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Experimental study on the rheological behavior of silver-heat transfer oil nanofluid and suggesting two empirical based correlations for thermal conductivity and viscosity of oil based nanofluids
Accepted Manuscript Title: Experimental study on the rheological behavior of silver- heat transfer oil nanofluid and suggesting two empirical based correlations for thermal conductivity and viscosity of oil based nanofluids Author: Sadegh Aberoumand, Amin Jafarimoghaddam, Mojtaba Moravej, Hossein Aberoumand, Kourosh Javaherdeh PII: DOI: Reference:
S1359-4311(16)30098-9 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.01.148 ATE 7708
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
11-6-2015 27-1-2016
Please cite this article as: Sadegh Aberoumand, Amin Jafarimoghaddam, Mojtaba Moravej, Hossein Aberoumand, Kourosh Javaherdeh, Experimental study on the rheological behavior of silver- heat transfer oil nanofluid and suggesting two empirical based correlations for thermal conductivity and viscosity of oil based nanofluids, Applied Thermal Engineering (2016), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.01.148. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Experimental study on the rheological behavior of Silver- Heat Transfer Oil nanofluid and suggesting two empirical based correlations for thermal conductivity and viscosity of oil based nanofluids Sadegh Aberoumand1*, Amin Jafarimoghaddam2, Mojtaba Moravej3, Hossein Aberoumand4, Kourosh Javaherdeh5 1
Department of Mechanical Engineering, Islamic Azad University, Takestan Branch,
Takestan, Iran, Email: [email protected], 2
Department of Aerospace Engineering, K. N. Toosi University of Technology, Tehran, Iran
3
Department of Engineering, Payame Noor University, Tehran, Iran
4
Department of Engineering, Payame Noor University, Behbahan, Iran
4
Department of Mechanical Engineering, University of Guilan, Rasht, Iran
Highlights
Measuring thermal conductivity and viscosity of three fractions of nanofluids. Introducing an empirical based correlation for thermal conductivity. Introducing an empirical based correlation for viscosity of oil based nanofluids. A novel one-step method for preparation nanofluids has been discussed in brief.
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Graphical Abstract
Abstract
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Thermal conductivity and viscosity of nanofluids are the most important parameters which have to be determined specially, for industrial applications. So it is so beneficial prediction of thermal conductivity and viscosity of nanofluids precisely. Because of the fact that experimental instruments are not passible in many situations and present models are not applicable for any nanofluids, new correlations have been developed based on the data of oil based nanofluids in literature. The proposed correlations are based on the bulk temperature, nanoparticle diameter and nanoparticle concentration as input variables. Since the published data studying on rheological properties of oil based nanofluids were not found to be in a huge database, thermal conductivity and viscosity of heat transfer oil were investigated experimentally to be added to our database. The results showed that previous models for thermal conductivity of nanofluids predict thermal conductivity of oil based nanofluids in an decreasing way versus baulk temperature while, thermal conductivity of oil based nanofluids increases with rising temperature. So, this could be the motivation to develop an accurate correlation for thermal conductivity, specialized for oil based nanofluids. In the other hand, a new correlation for predicting viscosity of oil based nanofluids has been introduced. According to the results, the accuracy of the proposed correlation is in a better situation than other popular models. Key words: Viscosity, Thermal Conductivity, Oil Based Nanofluids, Predictive models
1. Introduction In the last decade, nanofluids as the suspension of nanometer size particles and base fluids have been suggested and applied in almost all of the fluid mechanics and heat transfer problems. The ability to enhance thermal conductivity and viscosity of common fluids is behind of this fact. These significant properties including electrical characteristics, cooling
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capacity and rheological behavior have encouraged researchers to use nanofluids in so many engineering fields [1, 2]. Many innovations have also been introduced in disease diagnosis, heat exchanger design and enhanced oil recovery by using these nanofluids. Nanofluids also can be utilized for enhancing heat transfer and improving energy efficiency in thermal systems. They may be used in automotive and heavy duty engines as engine coolants. Some military devices require high heat flux cooling and at this level, using conventional fluids is challenging. So, using nanofluids can provide required cooling for these applications. Generally, nanofluids consist of typical nanometer-sized particles in a base fluid like water, oil, ethylene glycol and etc [1–3]. Thermo physical properties of these fluids such as thermal conductivity and viscosity are usually related to the diameter of nanoparticles which should be usually below 100nm. Viscosity is one of the rheological properties of fluids which shows the resistance of fluid to flow and is expressed in cp or mPa.s. Nanofluid viscosity is a very important property in nanofluids usage specially, in heat transfer and fluid mechanics applications. To study on the viscosity of nanofluids, the effect of nanoparticle concentration [1, 2, 4-8], bulk temperature [2, 5-8] and diameter of nanoparticles [1, 2, 8] have to be considered. A large variety of nanoparticle suspensions with different nanoparticle materials, shapes, sizes and concentrations have been extensively studied in last decade; the majority of studies have been conducted in polar base fluids such as water, ethylene glycol (EG) and their mixtures. However, there are just a few studies on nanofluids based on industrial oils for viscosity and heat transfer applications. So, thermal conductivity and viscosity of silver/ heat transfer oil were measured experimentally to fill the gap of lacking in database. Silver was chosen because of its high thermal conductivity and heat transfer oil was selected due to its great usage in heat transfer devises. Fakoor Pakdaman et al. [9] investigated the rheological behavior of a Multi Walled Carbon Nano Tube (MWCNT)/ heat transfer oil nanofluid. They reported thermo physical properties of nanofluid up to 0.4 %wt. They also reported that
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thermal conductivity of nanofluids of 0.4 %wt increases by 15% at 70°C. Saeednia et al. [10] studied on the rheological properties of CuO/ oil nanofluids with weight fractions of 0.2% to 2%. They reported 6.2% enhancement in thermal conductivity of 2 wt% nanofluid. They also showed the temperature dependency of viscosity of nanofluids. M. Kole and T.K. Dey [11] studied thermal conductivity and viscosity of Cu/ gear oil nanofluids. They determined 24% of enhancement and around 71% increment for 2Vol.% nanofluid, for thermal conductivity and viscosity respectively. Nabeel Rashin and Hemalatha [12] carried out the experiments on viscosity of ZnO/ coconut oil and they reported shear thinning in all samples and all temperature. According to them, in low volume concentrations the shear thinning was because of non- Newtonian behavior of nanofluids and in high volume fractions, it was due to nanoparticles- fluid interactions. Ettefaghi et al. [13] reported their study on the effect of different types of carbon nanostructures on thermal conductivity of engine oil based nanofluids. They showed that carbon nanoball particles had the most positive effect on thermal conductivity coefficient and flash point of the base fluid by improving them by 9.3% and 18% at 0.1 %wt concentration, respectively. Also, they said that graphene nanosheets caused improvement of about 11% in pour point of the base oil. In addition, they reported that the viscosity of nanofluids containing different carbon nanostructures with 0.1 %wt concentration had no appreciable changes with respect to the base oil; but, viscosity increased with the increasing concentration. Ettefaghi et al. [14] investigated thermal conductivity of MWCNT/ engine oil nanofluid and reported 13.2% of enhancement for 0.1 %wt nanofluid. Wang et al. [15] reported 11% to 36% of enhancement for graphite/ oil nanofluids of 0.68% to 1.36% Vol. respectively. They also observed slight increase in viscosity of 1.36% Vol. nanofluid. Kole and Dey [16] reported that viscosity of Cuo/ gear oil nanofluids is enhanced by 3 times of the base fluid with CuO volume fraction of 0.025, while it decreased significantly with the rise of temperature. They also studied the effect of Cu nanoparticles in
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gear oil as nanofluid on thermal conductivity and viscosity. 24% and 71% of enhancement were observed for 2% Vol. of nanofluid [11]. In addition, some correlations have been published to predict thermal conductivity and viscosity of nanofluids. Maxwel [17] was the first researcher who created a correlation for thermal conductivity of nanofluids. He noted that thermal conductivity of nanofluids doesn't relate to bulk temperature. Murshed et al. [18] represented a relationship for thermal conductivity of nanofluids and there is no effect of temperature in their relationship. Turian et al. [19] introduced a correlation for thermal conductivity of nanofluids. They also haven't mentioned to temperature in their correlation. Fakoor Pakdaman et al. [9], introduced a correlation to predict thermal conductivity of nanofluids based on the oil as base fluids and MWCNT nanoparticle. Temperature as a parameter is applied in their correlation and this correlation can predict only the rising trend of thermal conductivity of utilized nanofluids in this research because of the impact of MWCNT in correlation. Yu et al. [20] introduced a correlation for predicting thermal conductivity of nanofluids through modifying Maxwell model by considering interfacial layers. On the other hand, some formulations have been published to predict the viscosity of nanofluids in literature. Einstein [21] as the first researcher on the viscosity developed a formulation in 1906. After him, Brinkman [22], Chen et al. [23], Lundgren [24], Wang et al. [25] and Abedian et al.[26] introduced correlations to predict viscosity of nanofluids till 2010. All the correlations should be a modified model of Einstein’s model. Because, Einstein’s model is a theoretical model and based on the type of base fluid, it will be better to modify that. The aim of this paper is to study on thermal conductivity and viscosity of Ag based oil nanofluids in various weight fractions up to 0.72%. However, some correlations have been suggested in the literature to calculate thermal conductivity and viscosity of nanofluids, but these properties of applied nanofluids are measured experimentally for more accuracy,
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because public correlations to predict them were not able to predict thermal conductivity and viscosity of applied nanofluids well. Based on the measured experimental data and the published experimental results of other researchers, two general correlations for predicting thermal conductivity and viscosity of any oil based nanofluid have been reported in this paper. Moreover, a novel method known as Electrical Explosion of Wire (E.E.W) for preparation of a stable nanofluid has been introduced briefly.
