Study of viscosity and specific heat capacity characteristics of water-based Al 2 O 3 nanofluids at low particle concentrations

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1 Journal of Experimental Nanoscience ISSN: (Print) (Online) Journal homepage: Study of viscosity and specific heat capacity characteristics of water-based Al 2 O 3 nanofluids at low particle concentrations Y. Raja Sekhar & K.V. Sharma To cite this article: Y. Raja Sekhar & K.V. Sharma (2015) Study of viscosity and specific heat capacity characteristics of water-based Al 2 O 3 nanofluids at low particle concentrations, Journal of Experimental Nanoscience, 10:2, , DOI: / To link to this article: Published online: 09 Jun Submit your article to this journal Article views: 1143 View related articles View Crossmark data Citing articles: 18 View citing articles Full Terms & Conditions of access and use can be found at Download by: [ ] Date: 04 January 2018, At: 07:16

2 Journal of Experimental Nanoscience, 2015 Vol. 10, No. 2, , Study of viscosity and specific heat capacity characteristics of water-based Al 2 O 3 nanofluids at low particle concentrations Y. Raja Sekhar a,b * and K.V. Sharma b,c a School of Mechanical and Building Sciences, VIT University, Vellore , Tamil Nadu, India; b Centre for Energy Studies, Department of Mechanical Engineering, JNTU College of Engineering, Kukatpally, Hyderabad , Andhra Pradesh, India; c Department of Mechanical Engineering, JNTUH College of Engineering Manthani, Centenary Colony, Pannur, Kamanpur, Karimnagar , Andhra Pradesh, India (Received 12 June 2012; final version received 11 April 2013) In this paper, the specific heat capacity and viscosity properties of water-based nanofluids containing alumina nanoparticles of 47 nm average particle diameter at low concentrations are studied. Nanofluids were prepared with deionised water as base fluid at room temperature by adding nanoparticles at low volume concentration in the range of 0.01% 1% to measure viscosity. The effect of temperature on viscosity of the nanofluid was determined based on the experiments conducted in the temperature range of 25 Cto45 C. The results indicate a nonlinear increase of viscosity with particle concentration due to aggregation of particles. The estimated specific heat capacity of the nanofluid decreased with increase of particle concentration due to increase in thermal diffusivity. Generalised regression equations for estimating the viscosity and specific heat capacity of nanofluids for a particular range of particle concentration, particle diameter and temperature are established. Keywords: Al 2 O 3 nanofluids; viscosity; specific heat capacity; temperature effect; low volume concentration 1. Introduction The study of thermal and rheological properties of fluids has gained interest in recent years, as they play a vital role in heat transfer applications of thermal systems for industrial sectors. Plain heat transfer fluids, also called base fluids, have variable properties such as varying thermal conductivity and viscosity with change in temperature. When base fluids are added with metallic nanoparticles at a certain concentration, the physical and thermal properties of the fluids are affected since the thermal conductivity of solid metal particles is higher than that of fluids [1,2]. If base fluids are added with particles in the size range of less than 100 nm, the fluids are termed as nanofluids. Particles of nano-size diameter (<100 nm) are chosen as additives to the base fluids, since micron-size particles increase the pumping power and pressure drop across the heat transfer section. With the miniaturisation of heat transfer equipment, research and development for improving the effective heat transfer of conventional heat transfer fluids is the need of the day. *Corresponding author. rajasekhar.y@vit.ac.in Ó 2013 Taylor & Francis

