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AN INVESTIGATION ON THERMAL CONDUCTIVITY AND VISCOSITY OF WATER BASED NANOFLUIDS I. TAVMAN AND A. TURGUT Mechanical Engineering Department, Dokuz Eylul University, 35100 Bornova, Izmir, Turkey, [email protected]

Abstract. In this study we report a literature review on the research and development work concerning thermal conductivity of nanofluids as well as their viscosity. Different techniques used for the measurement of thermal conductivity of nanofluids are explained, especially the 3ω method which was used in our measurements. The models used to predict the thermal conductivity of nanofluids are presented. Our experimental results on the effective thermal conductivity by using 3ω method and effective viscosity by vibro-viscometer for SiO2–water, TiO2–water and Al2O3–water nanofluids at different particle concentrations and temperatures are presented. Measured results showed that the effective thermal conductivity of nanofluids increase as the concentration of the particles increase but not anomalously as indicated in the some publications and this enhancement is very close to Hamilton– Crosser model, also this increase is independent of the temperature. The effective viscosities of these nanofluids increased by the increasing particle concentration and decrease by the increase in temperature, and cannot be predicted by Einstein model.

1. Introduction Nanofluids are solid nanoparticles or nanofibers in suspension in a base fluid. To be qualified as nanofluid it is generally agreed that at least one size of the solid particle be less than 100 nm. Various industries such as transportation, electronics, food, medical industries require efficient heat transfer fluids to either evacuate or transfer heat by means of a flowing fluid. Especially with the miniaturization in electronic equipments, the need for heat evacuation has become more important in order to ensure proper working conditions for these elements. Thus, new strategies, such as the use of new, more conductive fluids are needed. Most of the fluids used for this purpose are generally poor heat conductors compared to solids (Fig. 1).

S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_8, © Springer Science + Business Media B.V. 2010

139

I. TAVMAN AND A. TURGUT

140

It is well known that fluids may become more conductive by the addition of conductive solid particles. However such mixtures have a lot of practical limitations, primarily arising from the sedimentation of particles and the associated blockage issues. These limitations can be overcome by using suspensions of nanometer-sized particles (nanoparticles) in liquids, known as nanofluids. After the pioneering work by Choi of the Argonne National Laboratory, USA in 1995 [1] and his publication [2] reporting an anomalous increase in thermal conductivity of the base fluid with the addition of low volume fractions of conducting nanoparticles, there has been a great interest for nanofluids research both experimentally and theoretically. More than 970 nanofluid-related research publications have appeared in literature since then and the number per year appears to be increasing as it can seen from Fig. 2. In 2008 alone, 282 research papers were published in Science Citation Index journals. However, the transition to industrial practice requires that nanofluid technology become further developed, and that some key barriers, like the stability and sedimentation problems be overcome. 1000

Heat transfer fluids

Metal Oxide

Metal Cu

Thermal Conductivity (W/mK)

Al

100

Al2O3 CuO TiO2

10

1

Water Ethylene Glycol Oil

0.1

Figure 1. Thermal conductivity of typical materials (solids and liquids) at 300 K.

A review of the literature showed that the nanoparticles used in the production of nanofluids were: aluminum oxide (Al2O3), titanium dioxide (TiO2), nitride ceramics (AlN, SiN), carbide ceramics (SiC, TiC), copper (Cu), copper oxide (CuO), gold (Au), silver (Ag), silica (SiO2) nanoparticles and carbon nanotubes (CNT). The base fluids used were water, oil, acetone, decene and ethylene glycol. Modern technology allows the fabrication of materials at the nanometer scale, they are usually available in the market under different particle sizes and purity conditions. They exhibit

THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 141

unique physical and chemical properties compared to those of larger (micron scale and larger) particles of the same material. Nanoparticles can be produced from several processes such as gas condensation, mechanical attrition or chemical precipitation techniques [3]. Papers in the title containing either “nanofluid” or “nanofluids” searched by the ISI web of science-with conference proceedings on October 2009

Number of paper published per year

300

282

250

230

200

170

150

121 91

100

40

50

21 4

1 0

99

6

3 00

01

02

03

04 year

05

06

07

08

09

Figure 2. Publications on nanofluids since 1999.