2. Nanofluid Preparation The tested nanofluids in this study are prepared by the E.E.W method. A PNC1K device created an electrical explosion by placing electrodes in liquid media. Nano powder production and distribution are carried out simultaneously (Fig. 1). It is necessary to mention that, in this process, a liquid phase could be consisted of deionized water (DW), oil, glycerin, alcohol, acetone, ethylene glycol, and hydrogen peroxide (H2O2). Another special feature of this system is the possibility of adding a surfactant to the liquid. So, the produced nanofluid remains the primary distribution for a very long time. Among all of the existing methods in the production of metal nanoparticles, electrical explosion method is the most economical and best industrial method to prepare nanofluid in large scales.
One of the greatest advantages of this method is the ability to produce nano powders from a wide range of materials. In fact for any material that can be shaped to thin wire it will be possible to convert to nanoparticles. For the created applied Ag/ oil nanofluid in this study, a PNC1K device and silver thin wire were prepared as specified in Table 1. From Fig. 2, it is clear that the Ag nanoparticles are dispersed well and the mean diameter of the Ag nanoparticles in utilized nanofluids was about 20 nm. It can be observed according to the scale of 20 nm that the distribution of Ag nanoparticles in the base fluid is well.
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3. Nanofluids Stability Assessing the dispersion of nanoparticles in the base fluid is the main factor in developing the applications of nanofluids. This factor is affected by nanoparticles surface charge and the index of that is zeta potential. In stable colloids (e.g. nanofluids), because of high electrostatic repulsion forces between the nanoparticles, the mentioned index should be in a high value. When the collisions between nanoparticles which is due to the low stability of nanofluids, is high, repulsive forces of nanoparticles will be weak and aggregation will be occurred and zeta potential index will be in a low value. Nanofluids with a zeta potential higher than 30 mV generally categorized as stable type [27, 28], and zeta potential index lower than 20 mV indicates the poor stability of nanofluids [29]. Zeta potential of utilized nanofluids and pH of them in three weight concentrations of 0.12%, 0.36% and 0.72% at two different temperatures of 313 K and 353 K were measured by a Zetasizer Nano ZS made by Malvern, Britain. The results show a very good stability for all of the test samples and fig. 3 clearly indicates the excellent stability of applied nanofluids. 3. Results and Discussion The thermal conductivity and viscosity of nanofluids are normally expressed in volume percent,
, while the loading analysis was obtained in weight percent (w). The conversion
between weight and volume fraction was done through the density of nanoparticles, np
and
f
are the density of nanoparticle material and base fluid respectively, ( k g
W
f
n p (1 W ) W
np
m
3
. ).
(1) f
3.1. Thermal Conductivity 3. 1.1 The Approach of Thermal Conductivity Measurement
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A KD2 Pro KS-1 made by Decagon Devices Inc. was utilized to measure thermal conductivity of applied nanofluids. The transient hot wire method is the base work of this device and the maximum deviation is 5.0%. Thermal conductivity in the range of 0.02 to 2.00 with the accuracy of
0 .0 0 1 could
be measured by this device. Usually a probe for this
measurement consists of a needle with a heater and temperature sensor inside. A current is delivered through the heater and the temperature of the probe is observed over time. The KD2 Pro evaluates probe temperature for verification of the thermal conductivity. Fluid samples were placed in a thermostatic bath (Firsteck B403L) to stabilize the temperature of the sample until it reached the expected temperature ±0.5 oC. Then, the KD2 Pro analyzed the data and corrected for sample temperature drift providing accurate thermal properties measurements for the fluids with different temperatures. The thermal conductivity of each sample of nanofluids was measured four times for reliability. As observed from Figs. 4, the increasing trend of thermal conductivity of the nanofluids is due to the increasing Brownian motion of the nanoparticles because of the increasing bulk temperature which is synonymous to an increase in the distribution of nanoparticles in the base fluid, while the trend for base fluid is decreasing. With increasing nanoparticles concentration, thermal conductivity behaves in an increasing way and this increasing way will be until the stability of nanofluids is remained. Due to the nanofluid preparation method of this study, 0.72% wt Ag- heat transfer oil was stable for around 87 days and after that by only a shaking, the nanofluid obtained its stability again.
3.1. 2. Thermal Conductivity Determination Determining thermal conductivity of nanofluids is an urgent factor in the heat transfer investigation of nanofluids. Some models to predict thermal conductivity have been reported in the literature but, these models are not able to precisely predict the thermal conductivity of
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any type of nanofluids. The reason is that, the data base for these models is given from only one type of nanofluids, so, these models cannot predict thermal conductivity of another type of nanofluids. This problem is the main reason to evaluate the thermal conductivity experimentally. There is a lack of a fairly accurate correlation to predict thermal conductivity of oil based nanofluids in literature. So, in this study, we collected many of the published experimental data of thermal conductivity of oil based nanofluids in order to be added to the experimental data of this study and be taken into consideration for generating an accurate correlation for predicting thermal conductivity of any oil based nanofluids. The method for developing correlation was least squire and some of the most popular models, which have been collected in table 2, have been compared to the proposed correlation. Data were collected from [9-11, 14, 15, 30, 31] plus the experimental data of this study, and a comparison between predicted thermal conductivity by the proposed correlation and other models has been shown in Fig. 5. As it can be observed from fig. 5, predicted thermal conductivity through equation (2) are closer than other predicted values by other equations to the experimental data and the relative deviation of the models has been shown in fig.6. 3.1. 3. Proposed Correlation: 5
2
4
4
k n f (T , , k n p ) (3 .9 1 0 T 0 .0 3 0 5) (0 .0 8 6 1 .6 1 0 T ) 3 .1 1 0 T 0 .1 2 9 5 .7 7 1 0
6
k np 4 0 1 0
4
(2)
While, T is the nanofluid bulk temperature in Celsius degrees and φ is the volume fraction which ranged from 0 to 2%. Moreover,
k np
is referred to the thermal conductivity of
nanoparticle material. As it can be observed from Fig.5, the predicted values by the proposed correlation show very good agreement to experimental data of thermal conductivity of nanofluid rather than the other models. So, the points of the proposed correlation are more concentrated near the 45° line. The accuracy of the proposed correlation is shown in Fig.6. As it can be seen, the
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relative deviation points of proposed correlation are more concentrated about the zero horizontal line while other models show greater error values. According to this fact that many of published models for predicting thermal conductivity of nanofluids are derived from data base of water based nanofluids, they cannot predict thermal conductivity of oil based nanofluids. As it can be observed from Fig.5, proposed model of Fakoor Pakdaman et al. to some extent is able to predict thermal conductivity of experimental data. Because, they derived the correlation based on the multi walled carbon nanotube (MWCNT)-oil nanofluid. But, since they inputted only the results of their own study, the correlation cannot predict thermal conductivity of any oil based nanofluids well.
Some of the famous correlations to predict thermal conductivity of nanofluids are listed in Table 2. Measured thermal conductivity of nanofluids in this study and their predicted values through the present correlation, Fakoor Pakdaman et al. model, Maxwell model, Turian et al. model, Murshed et al. model and Yu et al. model are collected in Table 3. As seen in Table 3, except Fakoor Pakdaman et al. model which has a greater deviation compared to the proposed correlation results, other models could not handle the downward trend of thermal conductivity of nanofluids with an increasing temperature. Calculated values of thermal conductivity of MWCNT based heat transfer oil nanofluid with published experimental data [9] are presented in Table 4. It is clear that the present correlation could predict the experimental results with a good accuracy and the maximum deviation is 3.5%.
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Calculated values of some published thermal conductivity ratio in [10, 11, 24] are presented in Table 5. It is clear that the present correlation could predict not only thermal conductivity but also thermal conductivity ratio of nanofluids with acceptable accuracy.
3.2. Viscosity 3.2.1 Viscosity Measurement In order to study the rheological properties of the utilized nanofluids, it is crucial to see whether they are categorized as Newtonian or non-Newtonian fluid. It is clear that if shear stress of nanofluid increases linearly with shear rate, the applied nanofluid will be classified as Newtonian as Eq. (8). (8)
τ γμ
Where τ is shear stress,
γ
is the shear rate and μ is the dynamic viscosity of Newtonian fluid.