3 Journal of Experimental Nanoscience 87 In heat transfer applications, heat transfer coefficients as well as the Prandtl and Reynolds number depend upon the flow property of the fluid such as viscosity. In thermal applications, addition of submicron particles to the working fluid improves the convective heat transfer rate and is calculated by substituting respective properties of the working fluid at that temperature. Since Choi [2] introduced the concept of nanofluids, numerous research groups started working on the measurement of thermal and rheological properties of water-based nanofluids for different applications including transportation, electronic cooling and energy production. Measurement of the viscosity of nanofluids is an important flow characteristic in determining the heat transfer performance. Increase in the viscosity of the nanofluids increases the pressure drop across the flow section, resulting in decrease of the heat transfer rate. A few experimental works are reported on the viscosity of nanofluids and correlations were developed to predict the viscosity of nanofluids in terms of particle volume concentration and density of the base fluid. For fluid mixtures, the viscosity model of Einstein [3] wasthe well-known equation to be used to determine the viscosity for particle volume concentrations lower than 5% in the base fluid. Later, Brinkman [4] and Batchelor [5] developed equations to determine the viscosity of fluid particle mixtures. Graham [6] suggested a generalised expression for low concentrations like the form of the Einstein formula based on the Frankel and Acrivos [7] work by including the particle diameter and interparticle spacing. With the introduction of nanofluids for heat transfer applications for the past two decades, estimating the thermal properties using mixture formulae is not valid since they are only valid for fluid mixtures with micro-size particles. So, for the estimation of the viscosity of nanofluids, Wang et al. [8] expressed a model of the second-order linear equation given by m nf ¼ m bf ð1 þ 7:3f þ 123f 2 Þ: Chen et al. [9] also gave a second-order linear equation for normalised shear viscosity for up to 10% volume concentration with an uncertainty of less than 6% based on their experimental data, and they have shown that increase in viscosity is temperature-independent but dependent only on the volume concentration. Later, Masoumi et al. [10] established a theoretical relation for relative viscosity based on the effect of Brownian motion on viscosity. They included the mean particle diameter, temperature, volume fraction of particles, and nanoparticle density along with the physical properties of the base fluid. The experimental studies and data on rheological properties of nanofluids are limited compared to the thermal properties of nanofluids in the literature. Wang et al. [8] conducted experimental studies for measuring the viscosity of water-based Al 2 O 3 nanofluids and found increase in relative viscosity between 20% and 30% with increase of particle concentration. Namburu et al. [11] conducted studies based on the results of Kulkarni et al. [12] to examine the Newtonian and non-newtonian behaviour of nanofluids. However, their results revealed that nanofluids show Newtonian behaviour at higher fluid temperatures. Das et al. [13] also measured the viscosity of water-based Al 2 O 3 nanofluids against shear rate, resulting in increase of viscosity with increase of particle concentration, indicating the non-newtonian behaviour of nanofluids. Anoop et al. [14] carried out rheological studies and flow characteristics of electrostatically stabilised water-based Al 2 O 3 nanofluids, explaining the influence of electroviscous forces and particle agglomeration on relative viscosity. They explained that the presence of an electrical double layer results in ð1þ

4 88 Y.R. Sekhar and K.V. Sharma additional electroviscous forces which increase the suspension viscosity. However, for alumina ethylene glycol nanofluids, where electroviscous forces were absent, particle aggregation was found to be the reason for the increase in viscosity. Chandrasekhar et al. [15] experimentally measured the viscosity of nanofluids, prepared using a two-step method, with various concentrations in the range of 0.33% 5%. They concluded that the nonlinear behaviour of viscosity at a high volume concentration is due to hydrodynamic interactions between particles, resulting in disturbances of the fluid around the particle. Lee et al. [16] also prepared water-based Al 2 O 3 nanofluids having a particle size of 30 5 nm at low concentrations of vol.% using a two-step method with ultrasonication and without a surfactant. Their measured viscosity results showed a nonlinear relationship between the viscosity and particle volume concentration even at very low particle concentrations up to 2% and observed decrease in viscosity values with increase in temperature. Sridhara and Satapathy [17] reported in their recent review on Al 2 O 3 nanofluids that Liu et al. [18] observed a similar phenomenon in their experiments on CuO nanofluids. Timofeeva et al. [19] conducted viscosity studies on Al 2 O 3 nanofluids with water and ethylene glycol having particle diameters of 11, 20 and 40 nm in the volume concentration range of 0.5% 10%. They found that the viscosity decreases with the particle diameter and the increases with temperature is due to dendritic agglomeration. Duan et al. [20] conducted viscosity measurements on Al 2 O 3 nanofluids in the volume fraction range of 1% 5% suspended for a fortnight and found that they behave as non-newtonian fluids since they were forming agglomeration which made the nanofluids highly viscous. They also observed that on reultrasonication they became Newtonian fluids and suggested more detailed studies to be conducted on the particle agglomeration effect on thermal properties of nanofluids. Williams et al. [21] carried out measurements on viscosity using a capillary viscometer for water-based alumina and zirconia nanofluids at vol% and vol% particle loadings for Al 2 O 3 and ZrO 2, respectively. Kole and Dey [22] recently performed experiments on engine-coolant-based Al 2 O 3 nanofluids and observed transition of the base fluid from Newtonian behaviour to non-newtonian with increase in the volume fraction of Al 2 O 3 nanoparticles in the engine coolant. Also, they observed an increase of viscosity with increase in concentration and decrease of viscosity with increase in temperature. Mahbubul et al. [23] presented another review paper on latest developments in the estimation of viscosity including the effect of the temperature, particle size and volume concentration of different nanofluids. However, a regression equation for the estimation of viscosity considering the effect of different parameters for low volume concentration water-based nanofluids is not attempted. The specific heat capacity determines the convective flow nature of the nanofluid and it necessarily depends on the volume fraction of the nanoparticles. Considering the fact that very limited experimental data on specific heat capacity values for various water-based nanofluids at different concentrations are available, the value of the specific heat capacity is estimated using theoretical models. Different authors [11,24 26] have used theoretical models based on the mixing theory of an ideal gas and thermal equilibrium concepts to calculate the specific heat capacity of nanofluids of different concentrations. The specific heat capacity of nanofluids, calculated at any particle concentration, which is valid for homogeneous mixtures[24], is given by C pnf ¼ ð1 fþðrc pþ bf þ fðrc p Þ p ð1-fþr bf þ fr p : ð2þ