Nanofluids are generally produced by two different techniques: a onestep technique and a two-step technique. The one-step technique makes and disperses the nanoparticles directly into a base fluid simultaneously. The two-step technique starts with nanoparticles which can usually be purchased and proceeds to disperse them into a base fluid. Most of the nanofluids containing oxide nanoparticles and carbon nanotubes reported in the open literature are produced by the two-step process. The major advantage of the two-step technique is the possibility to use commercially available nanoparticles, this method provides an economical way to produce nanofluids. But, the major drawback is the tendency of the particles to agglomerate due to attractive van der Waals forces between nanoparticles; then, the agglomerations of particles tend to quickly settle out of liquids. This problem is overcome by using ultrasonic vibration, to break down the agglomerations and homogenize the mixture. Figure 3 shows Al2O3–water nanofluids, (a) shows homogenization with ultrasonic vibration, (b) shows the same nanofluids without any homogenization process, we can easily see the settled nanoparticles.

142


Figure 3. Al2O3–water nanofluids (a) treated with ultrasonic vibration, (b) untreated – settlement of nanoparticles.

The first publications on thermal conductivity of nanofluids were with base fluids water or ethylene-glycol (EG) and with nanoparticles such as aluminum-oxide (Al2O3) [4–7], copper-oxide (CuO) [4, 5, 7], titaniumdioxide (TiO2) [8], copper (Cu) [9, 10]. They all measured great enhancement in thermal conductivity for low particles addition, typical enhancement was in the 15–40% range over the base fluid for 0.5–4% nanoparticles volume concentrations in various liquids. The increase was from 5% to 60% for nanoparticles additions ranging from 0.1% to 5% by volume. These unusual results have attracted great interest both experimentally and theoretically from many research groups because of their potential benefits and applications for cooling in many industrials from electronics to transportation. Recent papers provide detailed reviews on al aspects of nanofluids, including preparation, measurement and modeling of thermal conductivity and viscosity [11–13, 24]. Very few studies [7, 14–19] have been performed to investigate the temperature effect on the effective thermal conductivity of nanofluids. In a recent study by Turgut et al. [16] on relative thermal conductivity of TiO2–water nanofluids, no temperature effect has been found like in the study by Masuda et al. [18] and Zhang et al. [19]. However, Wang et al. [17] measured an increase in relative thermal conductivity for the same nanofluid. Hence, to confirm the effects of temperature on the effective thermal conductivity of nanofluids, more experimental studies are essential. The experimental data reported in the literature is very scattered, for the same base fluid and the same particles there are many different results. Some researchers [16–19] measured only a moderate increase of effective thermal conductivity with the addition of nanoparticles. Their experimental results can be explained by classical Maxwell [20], Hamilton and Crosser [21] models for mixtures. A recent publication by Keblinski et al. [22] reveals this controversy about the scatter of experimental data and compares the experimental data from different