For this major, in the first place the viscosity of heat transfer oil versus shear rate for the temperature range of
to
C was measured. Fig. 7 indicates Newtonian behavior of
heat transfer oil because the viscosity over the temperature range is not dependent of the shear rate. Increasing weight fraction of applied nanofluid leads to observing the fact that nonewtonian behavior appears in the temperature lower than higher than
(
) and in temperature
C, nanofluids behaves Newtonian. Figures 8-10.
Shear stress in different values of shear rate of utilized nanofluids at
C (308 K) is
presented in fig. 11. According to that, with increasing weight fraction from 0.12% wt to 0.72% wt, the linear trend tends to be non-linear. This transformation is due to the transformation from Newtonian to non- Newtonian behavior of nanofluids.
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iscosity of base fluid and nanofluids versus temperature over the range of
to
C is
presented in fig.12. As it can be seen from this figure, the value of viscosity tends to be in a decreasing way with increasing temperature. It is because of the effect of temperature rising on the weakening forces between particles or intermolecular forces. An enhancement in viscosity also can be observed with increasing weight fraction specially, in lower temperatures. In other word, increasing in Brownian motion that is due to temperature rising, and also, increasing of nanoparticle diameter which affects the interaction between base fluid and nanoparticles, cause to increase in chaos and this fact means decrease in viscosity of nanofluids.
According to the experimental data of various researcher [9- 12, 14, 16, 30] plus the experimental data of this study, based on the least square method the following correlation was developed to predict the viscosity of nanofluids based oil with any nanoparticle under particular conditions of temperature and volume fraction which shown bellows. Noting that, equation (9) is consisted of
bf
which changes by bulk temperature variations. This means
that the effect of temperature on viscosity of nanofluids is considered in the equation. n f b f (1 .1 5 1 .0 6 1 0 .5 4 4 2
2
0 .1 1 8 1 ) 3
(9) Where
is volume concentration of nanoparticles and
bf
is the viscosity of oil as the base
fluid in any desired temperature. Some of the most applicable models of viscosity of nanofluids in literature are presented in Table 6. All of the experimental data of viscosity of oil based nanofluids which are collected from literature have been calculated by models and proposed correlation. The results are shown in fig. 13 and fig. 14. From these figures, the accuracy of proposed correlation is clearly observable and it is also shown that the relative deviation of the proposed correlation
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is better than other popular models to predict the viscosity of oil based nanofluids. A possible reason is referred to the data bases of these models which were based on water almost.
4. Conclusion: The results on the viscosity and thermal conductivity of Ag- heat transfer oil nanofluids as a function of Ag nanoparticles volume fraction and temperature have been discussed. Studied Ag- heat transfer oil nanofluids are well dispersed and have good stability due to the novel method of nanofluid preparation. Newtonian behavior of the base fluid changes to nonNewtonian with increasing Ag volume fraction in the heat transfer oil. Based on the empirical data of this study and published measurements of thermal conductivity and viscosity of oil based nanofluids in literature and applying the least squire method, two general empirical based correlation have been derived and their predictions and accuracy have been discussed. Following are the main conclusion: 1- E.E.W method for high stability and low deposition of nanoparticles can be used as a reliable method for preparing nanofluids. Measuring zeta potential of utilized nanofluids showed this as well. 2- Thermal conductivity of applied nanofluids in this study as well as all published experimental results showed an upward trend with increasing temperature and nanoparticle concentration. 3- Two correlations versus concentration, temperature and nanoparticle type to predict the thermal conductivity and viscosity of any kind of oil based nanofluids have been introduced. It is clear that the results of these correlations would be better, if the experimental studies on thermophysical properties of various kind of oil based nanofluids are studied further.
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4- Newtonian to non- Newtonian behavior of utilized nanofluids in temperature of 35 ºC was observed in all three weight fractions. Acknowledgements: The authors would like to express their thanks to the PNF Company for providing the laboratory to produce the nanofluids and Iranian Nanotechnology Initiative (INI) for providing the financial support for the present work.
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[8] Timofeeva EV, Gavrilov AN, Mc Closkey JM, Tolmachev YV, Sprunt S, Lopatina LM, et al. Thermal conductivity and particle agglomeration in alumina nanofluids: experiment and theory. Phys Rev E 2007;76:061203. [9] Fakoor Pakdaman M, Akhavan-Behabadi MA, Razi P (2012) An experimental investigation on thermo-physical properties and overall performance of MWCNT/heat transfer oil nanofluid flow inside vertical helically coiled tubes. Exp. Thermal and Fluid Sci. 40: 103-111. [10] Saeedinia M, Akhavan-Behabadi MA, Razi P (2012) Thermal and rheological characteristics of CuO– Base oil nanofluid flow inside a circular tube Int. ommunications in Heat and Mass Transfer 39(1): 152 -159. [11] Madhusree Kole, T.K. Dey (2013) Enhanced thermophysical properties of copper nanoparticles dispersed in gear oil, Applied Thermal Engineering 56:45-53. [12] M. Nabeel Rashin, J. Hemalatha (2013) Synthesis and viscosity studies of novel ecofriendly ZnO–coconut oil nanofluid, Experimental Thermal and Fluid Science 51: 312– 318. [13] Ehsan-o-llah Ettefaghi, Alimorad Rashidi , Hojjat Ahmadi, Seyed Saeid Mohtasebi, Mahnaz Pourkhalil (2013) Thermal and rheological properties of oil-based nanofluids from different carbon nanostructures, International Communications in Heat and Mass Transfer 48: 178-182. [14] Ettefaghi Eol, Ahmadi H, Rashidi Amideddin Nouralishahi A, Mohtasebi S S (2013) Preparation and thermal properties of oil-based nanofluid from multi-walled carbon nanotubes and engine oil as nano-lubricant. Int. Communications in Heat and Mass Transfer, 46: 142–147.
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[17] Maxwell JC (1881) A Treatise on Electricity and Magnetism. Second edition, Clarendon Press, UK. [18] Murshed SMS, Leong KC, Yang C (2005) Enhanced thermal conductivity of TiO2– water based nanofluids” Int. j Thermal Sci. 44(4):
7–373.
[19] Turian M, Sung DJ, Hsu F L (1991) Thermal conductivity of granular coals, coal-water mixtures and multi-solid/liquid suspensions. Fuel. 70:1157–1172 . [20] W. Yu, S.U.S. Choi, The role of interfacial layers in enhanced thermal conductivity of nanofluids: a renovated Maxwell model, J. Nanopart. 5 (2003) 167–171. [21] Einstein A. Eine neue bestimmung dermoleküldimensionen. Ann Phys 1906; 324:289– 306. [22] Brinkman H. The viscosity of concentrated suspensions and solutions. J Chem Phys 1952; 20571–571. [23] Chen H, Ding Y, Tan C. Rheological behaviour of nanofluids. New J Phys 2007; 9:367. [24] Lundgren TS. Slow flow through stationary random beds and suspensions of spheres. J Fluid Mech 1972; 51: 273–99. [25] Wang X, Xu X, Choi SUS. Thermal conductivity of nanoparticle – fluid mixture. J Thermophys Heat Transf 1999; 13: 474–80.
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[26] Abedian B, Kachanov M. On the effective viscosity of suspensions. Int J Eng Sci 2010; 48: 962–5. [27] ISO, 14887: 2000(E): Sample preparation dispersing procedures for powders in liquids, International Organization for Standardization, Geneva, Switzerland, 2000. [28] Y. Liu, Y. Liu, P. Hu, X. Li, R. Gao, Q. Peng, L. Wei, (2015) The effects of graphene oxide nanosheets and ultrasonic oscillation on the supercooling and nucleation behavior of nanofluids PCMs, Microfluid. Nanofluid. 18 (1) 81–89. [29] J.-H. Lee, K.S. Hwang, S.P. Jang, B.H. Lee, J.H. Kim, S.U. Choi, C.J. Choi, (2008) Effective viscosities and thermal conductivities of aqueous nanofluids containing low volume concentrations of Al2O3 nanoparticles, Int. J. Heat Mass Transfer 51 (11) 2651–2656. [30] Elena V. Timofeeva , Michael R. Moravek , Dileep Singh (2011) Improving the heat transfer efficiency of synthetic oil with silica nanoparticles, Journal of Colloid and Interface Science 364: 71–79. [31] Madhusree Kole, T.K. Dey (2011) Role of interfacial layer and clustering on the effective thermal conductivity of CuO–gear oil nanofluids. Exp. Thermal and Fluid Science 35: 1490–1495.
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Fig. 1 PNC1K device
Fig. 2. TEM image of Ag/ heat transfer oil nanofluid.
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Fig.3. Absolute zeta potential of Ag/ heat transfer oil nanofluids as a function of weight concentration
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Fig.4. Thermal conductivity of Ag- heat transfer oil nanofluids
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Fig.5. Agreement between different models and experimental data of thermal conductivity.
Fig.6. Relative viscosity of different models of thermal conductivity.
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Fig.7. Viscosity vs. shear rate of heat transfer oil
Fig.8. Viscosity vs. shear rate of Ag/ heat transfer oil nanofluid with 0.12% wt.