5 Journal of Experimental Nanoscience 89 Buongiorno [27] and Xuan and Reotzel [28] have used the above model for calculating the specific heat capacity of the nanofluid based on the heat capacity concept, assuming the nanoparticles and the base fluid at thermal equilibrium, whereas Pak and Cho [29] and Alammar and Hu [30] applied Equation (3) for calculating the specific heat capacity of nanofluids which is based on the mixing theory of ideal gas mixtures: C p ¼ð1 fþðc p Þ bf þ fðc p Þ p : ð3þ Very few experiments were carried out by researchers to study the effective specific heat capacity of Al 2 O 3 nanofluids. Zhou and Ni [31] carried out the measurement of the specific heat capacity for water-based Al 2 O 3 nanofluids and were in good agreement with the model of Buongiorno [27]. However, results of Kulkarni et al. [12] for water and ethylene glycol based Al 2 O 3 nanofluid suspensions as coolants matched with models developed by earlier researchers [27,29]. It was evident from experimental results of Kulkarni et al. [12] that the specific heat capacity of the nanofluid decreases with increase in particle concentration and increases with increase in temperature. Recently, the differential scanning calorimeter and double hot wire methods were used to estimate the specific heat capacities of water-based silica, alumina and copper oxide nanofluids[31,32]. These experimental results were well predicted by the theoretical model based on classical and statistical mechanisms. In the present study, viscosity measurements of water-based nanofluids containing low concentrations of Al 2 O 3 nanoparticles are carried out experimentally, considering nanofluids as a homogeneous medium. The change in effective viscosity of nanofluids is shown in terms of the dynamic viscosity index (DVI). The DVI is defined as the ratio of the difference between nanofluid viscosity and base fluid viscosity to the viscosity of the base fluid [14]. The viscosity characteristics of water-based nanofluids containing low concentrations of Al 2 O 3 nanoparticles are studied using the regression equation developed based on data from the present analysis and data available for different particle diameters, temperatures and volume concentrations in the literature. Also, studies of specific heat capacity characteristics of water-based nanofluids containing a low volume concentration of Al 2 O 3 nanoparticles are considered using the regression equation developed, including the effect of the particle diameter, temperature and volume concentration based on specific heat capacity data of different nanofluids from various sources available in the literature. 2. Experimental procedure for viscosity measurement The properties of working fluids, such as thermal conductivity and viscosity, at different temperatures determine the efficacy of the system for the specified application. In our experiments, water-based Al 2 O 3 dilute nanofluid suspensions in the particle volume concentration of 0.01% 1% were prepared by the method described by Sundar and Sharma [24]. The volume fraction of the nanoparticles was determined using the following expression: f ¼ m n =r n m n =r n þ m water =r water ; ð4þ

