intrinsic viscosity, which for monodisperse systems has a typical value of 2.5. Frankel and Acrivos [30] derive a suspension viscosity model by using an asymptotic mathematical analysis of governing equations of change. According to the Frankel and Acrivos model, the effective Newtonian viscosity of a suspension of uniform solid spheres is shown as Eq. (5):

μbf

= 1 , for p=bf (equal conductivity)

2.2. Viscosity Viscosity of nanofluids is less investigated compare to thermal conductivity; however, the rheological properties of liquid suspensions have been studied since Einstein [27]. Einstein’s equation can predict the effective viscosity of liquids in the low volume fraction having spherical suspended particles. The equation considers only the liquid particle interaction and is valid for volume concentration of less than 1.0%. The Einstein’s equation is given as Eq. (2):

μbf

μnf

μnf

Cases (a)–(c) show the theoretical effect, as predicted by the Maxwell's model, of the particle volume fraction on the relative conductivity (eff / bf ) for a constant value of conductivity ratio (p/bf). A great number of extensions to the Maxwell equation have been carried out ever since Maxwell’s initial investigation. These extensions take into account various factors related to conductivity like particle shape, particle distribution, high volume concentration, Brownian motion induced nanoconvection, liquid layering, particle clustering and interface contact resistance. The applicability of the Maxwell's model has been successfully verified by experimental data [26] for dilute suspensions (1) with large particles (particle size larger than tens of micrometers). The present experimental situation corresponds to Case (a) in the Maxwell's model (alumina particles have very poor electrical conductivity characteristics), where the slope of the relative conductivity curve for insulating particles has a negative value (=1.5). Therefore, it is expected that the mixture's electrical conductivity is reduced.

μnf

Brinkman [28] extended the Einstein’s equation up to particle volume concentration of 4.0% given by Eq. (3):

1 3 9 m

= 1 8 1 3 m

(5)

The most important assumption in this model is that the suspension exhibits Newtonian behavior. Based on the comparisons with experimental data, Frankel and Acrivos found that the equation is greater than 0.5 in which the randomly packed valid for m spheres, m is 0.64. Lundgren [31] has proposed the following equation under the form of Taylor series as:

μnf μbf

( )

= 1+ 2.5 + 6.25 2 + O 3

(6)

It is obvious that if the terms O(3) or higher are neglected, the above formula reduces to that of Einstein. Batchelor [32] studied the effect of these hydrodynamic interactions or the Brownian motion on viscosity of suspensions and developed a relation valid for particle volume concentration up to 10% as:

μnf μbf

= 1+ 2.5 + 6.25 2

(7)

Graham [33] has proposed a generalized form of the Frankel and Acrivos [30] formula which is agrees well with Einstein’s for small . The Graham formula is shown as Eq. (8):

μnf μbf

1 = 1+ 2.5 + 4.5 2 h h h 2 + 1+ d p d p d p

(8)

where μnf is the viscosity of the nanofluids, μbf is the viscosity of the base fluid, dp is the particle radius, h is the interparticle spacing and is the nanoparticles volume fraction of the suspended solutes or particles consider only nanoparticles volume concentration on nanofluids viscosity prediction.

Electrical and Rheological Behavior Of Stabilized Al2O 3 Nanofluids

Current Nanoscience, 2013, Vol. 9, No. 1

Viscosity of nanofluids: experimental observations From the theoretical point of view, there is a new challenge to the researchers in fluid dynamics and heat transfer to understand various properties of nanofluids. There exist very few established theoretical formulas, some theoretical models such as Einstein model have been modified and use to predict the effective viscosity of nanofluids. A simple expression was proposed by Kitano et al.[34] involving m was also used to predict the viscosity of two phase mixture by Eq. (9):

μnf μbf

= 1 m

2

(9)

Nguyen et al. [35] has proposed a formula for calculating viscosity of nanofluids for 47 and 36 nm particle-sizes and particle volume fractions of 1 and 4% with particle volume concentration, and temperature, T respectively as shown by Eq. (10), Eq. (11), Eq. (12) and Eq. (13):