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Fig.9. Viscosity vs. shear rate of Ag/ heat transfer oil nanofluid with 0.36% wt.
Fig.10. Viscosity vs. shear rate of Ag/ heat transfer oil nanofluid with 0.72% wt.
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Fig.11. Shear stress vs. shear rate of Ag/ heat transfer oil nanofluids at
C.
Fig.12. Temperature dependence of the viscosity of Ag/ heat transfer oil nanofluids
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Fig. 13. Agreement between different models and experimentaldata of viscosity of oil based nanofluids.
Fig. 14. Relative deviation of different models.
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Table 1. Operational characteristics of the PNC1K in this study MODEL
PNC1k
Deviation
Output Voltage
0.5-1 kV
28 V
Input Power
1P 220VAC 500 W
±2 W
Shot Period
1-5 sec
0.1 s
Max. Diameter of Wire
0.25 mm
±0.01mm
Exploding Wire Length
1-5 mm
0.1 mm
Output Wire
Ag
Average Particle Size
15-25 nm
±3 nm
Table . Models for the effective thermal conductivity of nanofluids. Model
Equation
Number
Fakoor Pakdaman et al.
(3)
[9] Maxwell [17]
(4)
Murshed et al. [18]
(5)
Yu et al. [20]
(6)
Turian et al. [19]
(7)
∆= [(
,
α=
,
β=
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Table 3. Predicted values of thermal conductivity using the present correlation and other models. Turian Experiment
Exp.
Proposed
Fakoor Pakdaman
Murshed et
Maxwell
Yu et al.
al. Model
Model
Model
et al. Condition
Data
Correlation
et al. Model Model
Ag, T=40oC, 0.14
0.136
0.148
0.148
0.143
0.138
0.144
0.141
0.139
0.149
0.147
0.142
0.137
0.143
0.143
0.145
0.152
0.145
0.14
0.136
0.141
0.149
0.154
0.157
0.143
0.137
0.133
0.139
0.142
0.138
0.149
0.182
0.159
0.139
0.164
0.144
0.141
0.152
0.181
0.158
0.138
0.163
0.145
0.147
0.157
0.179
0.156
0.136
0.16
0.152
0.156
0.164
0.176
0.153
0.134
0.158
0.143
0.147
0.151
0.407
0.282
0.142
0.189
0.145
0.15
0.161
0.405
0.281
0.141
0.188
0.149
0.156
0.171
0.401
0.278
0.139
0.188
φ= . 11% ol. Ag, T=50oC, φ= . 11% ol. Ag, T=70oC, φ= . 11% ol. Ag, T=100oC, φ= . 11% ol.
Ag, T=40oC, φ= . 44% ol. Ag, T=50oC, φ= . 44% ol. Ag, T=70oC, φ= . 44% ol. Ag, T=100oC, φ= . 44% ol.
Ag, T=40oC, φ= .171% ol. Ag, T=50oC, φ= .171% ol. Ag, T=70oC, φ= .171% ol.
Page 28 of 33
Ag, T=100oC, 0.157
0.164
0.183
0.396
0.273
0.137
0.188
φ= .171% ol.
Table 4.Published thermal conductivity of MWCNT based heat transfer oil nanofluid [9] and their predictions through Eq. (2). Thermal Conductivi
Calculated
ty of
Value, Eq. (2)
Experiment's Conditions
Deviation
Ref.
Nanofluid MWCNT, 0.07% Vol., T= 40 oC
0.138
0.134
2.9%
[9]
MWCNT, 0.07% Vol., T= 50 oC
0.141
0.137
2.8%
[9]
MWCNT, 0.07% Vol., T= 60 oC
0.142
0.14
1.4%
[9]
MWCNT, 0.07% Vol., T= 70 oC
0.143
0.143
0
[9]
MWCNT, 0.14% Vol., T= 40 oC
0.14
0.139
0.7%
[9]
MWCNT, 0.14% Vol., T= 50 oC
0.143
0.142
0.7%
[9]
MWCNT, 0.14% Vol., T= 60 oC
0.146
0.145
0.7%
[9]
MWCNT, 0.14% Vol., T= 70 oC
0.149
0.148
0.6%
[9]
MWCNT, 0.29% Vol., T= 40 oC
0.144
0.149
3.5%
[9]
MWCNT, 0.29% Vol., T= 50 oC
0.148
0.152
2.7%
[9]
MWCNT, 0.29% Vol., T= 60 oC
0.15
0.154
2.6%
[9]
MWCNT, 0.29% Vol., T= 70 oC
0.152
0.157
3.3%
[9]
Page 29 of 33
Table 5. Calculated
values of published thermal conductivity ratio. Thermal Thermal Conductivity
Experiment's Conditions
Calculated
Conductivity
Deviation
Ref.
Value,
Ratio of of Base fluid Nanofluid Cu- Gear oil, 0.11% Vol. T= 10 oC
1.01
0.14
0.98
2.9%
[11]
Cu- Gear oil, 0.11% Vol. T= 20 oC
1.02
0.139
0.99
2.9%
[11]
Cu- Gear oil, 0.11% Vol. T= 30 oC
1.03
0.139
1.02
1%
[11]
Cu- Gear oil, 0.11% Vol. T= 40 oC
1.04
0.138
1.04
0
[11]
Cu- Gear oil, 0.11% Vol. T= 50 oC
1.05
0.137
1.06
0.9%
[11]
Cu- Gear oil, 0.11% Vol. T= 60 oC
1.053
0.136
1.08
3.1%
[11]
Cu- Gear oil, 0.57% Vol. T= 10 oC
1.08
0.14
1.17
8.3%
[11]
Cu- Gear oil, 0.57% Vol. T= 20 oC
1.09
0.139
1.19
9.2%
[11]
Cu- Gear oil, 0.57% Vol. T= 30 oC
1.11
0.139
1.21
9%
[11]
Cu- Gear oil, 0.57% Vol. T= 40 oC
1.11
0.138
1.23
10.8%
[11]
Cu- Gear oil, 0.57% Vol. T= 50 oC
1.12
0.137
1.26
12.5%
[11]
Cu- Gear oil, 0.57% Vol. T= 60 oC
1.13
0.136
1.28
13.3%
[11]
Cu- Gear oil, 2% Vol. T= 10 oC
1.2
0.14
1.24
3.3%
[11]
Cu- Gear oil, 2% Vol. T= 20 oC
1.22
0.139
1.25
4%
[11]
Cu- Gear oil, 2% Vol. T= 30 oC
1.24
0.139
1.27
2.4%
[11]
Cu- Gear oil, 2% Vol. T= 40 oC
1.25
0.138
1.29
3.2%
[11]
Cu- Gear oil, 2% Vol. T= 50 oC
1.26
0.137
1.31
4%
[11]
Cuo- Gear oil, 0.005% Vol. T= 10 oC
1.01
0.14
1.003
0.7%
[31]
Page 30 of 33
Cuo- Gear oil, 0.005% Vol. T= 20 oC
1.02
0.139
1.03
1%
[31]
Cuo- Gear oil, 0.005% Vol. T= 30 oC
1.021
0.139
1.06
3.2%
[31]
Cuo- Gear oil, 0.005% Vol. T= 40 oC
1.022
0.138
1.08
4.7%
[31]
Cuo- Gear oil, 0.005% Vol. T= 50 oC
1.028
0.137
1.11
8.1%
[31]
Cuo- Gear oil, 0.005% Vol. T= 60 oC
1.025
0.136
1.13
10.2%
[31]
Cuo- Gear oil, 0.005% Vol. T= 70 oC
1.03
0.134
1.15
11.6%
[31]
Cuo- Gear oil, 0.015% Vol. T= 10 oC
1.05
0.14
1.01
3.8%
[31]
Cuo- Gear oil, 0.015% Vol. T= 20 oC
1.052
0.139
1.04
1.4%
[31]
Cuo- Gear oil, 0.015% Vol. T= 30 oC
1.058
0.139
1.06
0.2%
[31]
Cuo- Gear oil, 0.015% Vol. T= 40 oC
1.063
0.138
1.09
2.5%
[31]
Cuo- Gear oil, 0.015% Vol. T= 50 oC
1.066
0.137
1.12
5%
[31]
Cuo- Gear oil, 0.015% Vol. T= 60 oC
1.069
0.136
1.15
7.6%
[31]
Cuo- Gear oil, 0.015% Vol. T= 70 oC
1.074
0.134
1.17
8.9%
[31]
Cuo- Gear oil, 0.025% Vol. T= 10 oC
1.08
0.14
1.02
5.5%
[31]
Cuo- Gear oil, 0.025% Vol. T= 20 oC
1.09
0.139
1.05
3.7%
[31]
Cuo- Gear oil, 0.025% Vol. T= 30 oC
1.1
0.139
1.07
2.7%
[31]
Cuo- Gear oil, 0.025% Vol. T= 40 oC
1.105
0.138
1.10
0.4%
[31]
Cuo- Gear oil, 0.025% Vol. T= 50 oC
1.108
0.137
1.13
2%
[31]
Cuo- Gear oil, 0.025% Vol. T= 60 oC
1.112
0.136
1.16
4.3%
[31]
Cuo- Gear oil, 0.025% Vol. T= 70 oC
1.12
0.134
1.18
5.3%
[31]
Cuo- oil, 0.13% Vol. T= 24 oC
1.02
0.141
1.023
0.3%
[10]
Cuo- oil, 0.13% Vol. T= 30 oC
1.04
0.139
1.046
0.6%
[10]
Cuo- oil, 0.13% Vol. T= 38 oC
1.08
0.138
1.086
0.5%
[10]
Page 31 of 33
Cuo- oil, 0.13% Vol. T= 48 oC
1.10
0.137
1.114
1.3%
[10]
Cuo- oil, 0.13% Vol. T= 60 oC
1.13
0.136
1.15
1.8%
[10]
Cuo- oil, 0.13% Vol. T= 70 oC
1.15
0.135
1.18
2.6%
[10]
Cuo- oil, 0.27% Vol. T= 24 oC
1.04
1.06
1.9%
[10]
Cuo- oil, 0.27% Vol. T= 30 oC
1.06
0.139
1.07
0.9%
[10]
Cuo- oil, 0.27% Vol. T= 38 oC
1.095
0.138
1.09
0.4%
[10]
Cuo- oil, 0.27% Vol. T= 48 oC
1.12
0.137
1.137
1.5%
[10]
Cuo- oil, 0.27% Vol. T= 60 oC
1.15
0.136
1.18
2.6%
[10]
Cuo- oil, 0.27% Vol. T= 70 oC
1.17
0.135
1.196
2.2%
[10]
0.141
Table 6. The most popular models for predicting viscosity of nanofluids in literature. Model n f b f (1 2 .5 )
nf
1906
Einstein [21]
1952
Brinkman [22]
1972
Lundgren [24]
1999
Wang et al. [25]
2007
Chen et al. [23]
2010
Abedian et al.