authors for various water based nanofluids. He shows that this results fall within the upper and lower limits of classical two phase mixture theories. There are many publications on predictive models for effective thermal conductivity of nanofluids [5, 11, 23, 25–27], some of these publications make an overview of the existing models, and some drives their own model and compares with experimental data. None of the models is able to explain and predict an effective thermal conductivity value for the nanofluids. Although some review articles [28–30] emphasized the importance of investigating the viscosity of nanofluids, very few studies on effective viscosity were reported. Viscosity is as critical as thermal conductivity in engineering systems that employ fluid flow. Pumping power is proportional to the pressure drop, which in turn is related to fluid viscosity. More viscous fluids require more pumping power. In laminar flow, the pressure drop is directly proportional to the viscosity. Masuda et al. [18] measured the viscosity of TiO2–water nanofluids suspensions, they found that for 27 nm TiO2 particles at a volumetric concentration of 4.3% the viscosity increased by 60% with respect to pure water. In his work on the effective viscosity of Al2O3–water nanofluids, Wang et al. [5] measured an increase of about 86% for 5 vol% of 28 nm nanoparticles content. In their case, a mechanical blending technique was used for dispersion of Al2O3 nanoparticles in distilled water. They also measured an increase of about 40% in viscosity of ethylene glycol at a volumetric loading of 3.5% of Al2O3 nanoparticles. Das et al. [31] and Putra et al. [32] measured the viscosity of water-based nanofluids, for Al2O3 and CuO particles inclusions, as a function of shear rate they both showed Newtonian behavior for a range of volume percentage between 1% and 4%. Das et al. [50] also observed an increase in viscosity with an increase of particle volume fraction, for Al2O3/water-based nanofluids. In all cases the viscosity results were significantly larger than the predictions from the classical theory of suspension rheology such as Einstein’s model [33]. 2. Models for the Effective Thermal Conductivity of Nanofluids Many theoretical and empirical models have been proposed to predict the effective thermal conductivity of two phase mixtures. Comprehensive review articles have discussed the applicability of many of these models that appear to be more promising [34–36]. First, using potential theory, Maxwell [20] obtained a simple relationship for the conductivity of randomly distributed and non-interacting homogeneous spheres in a homogeneous medium. Maxwell model is good for low solid concentrations. Relative thermal conductivity enhancement (ratio of the effective thermal conductivity keff of nanofluid to base fluid kf) is,

144


k eff / k f =

k p + 2k f + 2φ (k p − k f )

(1)

k p + 2k f − φ ( k p − k f )

where φ is the particle volume fraction of the suspension, kp is the thermal conductivity of the particle. According to Maxwell model the effective thermal conductivity of suspensions depending on the thermal conductivity of spherical particles, base liquid and the volume fraction of solid particles. Bruggeman [37] proposed a model to analyze the interactions among randomly distributed particles by using the mean field approach.

keff =

k 1 (3φ − 1)kp + (2 − 3φ )kf + f 4 4

[

]

Δ

(2)

where, (3) When Maxwell model fails to provide a good match with experimental results for higher concentration of inclusions, Bruggeman model can sufficiently be used. Hamilton and Crosser [21] modified Maxwell’s model to determine the effective thermal conductivity of non-spherical particles by applying a shape factor n. The formula yields, (4) where n = 3/ψ and ψ is the sphericity, defined by the ratio of the surface area of a sphere, having a volume equal to that of the particle, to the surface area of the particle. Yu and Choi [38] derived a model for the effective thermal conductivity of nanofluid by assuming that there is no agglomeration by nanoparticles in nanofluids. They assumed that the nanolayer surrounding each particle could combine with the particle to form an equivalent particle and obtained the equivalent thermal conductivity kpe of equivalent particles as fallows,

k pe =

[2(1 − γ ) + (1 + β ) (1 + 2γ )γ ] k 3

− (1 − γ ) + (1 + β )3 (1 + 2γ )

p

(5)


where γ = klayer/kp, is the ratio of the nanolayer thermal conductivity to particle conductivity, and β = h/r is the ratio of nanolayer thickness to the original particle radius.

k eff / k f =

k pe + 2 k f + 2φ ( k pe − k f )(1 − β ) 3 k pe + 2 k f − φ ( k pe − k f )(1 + β )

3

(6)

Jang and Choi [39] devised a theoretical model that includes four modes of energy transport; the collision between basefluid molecules, the thermal diffusion of nanoparticles in the fluid, the collision between nanoparticles due to Brownian motion, and the thermal interactions of dynamic nanoparticles with base fluid molecules.

k eff / k f = (1 − φ ) +

kp kf

φ + 3C

df dp

φ Re 2d P Pr

(7)

where Redp is the Reynolds number defined by Redp=(CRMdp)/ν, C is a proportional constant, CRM is the random motion velocity of nanoparticles, ν is the dynamic viscosity of the base fluid, Pr is the Prandtl number, df and dp are the diameter of the base fluid molecule and particle. For typical nanofluids, the order of the Reynolds number and the Prandtl numbers are 1 and 10, respectively. Xie et al. [40] derived an expression for calculating enhanced thermal conductivity of nanofluid by considering The effects of nanolayer thickness, nanoparticle size, volume fraction, and thermal conductivity ratio of particle to fluid. The expression is: (8) with Θ=