6 90 Y.R. Sekhar and K.V. Sharma where m n and m water are the mass, and r n and r water are the density of nanoparticles and water, respectively. Alumina does not dissolve in water, so initially, when the metal oxide particles are added to the fluid, they settle down with time. To improve the dispersion of the particles, a very small concentration of the sodium dodecylbenzene sulfonate surfactant was added to the base fluid which is much lower than its critical micelle concentration without affecting the nanofluid thermophysical properties. The addition of a surfactant will not affect the viscosity property of the nanofluid and the results of Kole and Dey [22] report the same for using a surfactant in the car engine coolant. The suspensions were kept under 48-hour examination and allowed to check particle dispersion. The dispersed solution of nanofluids is characterised for an average particle size and shape using scanning electron microscope (SEM) analysis. The morphology of the sample is observed under FESEM using the S4300 SE/N model Hitachi, Japan, at 20 kv. During the analysis, sufficient amount of suspension, one or two drops, is placed on the properly prepared surface. The SEM image of stable suspension of Al 2 O 3 nanoparticles dispersed in water is shown in Figure 1(a). The stability of prepared nanofluid suspensions after 2 weeks is shown in Figure 1(b), thus validating the present procedure used for the preparation of stable nanofluids. Usually, the commercial alumina nanoparticles available in the market have an acidic surface and result in a stable solution electrostatically when they are mixed with water [14]. Though there are a few larger particles due to the agglomeration of smaller particles as observed in Figure 1(a), the average particle size is taken as 47 nm. It is also observed that the particle distribution is relatively well dispersed and the particles are spherical or near spherical. The stable solutions of nanofluids already prepared at different concentrations were taken in small quantities as samples during each experiment run for measuring viscosity. In the present measurements, a magnetic stirrer having a heater plate was used for heating the fluid to reach a specific desired temperature. The heater plate is supplied with a specific voltage along with continuous stirring until a requisite steady temperature is reached and stability is verified at that temperature. A few research groups performed studies on determining the temperature effect on the viscosity using different nanoparticle suspensions from room temperature to higher temperatures[14,15,33]. To measure the viscosity of the prepared samples of nanofluids, the rheometer model R/S-CPSþ of Brookefield Instruments, UK, was used in the present study. The viscometer is programmable and is provided with a temperature-controlled bath to vary the temperature of the fluid sample as shown in Figure 2. The temperature of a nanofluid sample is varied by varying the temperature of methanol in the temperaturecontrolled bath. When the temperature control system is switched on the temperature of methanol gradually rises to the set temperature and exchanges heat with the fluid sample. The temperature-controlled bath attached to the system was used to control the sample temperature from ambient to 50 C. The viscosity of the fluid is measured in a sample chamber which is monitored using an RTD sensor. In the present study, the fluid sample temperature under test was first measured at 45 C and then the temperature was gradually reduced up to 20 C in steps of 5 C. The data from the rheometer at different temperatures are automatically logged to the computer using the RHEO3000 software [34]. Various operational parameters of the rheometer setup such as the cone spindle RPM, torque, viscosity, shear stress, shear rate, temperature and time are collected by the software. The rheometer has a viscosity range of ,000 Pas with a temperature range of 20 to 250 C.

7 Journal of Experimental Nanoscience 91 Figure 1. (a) SEM image of Al 2 O 3 nanoparticles dispersed in water. (b) Photograph showing nanofluid stability after 2 weeks. The measurements produce satisfactory results when the applied torque is between 10% and 100% for different cone spindle type and speed combinations. So, the cone spindle type and speed are to be properly chosen such that the torque lies in the prescribed range. The rheometer has a wide spindle speed range of RPM. Cone Spindle C50-1 was used in the viscometer for measurement and was calibrated by standard procedures using Brookfield standard fluids. To verify the accuracy of the experiment setup and procedure, viscosity values obtained from the experiment were compared with reference values from the literature.[35,36] The measured values were in good agreement with the reference data with a deviation of less than 2% in the temperature range of C. Before placing the sample of nanofluids in the sample container, the nanofluid was stirred and agitated for more than 30 minutes to get a uniform particle dispersion as adopted by He et al. [37] for aqueous suspensions.