2 .5
(11)
n f b f (1 2 .5 6 .2 5 ) 2
n f b f (1 7 .3 1 2 3 )
(12)
2
(13)
n f b f (1 1 0 .6 (1 0 .6 ) ) 2
nf
Ref.
(10)
bf (1 )
Year
bf (1 2 .5 ) (15)
(14)
[26]
Page 32 of 33
Page 33 of 33
S1359-4311(16)30098-9 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.01.148 ATE 7708
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
11-6-2015 27-1-2016
Please cite this article as: Sadegh Aberoumand, Amin Jafarimoghaddam, Mojtaba Moravej, Hossein Aberoumand, Kourosh Javaherdeh, Experimental study on the rheological behavior of silver- heat transfer oil nanofluid and suggesting two empirical based correlations for thermal conductivity and viscosity of oil based nanofluids, Applied Thermal Engineering (2016), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.01.148. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Experimental study on the rheological behavior of Silver- Heat Transfer Oil nanofluid and suggesting two empirical based correlations for thermal conductivity and viscosity of oil based nanofluids Sadegh Aberoumand1*, Amin Jafarimoghaddam2, Mojtaba Moravej3, Hossein Aberoumand4, Kourosh Javaherdeh5 1
Department of Mechanical Engineering, Islamic Azad University, Takestan Branch,
Takestan, Iran, Email: [email protected], 2
Department of Aerospace Engineering, K. N. Toosi University of Technology, Tehran, Iran
3
Department of Engineering, Payame Noor University, Tehran, Iran
4
Department of Engineering, Payame Noor University, Behbahan, Iran
4
Department of Mechanical Engineering, University of Guilan, Rasht, Iran
Highlights
Measuring thermal conductivity and viscosity of three fractions of nanofluids. Introducing an empirical based correlation for thermal conductivity. Introducing an empirical based correlation for viscosity of oil based nanofluids. A novel one-step method for preparation nanofluids has been discussed in brief.
Page 1 of 33
Graphical Abstract
Abstract
Page 2 of 33
Thermal conductivity and viscosity of nanofluids are the most important parameters which have to be determined specially, for industrial applications. So it is so beneficial prediction of thermal conductivity and viscosity of nanofluids precisely. Because of the fact that experimental instruments are not passible in many situations and present models are not applicable for any nanofluids, new correlations have been developed based on the data of oil based nanofluids in literature. The proposed correlations are based on the bulk temperature, nanoparticle diameter and nanoparticle concentration as input variables. Since the published data studying on rheological properties of oil based nanofluids were not found to be in a huge database, thermal conductivity and viscosity of heat transfer oil were investigated experimentally to be added to our database. The results showed that previous models for thermal conductivity of nanofluids predict thermal conductivity of oil based nanofluids in an decreasing way versus baulk temperature while, thermal conductivity of oil based nanofluids increases with rising temperature. So, this could be the motivation to develop an accurate correlation for thermal conductivity, specialized for oil based nanofluids. In the other hand, a new correlation for predicting viscosity of oil based nanofluids has been introduced. According to the results, the accuracy of the proposed correlation is in a better situation than other popular models. Key words: Viscosity, Thermal Conductivity, Oil Based Nanofluids, Predictive models
1. Introduction In the last decade, nanofluids as the suspension of nanometer size particles and base fluids have been suggested and applied in almost all of the fluid mechanics and heat transfer problems. The ability to enhance thermal conductivity and viscosity of common fluids is behind of this fact. These significant properties including electrical characteristics, cooling
Page 3 of 33
capacity and rheological behavior have encouraged researchers to use nanofluids in so many engineering fields [1, 2]. Many innovations have also been introduced in disease diagnosis, heat exchanger design and enhanced oil recovery by using these nanofluids. Nanofluids also can be utilized for enhancing heat transfer and improving energy efficiency in thermal systems. They may be used in automotive and heavy duty engines as engine coolants. Some military devices require high heat flux cooling and at this level, using conventional fluids is challenging. So, using nanofluids can provide required cooling for these applications. Generally, nanofluids consist of typical nanometer-sized particles in a base fluid like water, oil, ethylene glycol and etc [1–3]. Thermo physical properties of these fluids such as thermal conductivity and viscosity are usually related to the diameter of nanoparticles which should be usually below 100nm. Viscosity is one of the rheological properties of fluids which shows the resistance of fluid to flow and is expressed in cp or mPa.s. Nanofluid viscosity is a very important property in nanofluids usage specially, in heat transfer and fluid mechanics applications. To study on the viscosity of nanofluids, the effect of nanoparticle concentration [1, 2, 4-8], bulk temperature [2, 5-8] and diameter of nanoparticles [1, 2, 8] have to be considered. A large variety of nanoparticle suspensions with different nanoparticle materials, shapes, sizes and concentrations have been extensively studied in last decade; the majority of studies have been conducted in polar base fluids such as water, ethylene glycol (EG) and their mixtures. However, there are just a few studies on nanofluids based on industrial oils for viscosity and heat transfer applications. So, thermal conductivity and viscosity of silver/ heat transfer oil were measured experimentally to fill the gap of lacking in database. Silver was chosen because of its high thermal conductivity and heat transfer oil was selected due to its great usage in heat transfer devises. Fakoor Pakdaman et al. [9] investigated the rheological behavior of a Multi Walled Carbon Nano Tube (MWCNT)/ heat transfer oil nanofluid. They reported thermo physical properties of nanofluid up to 0.4 %wt. They also reported that
Page 4 of 33
thermal conductivity of nanofluids of 0.4 %wt increases by 15% at 70°C. Saeednia et al. [10] studied on the rheological properties of CuO/ oil nanofluids with weight fractions of 0.2% to 2%. They reported 6.2% enhancement in thermal conductivity of 2 wt% nanofluid. They also showed the temperature dependency of viscosity of nanofluids. M. Kole and T.K. Dey [11] studied thermal conductivity and viscosity of Cu/ gear oil nanofluids. They determined 24% of enhancement and around 71% increment for 2Vol.% nanofluid, for thermal conductivity and viscosity respectively. Nabeel Rashin and Hemalatha [12] carried out the experiments on viscosity of ZnO/ coconut oil and they reported shear thinning in all samples and all temperature. According to them, in low volume concentrations the shear thinning was because of non- Newtonian behavior of nanofluids and in high volume fractions, it was due to nanoparticles- fluid interactions. Ettefaghi et al. [13] reported their study on the effect of different types of carbon nanostructures on thermal conductivity of engine oil based nanofluids. They showed that carbon nanoball particles had the most positive effect on thermal conductivity coefficient and flash point of the base fluid by improving them by 9.3% and 18% at 0.1 %wt concentration, respectively. Also, they said that graphene nanosheets caused improvement of about 11% in pour point of the base oil. In addition, they reported that the viscosity of nanofluids containing different carbon nanostructures with 0.1 %wt concentration had no appreciable changes with respect to the base oil; but, viscosity increased with the increasing concentration. Ettefaghi et al. [14] investigated thermal conductivity of MWCNT/ engine oil nanofluid and reported 13.2% of enhancement for 0.1 %wt nanofluid. Wang et al. [15] reported 11% to 36% of enhancement for graphite/ oil nanofluids of 0.68% to 1.36% Vol. respectively. They also observed slight increase in viscosity of 1.36% Vol. nanofluid. Kole and Dey [16] reported that viscosity of Cuo/ gear oil nanofluids is enhanced by 3 times of the base fluid with CuO volume fraction of 0.025, while it decreased significantly with the rise of temperature. They also studied the effect of Cu nanoparticles in
Page 5 of 33
gear oil as nanofluid on thermal conductivity and viscosity. 24% and 71% of enhancement were observed for 2% Vol. of nanofluid [11]. In addition, some correlations have been published to predict thermal conductivity and viscosity of nanofluids. Maxwel [17] was the first researcher who created a correlation for thermal conductivity of nanofluids. He noted that thermal conductivity of nanofluids doesn't relate to bulk temperature. Murshed et al. [18] represented a relationship for thermal conductivity of nanofluids and there is no effect of temperature in their relationship. Turian et al. [19] introduced a correlation for thermal conductivity of nanofluids. They also haven't mentioned to temperature in their correlation. Fakoor Pakdaman et al. [9], introduced a correlation to predict thermal conductivity of nanofluids based on the oil as base fluids and MWCNT nanoparticle. Temperature as a parameter is applied in their correlation and this correlation can predict only the rising trend of thermal conductivity of utilized nanofluids in this research because of the impact of MWCNT in correlation. Yu et al. [20] introduced a correlation for predicting thermal conductivity of nanofluids through modifying Maxwell model by considering interfacial layers. On the other hand, some formulations have been published to predict the viscosity of nanofluids in literature. Einstein [21] as the first researcher on the viscosity developed a formulation in 1906. After him, Brinkman [22], Chen et al. [23], Lundgren [24], Wang et al. [25] and Abedian et al.[26] introduced correlations to predict viscosity of nanofluids till 2010. All the correlations should be a modified model of Einstein’s model. Because, Einstein’s model is a theoretical model and based on the type of base fluid, it will be better to modify that. The aim of this paper is to study on thermal conductivity and viscosity of Ag based oil nanofluids in various weight fractions up to 0.72%. However, some correlations have been suggested in the literature to calculate thermal conductivity and viscosity of nanofluids, but these properties of applied nanofluids are measured experimentally for more accuracy,