β lf ⎡⎢(1 + γ )3 − β pl / β fl ⎤⎥ ⎣

(1+ γ )3 + 2β lf β pl

⎦

(9)

where

k −k β lf = l f

k l + 2k f

β pl =

k p − kl k p + 2k l

k −k β fl = f l

k f + 2k l


146

and γ = δ/rp is the thickness ratio of nano-layer and nanoparticle. φT is the modified total volume fraction of the original nanoparticle and nano-layer, φT =φ (1+ γ)3. Besides these models there are many others models, but no single model explains the effective thermal conductivity in all cases. Besides the thermal conductivities of the base fluid and nanoparticles and the volume fraction of the particles, there are many other factors influencing the effective thermal conductivity of the nanofluids. Some of these factors are: the size and shape of nanoparticles, the agglomeration of particle, the mode of preparation of nanofluids, the degree of purity of the particles, surface resistance between the particles and the fluid. Some of these factors may not be predicted adequately and may be changing with time. This situation emphasizes the importance of having experimental results for each special nanofluid produced. 3. Experimental 3.1. MATERIALS

Properties of nanoparticles and base fluid used in this study are shown in Table 1. De-ionized water was used as a base fluid. In the nanofluid, nanoparticles tend to cluster and form agglomerates which reduce the effective thermal conductivity. It is known that ultrasonication break the nanoclusters into smaller clusters. Hong et al. [41] investigated the role of sonication time on thermal conductivity of iron (Fe) nanofluids. The thermal conductivity of each nanofluid showed saturation after a gradual increase as the sonication time was increased. The thermal conductivity of 0.2 vol% Fe nanofluid exhibited 18% enhancement with a 30 min sonication and was saturated after 30 min. So, in order to obtain good quality nanofluids, it is essential that the solid–liquid mixture be exposed to ultrasonication. TABLE 1. Properties of nanoparticles and base fluid used in nanofluids preparation.

3

Density (kg/m ) Thermal conductivity (W/mK) Average particle diameter (nm)

SiO 2

TiO 2

Al2O 3

water

2,220

3,800

3,700

1,000

1.38

10

46

0.613

12

21

30

–

A two-step method was used to produce water based nanofluids with, 0.45, 1.85 vol% concentrations of SiO2 nanoparticles; 0.2, 1.0 and 2.0 vol% concentrations of TiO2 nanoparticles and 0.5 and 1.5 vol% concentrations


of Al2O3 nanoparticles. In the first stage of preparation of nanofluids, the proper amount of dry nanoparticles necessary to obtain the desired volume percentage was mechanically mixed in de-ionized water. The next step was to homogenize the mixture using ultrasonic vibration, to break down the agglomerations. In order to decide on a sonication time to be used in the preparation of nanofluids, we applied different sonication times for 1% by volume TiO2–water nanofluids and measured their thermal conductivity (Fig. 4). It may be seen that sonication time has practically no effect on thermal conductivity after 30 min, so we decided to use 30 min of sonication time. No surfactant was used in these experiments. Another possibility for preventing clustering of nanoparticles was to eventually use a surfactant. For this purpose sodium dodecylbenzenesulfonate (SDBS) was used as surfactant, it was mixed to pure de-ionized water at different ratio of SDBS/Al2O3, it was observed that the thermal conductivity of SDBS – water mixture decreased with the increasing SDBS ratios which means that the effect of this surfactant was to decrease the thermal conductivity of the base fluid (see Fig. 5). We further used this surfactant in 1% by volume Al2O3–water nanofluids at different ratio of SDBS/Al2O3, as it can be seen from Fig. 5, its effect on thermal conductivity was still negative. In other words, thermal conductivity of Al2O3–water nanofluids was better than with the same nanofluid with surfactant. So, we decided not to use a surfactant in the preparation of nanofluids. 1.035

Relative Thermal Conductivity

1.03 1.025 1.02 1.015 1.01 TiO2 -water 1% volume

1.005 1 0

5

10

15

20 25 30 35 40 45 Sonication Time (minute)

50

55

60

Figure 4. Relative thermal conductivity of (1% vol.) TiO2–water nanofluid as a function of the sonication time.