8 92 Y.R. Sekhar and K.V. Sharma Figure 2. Brookfield Rheometer R/S plus experimental setup. 3. Results and discussion 3.1. Viscosity characteristics of water-based Al 2 O 3 nanofluids Experiments were conducted to measure rheological properties of aqueous alumina nanofluids in the particle volume concentration range of 0.01% 1% and in the temperature range of 20 C 45 C. Calibration tests were conducted for the viscometer with water as the sampling fluid at different temperatures. Figure 3 shows the comparison of measured viscosity values of water with the reference data available in the literature [35] having an average deviation of 3% in the measured temperature range. A comparison of present measured experimental values of viscosity of nanofluids with theoretical models at different volume concentrations is shown in Figure 4. As shown in Figure 4, the theoretical predictions from viscosity models [3 6] and the experimental results follow a similar trend. It can be observed from Figure 4 that the experimental data are under predicted by the theoretical models. This may be due to the surface adsorption of nanoparticles from the neighbouring fluid particles, thereby forming clusters leading to increase in relative viscosity. The other possible reasons for the variation in experimental values and theoretical predictions could be change in the ph, surfactant or intermolecular forces which play a significant role in altering the viscosity of nanofluids[15,33]. It is also observed from Figure 4 that there is a nonlinear increase of viscosity with increase of particle concentration. The experimental results reported by Lee et al. [16] and He et al. [37] also confirm the nonlinear increase of viscosity with particle concentration typically due to particle particle

9 Journal of Experimental Nanoscience 93 Figure 3. Comparison of the measured viscosity of water with data of ASHRAE [35]. Figure 4. Comparison of the present experimental data with various theoretical models.

10 94 Y.R. Sekhar and K.V. Sharma interactions and hydrodynamic forces acting on the surface of the solid particles [19]. Usually, organic soluble electrolytes are used as charging agents in the colloidal suspensions to maintain a uniform dispersion, where the interfacial charge developed between the surfactant ions and aqueous media may change the thermal properties [29]. For concentrated suspensions, the particle collisions decrease with time and the effective radius of the particle increases which is the combined radius of the particle and interfacial sheath thickness (d). The variation of viscosity of nanofluids for different particle loadings with temperature is shown in Figure 5. It is observed that nanofluids with volumetric concentration at 1% particle concentration have higher viscosity which decreases with increase in temperature. The variation of the DVI with varying particle volume concentration for different temperatures is shown in Figure 7. It is observed that the DVI for nanofluids at low volume concentration is much less compared to higher volume concentrations. It is also observed that at a low particle concentration of nanofluids, the DVI is not significant with increase in temperature as reported by Namburu et al. [11]. However, with increasing particle volume concentration and temperature, the DVI increases up to 12% at 1% particle volume concentration. The reason for increase in viscosity can be interpreted as the strong van der Waals attraction between the particles and viscous interactions between the fluid and particles possibly due to aggregation of particles at low shear rates. The DVI of a nanofluid is calculated by using Equation (5) [11]: m eff m bf 100 : ð5þ m bf Figure 5. Viscosity of the nanofluid at various concentrations as a function of temperature.

11 Journal of Experimental Nanoscience 95 The viscosity characteristics of water-based Al 2 O 3 nanofluids are studied by developing a regression equation, including the effect of the particle concentration, particle diameter and temperature of the fluid. The viscosity measurements of Al 2 O 3 nanofluids having an average particle diameter of 47 nm are performed at different volume concentrations and temperatures in this study. In order to develop a generalised regression equation for estimating the relative viscosity of water-based Al 2 O 3 nanofluids, present experimental data as well as viscosity experimental data for different nanoparticles and particle sizes of different authors [13 16,19 21,29,38 42] are considered. The regression Equation (6) results from the regression analysis of viscosity data of different water-based nanofluids with a standard deviation of 15% and an average deviation of 9%. m r ¼ 0:935 1 þ T 0:5602 nf 1 þ d 0:05915 p 1 þ f 10:51 : ð6þ The above equation is valid in the range of 20 C < T nf < 70 C, 13 < d p < 100 nm and 0:01% < f < 5:00%. To verify the validity of the expression, the calculated values from the regression equation were compared with the experimental data of different authors. It is observed that the calculated values were in good agreement with the experimental data of different authors with a deviation of þ18% and 10% as shown in Figure 6, thus confirming the validity of the expression. The effective viscosity of water-based nanofluids for increasing particle Figure 6. Comparison of experimental viscosity data with calculated values from the regression equation.