Page 6 of 33
because public correlations to predict them were not able to predict thermal conductivity and viscosity of applied nanofluids well. Based on the measured experimental data and the published experimental results of other researchers, two general correlations for predicting thermal conductivity and viscosity of any oil based nanofluid have been reported in this paper. Moreover, a novel method known as Electrical Explosion of Wire (E.E.W) for preparation of a stable nanofluid has been introduced briefly.
2. Nanofluid Preparation The tested nanofluids in this study are prepared by the E.E.W method. A PNC1K device created an electrical explosion by placing electrodes in liquid media. Nano powder production and distribution are carried out simultaneously (Fig. 1). It is necessary to mention that, in this process, a liquid phase could be consisted of deionized water (DW), oil, glycerin, alcohol, acetone, ethylene glycol, and hydrogen peroxide (H2O2). Another special feature of this system is the possibility of adding a surfactant to the liquid. So, the produced nanofluid remains the primary distribution for a very long time. Among all of the existing methods in the production of metal nanoparticles, electrical explosion method is the most economical and best industrial method to prepare nanofluid in large scales.
One of the greatest advantages of this method is the ability to produce nano powders from a wide range of materials. In fact for any material that can be shaped to thin wire it will be possible to convert to nanoparticles. For the created applied Ag/ oil nanofluid in this study, a PNC1K device and silver thin wire were prepared as specified in Table 1. From Fig. 2, it is clear that the Ag nanoparticles are dispersed well and the mean diameter of the Ag nanoparticles in utilized nanofluids was about 20 nm. It can be observed according to the scale of 20 nm that the distribution of Ag nanoparticles in the base fluid is well.
Page 7 of 33
3. Nanofluids Stability Assessing the dispersion of nanoparticles in the base fluid is the main factor in developing the applications of nanofluids. This factor is affected by nanoparticles surface charge and the index of that is zeta potential. In stable colloids (e.g. nanofluids), because of high electrostatic repulsion forces between the nanoparticles, the mentioned index should be in a high value. When the collisions between nanoparticles which is due to the low stability of nanofluids, is high, repulsive forces of nanoparticles will be weak and aggregation will be occurred and zeta potential index will be in a low value. Nanofluids with a zeta potential higher than 30 mV generally categorized as stable type [27, 28], and zeta potential index lower than 20 mV indicates the poor stability of nanofluids [29]. Zeta potential of utilized nanofluids and pH of them in three weight concentrations of 0.12%, 0.36% and 0.72% at two different temperatures of 313 K and 353 K were measured by a Zetasizer Nano ZS made by Malvern, Britain. The results show a very good stability for all of the test samples and fig. 3 clearly indicates the excellent stability of applied nanofluids. 3. Results and Discussion The thermal conductivity and viscosity of nanofluids are normally expressed in volume percent,
, while the loading analysis was obtained in weight percent (w). The conversion
between weight and volume fraction was done through the density of nanoparticles, np
and
f
are the density of nanoparticle material and base fluid respectively, ( k g
W
f
n p (1 W ) W
np
m
3
. ).
(1) f
3.1. Thermal Conductivity 3. 1.1 The Approach of Thermal Conductivity Measurement
Page 8 of 33
A KD2 Pro KS-1 made by Decagon Devices Inc. was utilized to measure thermal conductivity of applied nanofluids. The transient hot wire method is the base work of this device and the maximum deviation is 5.0%. Thermal conductivity in the range of 0.02 to 2.00 with the accuracy of
0 .0 0 1 could
be measured by this device. Usually a probe for this
measurement consists of a needle with a heater and temperature sensor inside. A current is delivered through the heater and the temperature of the probe is observed over time. The KD2 Pro evaluates probe temperature for verification of the thermal conductivity. Fluid samples were placed in a thermostatic bath (Firsteck B403L) to stabilize the temperature of the sample until it reached the expected temperature ±0.5 oC. Then, the KD2 Pro analyzed the data and corrected for sample temperature drift providing accurate thermal properties measurements for the fluids with different temperatures. The thermal conductivity of each sample of nanofluids was measured four times for reliability. As observed from Figs. 4, the increasing trend of thermal conductivity of the nanofluids is due to the increasing Brownian motion of the nanoparticles because of the increasing bulk temperature which is synonymous to an increase in the distribution of nanoparticles in the base fluid, while the trend for base fluid is decreasing. With increasing nanoparticles concentration, thermal conductivity behaves in an increasing way and this increasing way will be until the stability of nanofluids is remained. Due to the nanofluid preparation method of this study, 0.72% wt Ag- heat transfer oil was stable for around 87 days and after that by only a shaking, the nanofluid obtained its stability again.
3.1. 2. Thermal Conductivity Determination Determining thermal conductivity of nanofluids is an urgent factor in the heat transfer investigation of nanofluids. Some models to predict thermal conductivity have been reported in the literature but, these models are not able to precisely predict the thermal conductivity of
Page 9 of 33
any type of nanofluids. The reason is that, the data base for these models is given from only one type of nanofluids, so, these models cannot predict thermal conductivity of another type of nanofluids. This problem is the main reason to evaluate the thermal conductivity experimentally. There is a lack of a fairly accurate correlation to predict thermal conductivity of oil based nanofluids in literature. So, in this study, we collected many of the published experimental data of thermal conductivity of oil based nanofluids in order to be added to the experimental data of this study and be taken into consideration for generating an accurate correlation for predicting thermal conductivity of any oil based nanofluids. The method for developing correlation was least squire and some of the most popular models, which have been collected in table 2, have been compared to the proposed correlation. Data were collected from [9-11, 14, 15, 30, 31] plus the experimental data of this study, and a comparison between predicted thermal conductivity by the proposed correlation and other models has been shown in Fig. 5. As it can be observed from fig. 5, predicted thermal conductivity through equation (2) are closer than other predicted values by other equations to the experimental data and the relative deviation of the models has been shown in fig.6. 3.1. 3. Proposed Correlation: 5
2
4
4
k n f (T , , k n p ) (3 .9 1 0 T 0 .0 3 0 5) (0 .0 8 6 1 .6 1 0 T ) 3 .1 1 0 T 0 .1 2 9 5 .7 7 1 0
6
k np 4 0 1 0
4
(2)
While, T is the nanofluid bulk temperature in Celsius degrees and φ is the volume fraction which ranged from 0 to 2%. Moreover,
k np
is referred to the thermal conductivity of
nanoparticle material. As it can be observed from Fig.5, the predicted values by the proposed correlation show very good agreement to experimental data of thermal conductivity of nanofluid rather than the other models. So, the points of the proposed correlation are more concentrated near the 45° line. The accuracy of the proposed correlation is shown in Fig.6. As it can be seen, the
Page 10 of 33
relative deviation points of proposed correlation are more concentrated about the zero horizontal line while other models show greater error values. According to this fact that many of published models for predicting thermal conductivity of nanofluids are derived from data base of water based nanofluids, they cannot predict thermal conductivity of oil based nanofluids. As it can be observed from Fig.5, proposed model of Fakoor Pakdaman et al. to some extent is able to predict thermal conductivity of experimental data. Because, they derived the correlation based on the multi walled carbon nanotube (MWCNT)-oil nanofluid. But, since they inputted only the results of their own study, the correlation cannot predict thermal conductivity of any oil based nanofluids well.