148

1.05

(Al2O3+water)/(water)

1.04

(Al2O3-SDBS+water)/(water)

1.03

(SDBS+water)/(water)

1.02 1.01 1 0.99 0.98 0.97 0.96 0.95

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

(SDBS/Al2O3), mass ratio

Figure 5. Effect of SDBS surfactant on relative thermal conductivity of 1% by volume Al2O3–water nanofluids at different mass ratio of SDBS/Al2O3.

3.2. METHODS FOR MEASURING THERMAL CONDUCTIVITY OF NANOFLUIDS

Experimental studies on the thermophysical properties of liquids are especially very difficult. The main problem lies in the elimination of convectional heat transfer in the liquid and monitoring of the temperature fields and gradients during the measurement. Stationary as well as transient methods for measuring thermal conductivity or diffusivity of liquids are associated with a temperature gradient which in some cases may induce natural convection in the liquid. If there is a natural convection, the thermal conductivity of the liquid is then measured higher than the real thermal conductivity value. For this reason the temperature gradient must be kept as low as possible and the measurement time must be as short as possible. Although many methods are reported in the literature for the determination of thermal conductivity [42, 43] reliable data for these classes of materials are still lacking. With the growing interest for different commercial composite materials used in the casting industry and demands for more efficient coolants with greater heat transfer capabilities in the auto industry, more accurate measurement techniques are needed. The different techniques for measuring the thermal conductivity of liquids can be classified into two main categories: steady-state and transient methods. Both of these methods have some merits and disadvantages. The equipment for steady state method is simple and the governing equations for heat transfer are well known and simple. The main disadvantage is the very long experimental times required for the measurement and the necessity to keep


all the conditions stable during this time. For nanofluids, the steady state methods are not very adequate, during the long measurement time particles may settle down or migrate; it is extremely difficult to keep everything stable during the experimental run. That is the reason why there are very few studies on thermal conductivity of nanofluids with steady state methods. Wang et al. [5] measured the effective thermal conductivity of metal oxide nanoparticle suspensions using a steady-state method. Somewhat later, Das and co-workers [7, 44] measured the effective thermal conductivity of metal and metal oxide nanoparticle suspensions using a temperature oscillation method. The transient hot wire (THW) method has been well developed and widely used for measurements of the thermal conductivities and, in some cases, the thermal diffusivities of fluids with a high degree of accuracy [6, 42]. More than 80% of the thermal conductivity measurements on nanofluids were performed by transient hot wire method [6, 8, 18, 19, 45–47]. Another method for measuring thermal diffusivity is the flash method developed by Parker et al. [48] and successfully used for the thermal diffusivity measurement of solid materials [49]. A high intensity short duration heat pulse is absorbed in the front surface of a thermally insulated sample of a few millimeters thick. The sample is coated with absorbing black paint if the sample is transparent to the heat pulse. The resulting temperature of the rear surface is measured by a thermocouple or infrared detector, as a function of time and is recorded either by an oscilloscope or a computer having a data acquisition system. The thermal diffusivity is calculated from this time–temperature curve and the thickness of the sample. This method is commercialized now, and there are ready made apparatus with sample holders for fluids. There is only one publication on nanofluids with this method, Shaikh et al. [50] measured thermal conductivity of carbon nanoparticle doped PAO oil. Finally, recent works on thermal conductivity measurements using the 3ω method have reported [16, 17]. This method is very accurate and fast will be explained fully in the next section. We used this method which has also the advantage of requiring small amounts of liquids for the measurement. 3.2.1. 3ω Method for Measuring Thermal Conductivity of Fluids This technique based on a hot wire thermal probe with AC excitation and 3ω lock-in detection. Since the principle and procedures of the technique have been described in details previously [51] only a brief description is given here. We consider a thermal probe (ThP) consisting of a metallic wire of length 2l and radius r immersed in a liquid sample, acting simultaneously as a heater and as a thermometer. The sample and probe thermophysical properties are the volume specific heat ρc and the thermal conductivity k, with the respective subscripts (s) and (p). The wire is excited by ac current