12 96 Y.R. Sekhar and K.V. Sharma Figure 7. Variation of the DVI for different particle concentrations and temperatures. diameter is studied at different particle concentrations using the regression equation. It is observed from Figure 8 that the viscosity is decreasing with increase of particle diameter as expected following the classical behaviour for dispersions and is in agreement with the numerical results of Lu and Fan [43] and experimental results of different authors [11,44 46]. The reason for decrease in viscosity of nanofluids with increasing particle diameter could be due to the effect of electric double layer repulsion [47] as shown in Figure 8. Also, the particle aggregation size varies with particle size which affects the viscosity. The surface charge of the particle is on of the primary driving force for the formation of particle aggregation resulting in clusters. So, the smaller the diameter of the particle, the larger could be the particle aggregation size of the cluster, depending on the surface charge [48] which must be higher than the particle aggregation size of the larger particles. The effective viscosity of water-based nanofluids for increasing particle concentration is studied at different temperatures using the regression equation. It is observed form Figure 9 that effective viscosity increases with particle concentration and decreases with temperature which is in agreement with experimental results of different authors.[41 50] 3.2. Specific heat capacity characteristics of water-based nanofluids In the present analysis, data of different water-based nanofluids such as alumina water, copper oxide water, SiO 2 water and TiO 2 water are considered to develop the regression equation, since very limited experimental data are available from the literature for a particular nanofluid. Experiment data were chosen such that the effect of the particle volume

13 Journal of Experimental Nanoscience 97 Figure 8. Effective viscosity with increase of particle diameter at different particle concentrations. Figure 9. Effective viscosity with increase of particle concentration at different fluid temperatures.

14 98 Y.R. Sekhar and K.V. Sharma concentration, particle diameter and temperature of the fluid is present. Based on the experimental data from the literature [12,31,40,51] for different water-based nanofluids, a regression equation for specific heat capacity has been established. Based on the experimental data of the specific heat capacity of nanofluids from the literature, a regression equation has been obtained using the regression analysis given by Equation (7) valid in the range of 20 < T nf < 50 C, 15 < d p < 50 nm and 0:01% < f < 4:00%. The regression equation is developed based on 81 experimental data points of water-based Al 2 O 3, CuO, SiO 2 and TiO 2 nanofluids obtained from the literature [12,31,40,51]. In the present calculations, the specific heat capacity of the nanofluid at any given concentration is calculated by the regression Equation (7) developed for water-based nanofluids. The calculated values are compared with values obtained using Equation (3) which is valid for homogeneous mixtures and dilute suspensions[24]. C pr ¼ 0: þ T 0:3037 nf 1 þ d 0:4167 p 1 þ f 2:272 ð7þ The specific heat capacity characteristics of nanofluids were studied for the effect of the particle volume concentration, particle diameter and temperature of the fluid. To verify the validity of the expression, the calculated values from the regression equation were compared with the experimental data of different authors. It is observed that calculated values were in good agreement with the experimental data of different authors with a deviation of þ10% and 8% as shown in Figure 10, thus confirming the validity of the expression. The Figure 10. Comparison of the calculated relative specific heat capacity with the experimental relative specific heat capacity from the literature.