μr = μr =

μr = μr =

μnf μbf μnf μbf

μnf μbf μnf μbf

= 0.904e0.1483

(10)

= 1+ 0.025 + 0.015 2

(11)

= 1.125 0.0007T

(12)

= 2.1275 0.0215T + 0.002T 2

(13)

(

μ Al2O3 = exp 3.003 0.04203T 0.5445 + 0.0002553T 2 0.0534 2 1.622 1

)

(14) Massimo Corcione [37] proposed an equation for the nanofluids effective dynamic viscosity, μeff normalized by the dynamic viscosity of the base liquid, μf is derived from a wide variety of experimental data available in the literature. These experimental data relative to nanofluids consisting of alumina, titanium, silica and copper nanoparticles with a diameter ranging between 25 nm and 200 nm which suspended in water, ethylene glycol, propylene glycol or ethanol. The best-fit of the selected data enumerated mean empirical correlation with standard deviation of error 1.84% and the equation is shown as Eq. (15).

μf

=

3. EXPERIMENTAL -Al2O3 nanoparticles in 20% wt. aqueous solution (Nanostructured and Amorphous Material, Inc., USA) were used for this investigation. The base fluid was distilled water. The suspensions of nanoparticles in water were subjected to ultrasonic vibration for about 1 h to ensure uniform nanoparticle dispersion was obtained. Then, appropriate amounts of distilled water were added to the suspensions and thoroughly mixed to achieve the desired concentration of nanofluids. It should be noted that the suspension stability of nanoparticles within the base fluid, distilled water, has been found to be very good even after a relatively long resting period, even few months. To investigate the effect of nanoparticle concentration, nanofluids of 1, 2, 3 and 4% by volume were prepared. Measurements were carried out at the room temperature (25°C). Rheological characteristics of nanofluids were measured using a modular rheometer (Anton Paar Physica MCR 501) with a Peltier system for temperature control. The experimental procedure is quite simple. At the beginning of an experiment, the piston is first removed from the measurement chamber; the latter is then half filled with the fluid. A reading of viscosity was taken only once the viscosity/temperature data are stabilized. In order to verify the rheometer accuracy as well as to assess the reliability of the experimental procedures, three different sets of viscosity measurement were carried out. Table 1 consists in nanofluid properties. Table 1.

Main Characteristics of the Tested Nanofluids Al2O3 - water

Abu-Nada et al. [36] performed a two-dimensional regression on experimental data of Nguyen et al.[35] and developed the following relation including temperature T and volume fraction as shown in Eq. (14).

μeff

3

1 dp 1 34.87 df

(15)

0.3

gamma

purity

99.9%

average particle diameter

10±5 nm

structure percentages of original solution

79% water + 20.3% Al2O 3 + 0.003 % Fe

surfactant

none

To measure the electrical conductivity of nanofluids, a precision conductivity cell (Multiparameter Consort C 831) with an application range of 1 μS/cm– 200 mS/cm has been used. The resolution is 0.01 μS/cm. The electrical conductivity of Al2O3-water nanofluid was measured at room temperature (25 °C) and subsequent measurements were conducted to examine the effects of volume fractions (1- 4%) on the effective electrical conductivity of the nanofluid. For each case, five to six measurements were performed, and the mean value was reported. Table 2 contains the mean experimental data. Table 2.

Experimental for Electrical Conductivity at 25 °C

1.03

where df is the equivalent diameter of a base fluid molecule, given by Eq. (16): 1

6M 3 d f = 0.1 N f 0

Structure

(16)

in which M is the molecular weight of the base fluid, N is the Avogadro number, and f0 is the mass density of the base fluid calculated at temperature T = 293 K.