150

at frequency f/2 and we assume that it is thermally thin in the radial direction so that the temperature θ ( f ) is uniform over its cross section. Since the electrical resistance of the wire is modulated by the temperature increase, the voltage across the wire contains a third harmonic V3ω proportional to θ ( f ). It is convenient to use a normalized (reduced) 3ω signal, F( f ) [52]. For r/μs 1, the temperature increase θ ( f ) generated by a modulated line heat source P in an infinite and homogeneous medium can be approximated by [53, 54]:

F( f ) ∝θ ( f ) = −

P/l 2π k s

σ r⎞ P/l ⎛ ⎜ γ + ln s ⎟ = − 2 ⎠ 2π k s ⎝

⎛ 1.26 r π ⎞ ⎜⎜ ln + i ⎟⎟ μs 4⎠ ⎝

(10)

where γ = 0.5772 is the Euler constant. The complex quantity σs is given by σs = (1 + i)/μs = (i2πf/αs)1/2 with μs the thermal diffusion length at frequency f and αs = ks/ρscs the thermal diffusivity. In this work we are concerned with the measurement of thermal properties of water-based nanofluids, relative to pure water (subscript w). From Eq. (10) one has:

k s Im(Fw ) = k w Im(Fs )

cot ϕ s − cot ϕ w =

and

sin(ϕ w − ϕ s ) 2 α = − ln s π αw sin ϕ s sin ϕ w

(11)

For small diffusivity difference the phase yields:

αs π (ϕ s − ϕ w ) = 1+ αw 2 sin 2 ϕ w

(12)

In principle, Eq. (11) give frequency-independent results of, but in practice there is an optimum frequency range such that r/μs < 1 in which ks and αs have stable and low noise values as a function of frequency. The first harmonic in the voltage signal is dominant and must be cancelled by a Wheatstone bridge arrangement. The selection of the third harmonic from the differential signal across the bridge is performed by a Stanford SR850 lock-in amplifier tuned to this frequency (Fig. 6 [55]). The thermal probe (ThP) is made of 40 μm in diameter and 2l = 19.0 mm long


Ni wire (Fig. 7). The temperature amplitude θ in water was 1.25 K. The minimum sample volume for Eq. (10) to apply is that of a liquid cylinder centered on the wire and having a radius equal to about 3μs. At 2f = 1 Hz, this amounts to 25 μl. The method was validated with pure fluids (water, methanol, ethanol and ethylene glycol), yielding accurate k-ratios within ±2% (Eq. 11) and absolute α value for water within ±1.5% (Eq. 12).

Figure 6. Schematic diagram of 3ω experimental set-up.

Figure 7. Experimental set-up for 3ω method consisting of thermal probe (ThP), Wheatstone bridge and lock-in amplifier.

152


3.3. VIBRATION VISCOMETER FOR MEASURING VISCOSITY OF NANOFLUIDS

The experimental setup for measuring the effective viscosity of nanofluids, consists of a Sine-wave Vibro Viscometer SV-10 and Haake temperaturecontrolled bath with 0.1°C. The SV-10 viscometer (A&D, Japan), has two thin sensor plates that are driven with electromagnetic force at the same frequency by vibrating at constant sine-wave vibration in reverse phase like a tuning-fork. The electromagnetic drive controls the vibration of the sensor plates to maintain constant amplitude. The driving electric current, which is an exciting force, will be detected as the magnitude of viscidity produced between the sensor plates and the sample fluid (Fig. 8 [56]). The coefficient of viscosity is obtained by the correlation between the driving electric current and the magnitude of viscidity. Since the viscosity is very much dependent upon the temperature of the fluid, it is very important to measure the temperature of the fluid correctly. By this viscometer we can detect accurate temperature immediately because the fluid and the detection unit (sensor plates) with small surface area/thermal capacity reach the thermal equilibrium in only a few seconds (Fig. 9). Its measurement range of viscosity is 0.3–10,000 mPas.