15 Journal of Experimental Nanoscience 99 Figure 11. Effect of the fluid temperature and particle diameter on the effective specific heat capacity of the nanofluid at different particle concentrations and comparison with experimental data from the literature [33]. effective specific heat capacity of water-based nanofluids at a particle concentration, particle diameter and for different temperatures is studied using the regression equation. It is observed from Figure 11 that the effective specific heat capacity increases with particle diameter which is in agreement with experimental results of Zhou and Ni [31] and others [11,51]. The reason for increase in the specific heat capacity of the nanofluid with increase of particle diameter is that as the thermal conductivity increases with particle diameter, the specific heat capacity also varies considerably as shown in Figure 11. However, with increase of particle concentration of nanoparticles, the specific heat capacity of a nanofluid decreases, resulting in increase of thermal diffusivity of nanofluids as shown in Figure 11.It can also be noted that with increase of temperature the effective specific heat capacity of a nanofluid is decreasing. However, numerical and experimental studies for determining the specific heat capacity of nanofluids had been conducted by only a few researchers [52 55]at a specific room temperature. The value of the specific heat capacity is highly essential for evaluating the heat transfer coefficients in heat transfer studies. However, more studies on temperature-dependent specific heat capacity over a wide range of nanoparticle size and particle concentration combinations have to be conducted to prove the result. 4. Conclusion The viscosity of water-based nanofluids prepared by a one-step method at different particle concentrations was measured experimentally by using the Brookfield apparatus at

16 100 Y.R. Sekhar and K.V. Sharma different temperatures. The variation of viscosity of nanofluids is observed to be nonlinear with increase of particle concentration. The results were in good agreement with models of earlier researchers. Generalised regression equations were developed for the estimation of the viscosity and specific heat capacity of water-based nano-suspensions using experimental data available in the literature. In the present study, the viscosity and specific heat capacity characteristics of water-based nanoparticle suspensions, including the effect of the particle concentration, particle diameter and temperature of the fluid, are investigated using the regression equations. Acknowledgements The authors like to acknowledge the financial assistance provided by the JNTU College of Engineering, and the Heat Transfer Laboratory of the Department of Mechanical Engineering, JNTU College of Engineering, for providing necessary instrumentation to carry out the sample preparation and helping in the analysis of samples to complete the article in time. References [1] Wang X-Q, Majumdar SA. Heat transfer characteristics of nanofluids: a review. Int J Therm Sci. 2007;46:1 19. [2] Choi SUS. Enhancing thermal conductivity of fluids with nanoparticles. In: Singer DA, Wang HP, editors. Developments and applications of non-newtonian flows. New York, NY: American Society of Mechanical Engineers; p [3] Einstein A. Eine neue bestimmung der molekuldimensionen. Ann Phys. 1906;19:289. [4] Brinkman HC. The viscosity of concentrated suspensions and solution. J Chem Phys. 1952;20: [5] Batchelor GK. The effect of Brownian motion on the bulk stress in a suspension of spherical particles. J Fluid Mech. 1977;83(1): [6] Graham AL. On the viscosity of suspensions of solid spheres. Appl Sci Res. 1981;37(3): [7] Frankel N, Acrivos A. On the viscosity of a concentrated suspension on solid spheres. Chem Eng Sci. 1967;22(6): [8] Wang X, Xu X, Choi SUS. Thermal conductivity of nanoparticle fluid mixture. J Thermophys Heat Transfer. 1999;13(4): [9] Chen H, Ding Y, he Y, Tan C. Rheological behaviour of ethylene glycol based titania nanofluids. Chem Phys Lett. 2007;444(4 6): [10] Masoumi N, Shorabi N, Behzadmehr A. A new model for calculating the effective viscosity of nanofluids. J Phys D: Appl Phys. 2009;42: [11] Namburu PK, Kulkarni DP, Dandekar A, Das DK. Experimental investigation of viscosity and specific heat of silicone dioxide nanofluids. Micro Nano Lett. 2007;2: [12] Kulkarni DP, Vajjha RS, Das DK, Oliva D. Application of aluminium oxide nanofluids in diesel electric generator as jacket water coolant. Appl Therm Eng. 2008;28: [13] Das SK, Putra N, Roetzel W. Pool boiling characteristics of nano-fluids. Int J Heat Mass Transfer. 2003;46(5): [14] Anoop KB, Kabelac S, Sundararajan T, Das SK. Rheological characteristics of nanofluids: influence of electroviscous effects and particle agglomeration. J App Phys. 2009;106(3): [15] Chandrasekar M, Suresh S, Bose AC. Experimental investigations and theoretical determination of thermal conductivity and viscosity of Al 2 O 3 /water nanofluid. Exp Therm Fluid Sci. 2010;34(2):

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