volume concentration,

electrical conductivity,

[%]

k [μS/cm]

distilled water

5

1

638

2

1081

3

1474

4

1903


4. RESULTS AND DISCUSSIONS 4.1. Electrical Conductivity The electrical conductivity of alumina is reported as 108 μS/cm in the literature [38, 39]; conductivity of the base fluid (distilled water) used in the present study varies from 5 μS/cm to 3.5 μS/cm in the present experimental temperature range. Table 2 shows the measured electrical conductivity of water and of the nanofluid. It can be seen that the conductivity values obtained from the experiment agree well with the reference values available in literature [40-42], in an order of magnitude sense. Fig. (1) shows the effective electrical conductivity of alumina nanofluid at different volume fractions. It is seen that the electrical conductivity of alumina nanofluid increases almost linearly with increase in the volume fraction of the alumina nanoparticles. The highest value of electrical conductivity, 1903 μS/cm, was recorded for a volume fraction of 4% at a temperature of 25 °C. Fig. (1) also shows, also, the polynomial trendline obtained by statistical data-s interpretation [43], with the maximum confidence R2=1.

Fig. (1). Values for electrical conductivity along with the corresponding trendline.

It is of interest to examine the enhancement in electrical conductivity of the alumina nanofluid with respect to the base fluid. For this purpose, the rate of enhancement of the effective electrical conductivity, defined as the difference between the electrical conductivity of the nanoparticle suspension and the electrical conductivity of the base fluid, divided by the electrical conductivity of the base fluid, is plotted as a function of temperature, at volume fractions of 1, 2, 3 and 4%. As illustrated in Fig. (2), the rate of enhancement increases with respect to increase in the nanoparticle volume fraction, which indicates a dependence on volume fraction, the greater is the enhancement. A 379.6 % increase in the electrical conductivity was observed for 4% (=4) volume concentration of alumina nanoparticles in water at room temperature (T=25 °C). If it refers to Case (a) in the Maxwell's model (alumina particles have very poor electrical conductivity characteristics), it is expected that the mixture's electrical conductivity is reduced. However, from Fig. (1), it can be seen that the measured electrical conductivity of the suspension increases with volume fraction of the nanoparticles. Therefore, the theoretical model [24], which compared well with the measurements of dispersions with large size (micrometer or larger) particles, underpredicts the conductivity increase in nanoparticle- fluid mixtures. This is due to the fact that, apart from

Alina Adriana Minea

Fig. (2). Electrical conductivity enhancement of Al2O3-water nanofluid: variation with volume fraction at 25°C.

the physical properties of fluid and conductivity of particles and fluids, the effective electrical conductivity of colloidal nanosuspensions in a liquid exhibits a complex dependence on the EDL characteristics, volume fraction, ionic concentrations and other physicochemical properties, which is not effectively captured by the standard models. When alumina particles are suspended in a polar liquid (water in the present case), electric charges develop on their surfaces. Ions of charge opposite to that of the particle surface are attracted, causing the development of a charged diffuse layer surrounding the particle. With an increase in particle volume fraction, the availability of conducting pathways increases in the solution, which in turn increases the overall electrical conductivity of the solution. Since the experimental data demonstrated a polynomial relationship between the enhancement factor and nanoparticle volume fraction Fig. (2), a polynomial regression analysis was employed to develop an empirical relationship for the dimensionless enhancement factor at different volume fractions. The resulting expression is given in Eq. (17) with an R2 value of 1. (17) eff / bf = 2.8667 3 - 22.2 2 + 135.13 + 10.8 Here eff is the effective electrical conductivity of the nanofluid, bf is the electrical conductivity of the base fluid, is the volume fraction of the nanoparticle. It may be noted here that Eq. (17) indicates the relative importance of the impact of on eff of alumina nanofluid. The coefficient for the volume fraction is large, indicating a strong dependence of the effective electrical conductivity on volume fraction. 4.2. Rheology Fig. (3) and Fig. (4) contain the viscosity and shear stress of the nanofluids with four different nanoparticle concentrations as a function of the shear rate at 25 °C, respectively. Similar trends were observed for all nanofluids at all temperatures. These results clearly show that the four nanofluids used in this investigation possess shear-thinning behavior. In order to characterize the rheological properties of the base fluid and nanofluids, the shear stress was plotted against the shear rate. The power law model predicts that the apparent viscosity decreases with increasing shear rate. = Kn1 (18) In Eq. (18), is the apparent viscosity, is the shear rate and parameters K and n of the power law model are the consistency index and the power law index, respectively.