Figure 8. Schematic diagram of the vibro viscometer [56].


Figure 9. Vibrator (sensor plates) and sample cup.

4. Results and Discussion 4.1. THERMAL CONDUCTIVITY OF NANOFLUIDS


In Fig. 3 our experimental results for SiO2, Al2O3 and TiO2 samples at room temperature were compared with classical effective thermal conductivity model, known as Hamilton–Crosser model (Fig. 10) [21]. 1.08

water based nanofluids

1.07

TiO2 experimental

1.06

Al2O3 experimental SiO2 experimental

1.05

H-C model TiO2

1.04

H-C model Al2O3

1.03

H-C model SiO2

1.02 1.01 1 0

0.5

1

1.5

2

Particle Volume Fraction (%)

Figure 10. Relative thermal conductivity versus particle volume fraction of TiO2, Al2O3 and SiO2 nanofluids.

154


Our experimental results for water based SiO2, Al2O3 and TiO2 nanofluids are lower than the H-C model. Moreover, comparison of the TiO2 nanofluids with the Al2O3 nanofluids showed that the highly thermal conductive material is not always the excellent application for enhancing the thermal transport property of nanofluids. Thermal conductivity of TiO2–water nanofluid has higher enhancement than the Al2O3–water nanofluid, even TiO2 bulk thermal conductivity value is lower than the Al2O3. Similar result was presented by Hong et al. [41] for Fe nanofluids compared with the Cu nanofluids. 4.2. VISCOSITY OF NANOFLUIDS

There are some theoretical formulas in the literature which predict the viscosity of particle suspension in a fluid. Most of the existing formulas were derived from the Einstein’s pioneering work [33]. His formula was based on the assumption of a linearly viscous fluid that contains dilute suspended spherical particles. Then by calculating the energy dissipated by the fluid flow around a single particle and by associating that energy with the work done for moving this particle relatively to the surrounding fluid, he obtained:

μ eff = μ l (1 + 2.5φ )

(13)

where φ is the volume fraction of particles, μl and μeff are the viscosity of the base fluid and effective viscosity of the mixture. This formula is valid for non-interacting particle suspension in a base fluid that is for the volume concentrations is less than 5%. Krieger and Dougherty [57] formulated a semi-empirical equation for relative viscosity expressed as

μ eff

⎛ φ = μ l ⎜⎜ ⎜φ ⎝ m

⎞ ⎟ ⎟ ⎟ ⎠

− [η ]φ m

(14)

where φm is the maximum packing fraction and [η] is the intrinsic viscosity ([η] = 2.5 for hard spheres). For randomly mono-dispersed spheres, the maximum close packing fraction is approximately 0.64. Another model was proposed by Nielsen [58] for low concentration of particles. Nielsen’s equation is as follows:

φ / (1 − φm ) μ eff = μ l (1 + 1.5φ )e

(15)


where φ and φm are the volume fraction of particles and the maximum packing fraction, respectively. The measurements of effective viscosity of SiO2–water, TiO2–water and Al2O3–water nanofluids at different particle volume concentrations were performed using Vibro Viscometer SV-10. To be use of the accuracy of the measurement the viscosity of water was measured before and after each experiment. The results of the measurements performed at room temperature are shown in Figs. 11–14. For SiO2–water nanofluids of 12 nm particle size, the experimental results are compared with the above cited 3 models in Fig. 11. It may be seen that measured viscosity values are well above the prediction of the models, the difference becoming larger as the volume concentration is increasing. In Fig. 12, these same results are compared with the existing literature values for the same nanofluids by Wang et al. [59] for 7 and 40 nm particle sizes and Kang et al. [60]. Our experimental results are of the same as those by Wang et al. [59] for the particle size of 7 nm, but larger than the other results. 5 SiO2-water

4.5 This study

Relative Viscosity

4

Einstein model [33]) K-D model [57]

3.5

Nielsen model [58]

3 2.5 2 1.5 1 0

1

2 3 Particle Volume Fraction (%)

4

Figure 11. Relative viscosity of SiO2–water nanofluids as a function of nanoparticle volume fraction compared with the models.