Some of the famous correlations to predict thermal conductivity of nanofluids are listed in Table 2. Measured thermal conductivity of nanofluids in this study and their predicted values through the present correlation, Fakoor Pakdaman et al. model, Maxwell model, Turian et al. model, Murshed et al. model and Yu et al. model are collected in Table 3. As seen in Table 3, except Fakoor Pakdaman et al. model which has a greater deviation compared to the proposed correlation results, other models could not handle the downward trend of thermal conductivity of nanofluids with an increasing temperature. Calculated values of thermal conductivity of MWCNT based heat transfer oil nanofluid with published experimental data [9] are presented in Table 4. It is clear that the present correlation could predict the experimental results with a good accuracy and the maximum deviation is 3.5%.
Page 11 of 33
Calculated values of some published thermal conductivity ratio in [10, 11, 24] are presented in Table 5. It is clear that the present correlation could predict not only thermal conductivity but also thermal conductivity ratio of nanofluids with acceptable accuracy.
3.2. Viscosity 3.2.1 Viscosity Measurement In order to study the rheological properties of the utilized nanofluids, it is crucial to see whether they are categorized as Newtonian or non-Newtonian fluid. It is clear that if shear stress of nanofluid increases linearly with shear rate, the applied nanofluid will be classified as Newtonian as Eq. (8). (8)
τ γμ
Where τ is shear stress,
γ
is the shear rate and μ is the dynamic viscosity of Newtonian fluid.
For this major, in the first place the viscosity of heat transfer oil versus shear rate for the temperature range of
to
C was measured. Fig. 7 indicates Newtonian behavior of
heat transfer oil because the viscosity over the temperature range is not dependent of the shear rate. Increasing weight fraction of applied nanofluid leads to observing the fact that nonewtonian behavior appears in the temperature lower than higher than
(
) and in temperature
C, nanofluids behaves Newtonian. Figures 8-10.
Shear stress in different values of shear rate of utilized nanofluids at
C (308 K) is
presented in fig. 11. According to that, with increasing weight fraction from 0.12% wt to 0.72% wt, the linear trend tends to be non-linear. This transformation is due to the transformation from Newtonian to non- Newtonian behavior of nanofluids.
Page 12 of 33
iscosity of base fluid and nanofluids versus temperature over the range of
to
C is
presented in fig.12. As it can be seen from this figure, the value of viscosity tends to be in a decreasing way with increasing temperature. It is because of the effect of temperature rising on the weakening forces between particles or intermolecular forces. An enhancement in viscosity also can be observed with increasing weight fraction specially, in lower temperatures. In other word, increasing in Brownian motion that is due to temperature rising, and also, increasing of nanoparticle diameter which affects the interaction between base fluid and nanoparticles, cause to increase in chaos and this fact means decrease in viscosity of nanofluids.
According to the experimental data of various researcher [9- 12, 14, 16, 30] plus the experimental data of this study, based on the least square method the following correlation was developed to predict the viscosity of nanofluids based oil with any nanoparticle under particular conditions of temperature and volume fraction which shown bellows. Noting that, equation (9) is consisted of
bf
which changes by bulk temperature variations. This means
that the effect of temperature on viscosity of nanofluids is considered in the equation. n f b f (1 .1 5 1 .0 6 1 0 .5 4 4 2
2
0 .1 1 8 1 ) 3
(9) Where
is volume concentration of nanoparticles and
bf
is the viscosity of oil as the base
fluid in any desired temperature. Some of the most applicable models of viscosity of nanofluids in literature are presented in Table 6. All of the experimental data of viscosity of oil based nanofluids which are collected from literature have been calculated by models and proposed correlation. The results are shown in fig. 13 and fig. 14. From these figures, the accuracy of proposed correlation is clearly observable and it is also shown that the relative deviation of the proposed correlation
Page 13 of 33
is better than other popular models to predict the viscosity of oil based nanofluids. A possible reason is referred to the data bases of these models which were based on water almost.
4. Conclusion: The results on the viscosity and thermal conductivity of Ag- heat transfer oil nanofluids as a function of Ag nanoparticles volume fraction and temperature have been discussed. Studied Ag- heat transfer oil nanofluids are well dispersed and have good stability due to the novel method of nanofluid preparation. Newtonian behavior of the base fluid changes to nonNewtonian with increasing Ag volume fraction in the heat transfer oil. Based on the empirical data of this study and published measurements of thermal conductivity and viscosity of oil based nanofluids in literature and applying the least squire method, two general empirical based correlation have been derived and their predictions and accuracy have been discussed. Following are the main conclusion: 1- E.E.W method for high stability and low deposition of nanoparticles can be used as a reliable method for preparing nanofluids. Measuring zeta potential of utilized nanofluids showed this as well. 2- Thermal conductivity of applied nanofluids in this study as well as all published experimental results showed an upward trend with increasing temperature and nanoparticle concentration. 3- Two correlations versus concentration, temperature and nanoparticle type to predict the thermal conductivity and viscosity of any kind of oil based nanofluids have been introduced. It is clear that the results of these correlations would be better, if the experimental studies on thermophysical properties of various kind of oil based nanofluids are studied further.
Page 14 of 33
4- Newtonian to non- Newtonian behavior of utilized nanofluids in temperature of 35 ºC was observed in all three weight fractions. Acknowledgements: The authors would like to express their thanks to the PNF Company for providing the laboratory to produce the nanofluids and Iranian Nanotechnology Initiative (INI) for providing the financial support for the present work.
References: [1] Anoop KB, Kabelac S, Sundararajan T, Das SK. Rheological and flow characteristics of nanofluids: influence of electroviscous effects and particle agglomeration. J Appl Phys 2009; 106:034909. [2] Nguyen CT, Desgranges F, Roy G, Galanis N, Mare T, Boucher S, et al. Temperature and particle- size dependent viscosity data for water- based nanofluids– hysteresis phenomenon. Int J Heat Fluid Flow 2007; 28:1492–506. [3] Kavitha T, Rajendran ADAA. Heat transfer enhancement using nanofluids and innovative methods- an overview. Int J Mech Eng Tech 2012; 3:769–82. [4] Pak BC, Cho YI. Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp Heat Transf 1998; 11:151–70. [5] Prasher R, Song D, Wang J, Phelan P. Measurements of nanofluid viscosity and its implications for thermal applications. Appl Phys Lett 2006; 89: 133108. [6] Tavman I, Turgut A, Chirtoc M, Schuchmann H, Tavman S. Experimental investigation of viscosity and thermal conductivity of suspensions containing nanosized ceramic particles. Arch Mat Sci 2008: 100. [7] Duangthongsuk W, Wongwises S. Measurement of temperature- dependent thermal conductivity and viscosity of TiO2- water nanofluids. Exp Therm Fluid Sci 2009; 33:706-14.
Page 15 of 33
[8] Timofeeva EV, Gavrilov AN, Mc Closkey JM, Tolmachev YV, Sprunt S, Lopatina LM, et al. Thermal conductivity and particle agglomeration in alumina nanofluids: experiment and theory. Phys Rev E 2007;76:061203. [9] Fakoor Pakdaman M, Akhavan-Behabadi MA, Razi P (2012) An experimental investigation on thermo-physical properties and overall performance of MWCNT/heat transfer oil nanofluid flow inside vertical helically coiled tubes. Exp. Thermal and Fluid Sci. 40: 103-111. [10] Saeedinia M, Akhavan-Behabadi MA, Razi P (2012) Thermal and rheological characteristics of CuO– Base oil nanofluid flow inside a circular tube Int. ommunications in Heat and Mass Transfer 39(1): 152 -159. [11] Madhusree Kole, T.K. Dey (2013) Enhanced thermophysical properties of copper nanoparticles dispersed in gear oil, Applied Thermal Engineering 56:45-53. [12] M. Nabeel Rashin, J. Hemalatha (2013) Synthesis and viscosity studies of novel ecofriendly ZnO–coconut oil nanofluid, Experimental Thermal and Fluid Science 51: 312– 318. [13] Ehsan-o-llah Ettefaghi, Alimorad Rashidi , Hojjat Ahmadi, Seyed Saeid Mohtasebi, Mahnaz Pourkhalil (2013) Thermal and rheological properties of oil-based nanofluids from different carbon nanostructures, International Communications in Heat and Mass Transfer 48: 178-182. [14] Ettefaghi Eol, Ahmadi H, Rashidi Amideddin Nouralishahi A, Mohtasebi S S (2013) Preparation and thermal properties of oil-based nanofluid from multi-walled carbon nanotubes and engine oil as nano-lubricant. Int. Communications in Heat and Mass Transfer, 46: 142–147.