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Fig. (3). The viscosity of the studied nanofluids.

Fig. (4). Shear stress variation of the nanofluids.

Eq. (19) – (22) are the power law fitted equations referring to Fig. (3), along with their accuracy (R2), respectively. (19) = 4 %; k = 0.2562 -0.324; R = 0.9623 (20) = 3 %; k = 0.0458 -0.359; R = 0.8395 = 2 %; k = 0.0118 -0.386; R = 0.8579 (21) (22) = 1 %; k = 0.006 -0.401; R = 0.9054 Power law indices (n) of nanofluids as a function of the particle concentration for different temperatures are shown in Fig. (5). The

power law index of Al2O3 nanofluid generally linearly increases with increasing particle concentration. For example at 25 °C, the power law indices of 1 vol.% Al2O3 nanofluid decrease approximately 11.4 % relative to the 4% dilution. In general, the power law index of nanofluids is a weak function of nanoparticle concentration. Fig. (6) presents the consistency index (K) of nanofluids as a function of the particle concentration at room temperature. Results show that the consistency index of nanofluids is influenced by the volume concentration and is exponential rising with concentration increasing.


Fig. (5). Power law index of nanofluids vs. nanoparticle concentration.

Fig. (6). Consistency index of nanofluids vs. nanoparticle volume percent.

Fig. (7). Relative apparent viscosity of nanofluids vs. shear rate.

Alina Adriana Minea

Furthermore, if it considers the water viscosity as 0.001 Pa s, it can obtain the variation of relative apparent viscosity of the studied nanofluids. Fig. (7) presents the relative apparent viscosity of nanofluids as a function of the shear rate for different nanoparticle concentration at 25 °C. Predicted values using the Einstein equation (eq. 2) is also included for comparison. The relative apparent viscosity of Al2O3 nanofluids increases with increasing nanoparticle concentration. It is observed that at high nanoparticle concentrations, predicted values of the Einstein equation are not in agreement with experimental data. However, at higher nanoparticle concentrations, the difference between experimental and predicted values increases. Results of some previous investigations showed the shear thinning behavior for nanofluids in the case of Newtonian base fluids. These investigators argued that this shear-thinning behavior is due to the nanoparticle agglomeration clusters which break down when the shear rate is increased and, as a result, the apparent viscosity decreases. Based on the results of the present investigation, the apparent viscosity of the base fluid and the nanofluid decreases when the shear rate increases. In this investigation, this behavior can be related to the shear-thinning characteristics of the base fluid. 5. CONCLUSION This paper presents the electrical conductivity and the dynamic viscosity measurements carried out with Al2O3–water (1–4% particle volume fraction) nanofluids at atmospheric pressure and room temperature. Aluminum oxide nanoparticles were dispersed in distilled water to form stable nanofluids. Systematic experiments were carried out to investigate the effects of nanoparticle volume fraction on the effective electrical conductivity and viscosity of Al2O3-water nanofluid. The experimental results show that the electrical conductivity of alumina nanofluid is significantly greater than the base fluid. The increase in electrical conductivity is a function of volume fraction of nanoparticles. At room temperature (25 °C), an increase of 379.6 % in effective electrical conductivity of nanofluid is observed for a volume fraction of 4. The electrical conductivity of the nanofluid increases polynomial with increase in the volume fraction. A polynomial regression analysis based on volume fraction has been applied to develop an empirical relationship for the dimensionless enhancement factor (effbf)/bf at different volume fractions. The



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Fig. (8). Viscosity at 25°C and 2.07 1/s shear rate vs. volume fraction.

present analysis indicates the relative influence of this parameter on the electrical conductivity enhancement. Al2O3-water nanofluid seems to be promising as electrical medium. The nanofluids tested exhibit a non-Newtonian behaviour for all the particle volume fractions considered at the room temperature. The relative viscosity of the nanofluid shows a great sensitivity to particle volume fraction. Results have shown that the viscosity of the base fluid and all nanofluids follow very well the power law model with power law indices of less than unity (n