156

5

SiO2 - water

4.5

This study 12nm Wang et al. (7nm),[59]

Relative Viscosity

4

Wang et al. (40nm),[59] 3.5

Kang et al. (15 nm),[60]

3 2.5 2 1.5 1 0

1

2 3 Particle Volume Fraction (%)

4

Figure 12. Experimental results of relative viscosity of SiO2 nanofluids, compared to selected literature data.

In Fig. 13, we compared our experimental results on TiO2–water with the results of Masuda et al. [18], He et al. [46] and Murshed et al. [61] and also to Einstein model. All results are well above the prediction of the Einstein model. 1.7

TiO2-water

1.6 Turgut et al., [16] Masuda et al., [18] He et al., [46] Murshed et al., [61] Einstein model [33]

Relative Viscosity

1.5 1.4 1.3 1.2 1.1 1 0

0.5

1

1.5

2

Particle Volume Fraction (%)

Figure 13. Relative viscosity of TiO2–water nanofluids as a function of nanoparticle volume fraction.

THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 157 2

water based nanofluids

water 0.2% TiO2 1% TiO2 2% TiO2 0.45% SiO2 1.85% SiO2 0.50% Al2O3 1.50% Al2O3

.

1.6

Viscosity, mPa.s

1.8

1.4 1.2 1 0.8 0.6 0.4 20

25

30

35

40

45

50

Temperature, 8C

Figure 14. Comparison of effective viscosity of water based nanofluids with as a function of temperature.

Figure 14 shows the effective viscosity of all three nanofluids with different volume concentrations of particles, measured at temperatures between 20°C and 50°C. The viscosity of nanofluids increased dramatically with an increase in particle concentration and decreased with temperature, following the trend of the viscosity for pure water, for low particle concentrations. 5. Conclusions The thermal conductivities of SiO2–water, TiO2–water and Al2O3–water nanofluids were measured using a 3ω method for different particle concentrations and temperatures. The experimental results showed that the thermal conductivity enhancements were relatively in good agreement with the Hamilton–Crosser model, and they were moderated increases, not as high and sometimes qualified as anomalous increases as claimed by some researchers [4, 5, 7–10]. In fact the review of experimental studies clearly showed a lack of consistency in the reported results of various research groups. The effects of several important factors such as particle size and shapes, clustering of particles, temperature of the fluid, and dissociation of surfactant on the effective thermal conductivity of nanofluids were not investigated adequately. It is very important that more investigations should be performed, in order to confirm the effects of these factors on the thermal conductivity for wide range of nanofluids. From our results, we also noticed that, although thermal conductivity of TiO2 was much higher than Al2O3,

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the thermal conductivities of Al2O3–water nanofluids were significantly higher then TiO2–water nanofluids, which means that the thermal conductivity of the nanoparticles was not the only factor that determines the thermal conductivity of the nanofluids. We also found that the relative thermal conductivity of the nanofluid was not dependant on temperature. The effective viscosities of SiO2–water, TiO2–water and Al2O3–water nanofluids were measured. The results show that for low volume additions of nanoparticles the measured effective viscosity values follow quite well the viscosity values of pure water with a decrease in viscosity with increasing temperature and may be predicted by the Einstein law of viscosity. But, for higher additions of nanoparticles, the Einstein law of viscosity and other viscosity models failed to explain the large increase in viscosity values. Because of the large increase in effective viscosity, large pumping powers are required to circulate the nanofluid used in cooling systems. In order to have a good idea on the applicability of these nanofluids in real engineering systems, effective viscosity must be measured together with the thermal conductivity of the nanofluids. Acknowledgments This work has been supported by TUBITAK (Project no: 107M160), Research Foundation of Dokuz Eylul University (project no: 2009.KB.FEN.018) and Agence Universitaire de la Francophonie (Project no: AUF-PCSI 6316 PS821).

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