Page 16 of 33
[15] Wang B, Wang X, Lou W, Hao J (2012) Thermal conductivity and rheological properties of graphite/oil nanofluids. Colloids and Surfaces A: Physicochemical and Eng. Asp. 414:125– 131. [16] Madhusree Kole, T K D. (2011) Effect of aggregation on the viscosity of copper oxidegear oil nanofluids, Int. J. Therm. Sci.
: 1741–1747.
[17] Maxwell JC (1881) A Treatise on Electricity and Magnetism. Second edition, Clarendon Press, UK. [18] Murshed SMS, Leong KC, Yang C (2005) Enhanced thermal conductivity of TiO2– water based nanofluids” Int. j Thermal Sci. 44(4):
7–373.
[19] Turian M, Sung DJ, Hsu F L (1991) Thermal conductivity of granular coals, coal-water mixtures and multi-solid/liquid suspensions. Fuel. 70:1157–1172 . [20] W. Yu, S.U.S. Choi, The role of interfacial layers in enhanced thermal conductivity of nanofluids: a renovated Maxwell model, J. Nanopart. 5 (2003) 167–171. [21] Einstein A. Eine neue bestimmung dermoleküldimensionen. Ann Phys 1906; 324:289– 306. [22] Brinkman H. The viscosity of concentrated suspensions and solutions. J Chem Phys 1952; 20571–571. [23] Chen H, Ding Y, Tan C. Rheological behaviour of nanofluids. New J Phys 2007; 9:367. [24] Lundgren TS. Slow flow through stationary random beds and suspensions of spheres. J Fluid Mech 1972; 51: 273–99. [25] Wang X, Xu X, Choi SUS. Thermal conductivity of nanoparticle – fluid mixture. J Thermophys Heat Transf 1999; 13: 474–80.
Page 17 of 33
[26] Abedian B, Kachanov M. On the effective viscosity of suspensions. Int J Eng Sci 2010; 48: 962–5. [27] ISO, 14887: 2000(E): Sample preparation dispersing procedures for powders in liquids, International Organization for Standardization, Geneva, Switzerland, 2000. [28] Y. Liu, Y. Liu, P. Hu, X. Li, R. Gao, Q. Peng, L. Wei, (2015) The effects of graphene oxide nanosheets and ultrasonic oscillation on the supercooling and nucleation behavior of nanofluids PCMs, Microfluid. Nanofluid. 18 (1) 81–89. [29] J.-H. Lee, K.S. Hwang, S.P. Jang, B.H. Lee, J.H. Kim, S.U. Choi, C.J. Choi, (2008) Effective viscosities and thermal conductivities of aqueous nanofluids containing low volume concentrations of Al2O3 nanoparticles, Int. J. Heat Mass Transfer 51 (11) 2651–2656. [30] Elena V. Timofeeva , Michael R. Moravek , Dileep Singh (2011) Improving the heat transfer efficiency of synthetic oil with silica nanoparticles, Journal of Colloid and Interface Science 364: 71–79. [31] Madhusree Kole, T.K. Dey (2011) Role of interfacial layer and clustering on the effective thermal conductivity of CuO–gear oil nanofluids. Exp. Thermal and Fluid Science 35: 1490–1495.
Page 18 of 33
Fig. 1 PNC1K device
Fig. 2. TEM image of Ag/ heat transfer oil nanofluid.
Page 19 of 33
Fig.3. Absolute zeta potential of Ag/ heat transfer oil nanofluids as a function of weight concentration
Page 20 of 33
Fig.4. Thermal conductivity of Ag- heat transfer oil nanofluids
Page 21 of 33
Fig.5. Agreement between different models and experimental data of thermal conductivity.
Fig.6. Relative viscosity of different models of thermal conductivity.
Page 22 of 33
Fig.7. Viscosity vs. shear rate of heat transfer oil
Fig.8. Viscosity vs. shear rate of Ag/ heat transfer oil nanofluid with 0.12% wt.
Page 23 of 33
Fig.9. Viscosity vs. shear rate of Ag/ heat transfer oil nanofluid with 0.36% wt.
Fig.10. Viscosity vs. shear rate of Ag/ heat transfer oil nanofluid with 0.72% wt.
Page 24 of 33
Fig.11. Shear stress vs. shear rate of Ag/ heat transfer oil nanofluids at
C.
Fig.12. Temperature dependence of the viscosity of Ag/ heat transfer oil nanofluids
Page 25 of 33
Fig. 13. Agreement between different models and experimentaldata of viscosity of oil based nanofluids.
Fig. 14. Relative deviation of different models.
Page 26 of 33
Table 1. Operational characteristics of the PNC1K in this study MODEL
PNC1k
Deviation
Output Voltage
0.5-1 kV
28 V
Input Power
1P 220VAC 500 W
±2 W
Shot Period
1-5 sec
0.1 s
Max. Diameter of Wire
0.25 mm
±0.01mm
Exploding Wire Length
1-5 mm
0.1 mm
Output Wire
Ag
Average Particle Size
15-25 nm
±3 nm
Table . Models for the effective thermal conductivity of nanofluids. Model
Equation
Number
Fakoor Pakdaman et al.
(3)
[9] Maxwell [17]
(4)
Murshed et al. [18]
(5)
Yu et al. [20]
(6)
Turian et al. [19]
(7)
∆= [(
,
α=
,
β=
Page 27 of 33
Table 3. Predicted values of thermal conductivity using the present correlation and other models. Turian Experiment
Exp.
Proposed
Fakoor Pakdaman
Murshed et
Maxwell
Yu et al.
al. Model
Model
Model
et al. Condition
Data
Correlation
et al. Model Model
Ag, T=40oC, 0.14
0.136
0.148
0.148
0.143
0.138
0.144
0.141
0.139
0.149
0.147
0.142
0.137
0.143
0.143
0.145
0.152
0.145
0.14
0.136
0.141
0.149
0.154
0.157
0.143
0.137
0.133
0.139
0.142
0.138
0.149
0.182
0.159
0.139
0.164
0.144
0.141
0.152
0.181
0.158
0.138
0.163
0.145
0.147
0.157
0.179
0.156
0.136
0.16
0.152
0.156
0.164
0.176
0.153
0.134
0.158
0.143
0.147
0.151
0.407
0.282
0.142
0.189
0.145
0.15
0.161
0.405
0.281
0.141
0.188
0.149
0.156
0.171
0.401
0.278
0.139
0.188
φ= . 11% ol. Ag, T=50oC, φ= . 11% ol. Ag, T=70oC, φ= . 11% ol. Ag, T=100oC, φ= . 11% ol.
Ag, T=40oC, φ= . 44% ol. Ag, T=50oC, φ= . 44% ol. Ag, T=70oC, φ= . 44% ol. Ag, T=100oC, φ= . 44% ol.
Ag, T=40oC, φ= .171% ol. Ag, T=50oC, φ= .171% ol. Ag, T=70oC, φ= .171% ol.
Page 28 of 33
Ag, T=100oC, 0.157
0.164
0.183
0.396
0.273
0.137
0.188
φ= .171% ol.
Table 4.Published thermal conductivity of MWCNT based heat transfer oil nanofluid [9] and their predictions through Eq. (2). Thermal Conductivi
Calculated
ty of
Value, Eq. (2)
Experiment's Conditions
Deviation
Ref.
Nanofluid MWCNT, 0.07% Vol., T= 40 oC
0.138
0.134
2.9%
[9]
MWCNT, 0.07% Vol., T= 50 oC
0.141
0.137
2.8%
[9]
MWCNT, 0.07% Vol., T= 60 oC
0.142
0.14
1.4%
[9]
MWCNT, 0.07% Vol., T= 70 oC
0.143
0.143
0
[9]
MWCNT, 0.14% Vol., T= 40 oC
0.14
0.139
0.7%
[9]
MWCNT, 0.14% Vol., T= 50 oC
0.143
0.142
0.7%
[9]
MWCNT, 0.14% Vol., T= 60 oC
0.146
0.145
0.7%
[9]
MWCNT, 0.14% Vol., T= 70 oC
0.149
0.148
0.6%
[9]
MWCNT, 0.29% Vol., T= 40 oC
0.144
0.149
3.5%
[9]
MWCNT, 0.29% Vol., T= 50 oC
0.148
0.152
2.7%
[9]
MWCNT, 0.29% Vol., T= 60 oC
0.15
0.154
2.6%
[9]
MWCNT, 0.29% Vol., T= 70 oC
0.152
0.157
3.3%
[9]
Page 29 of 33
Table 5. Calculated
values of published thermal conductivity ratio. Thermal Thermal Conductivity
Experiment's Conditions
Calculated
Conductivity
Deviation
Ref.
Value,
Ratio of of Base fluid Nanofluid Cu- Gear oil, 0.11% Vol. T= 10 oC
1.01
0.14
0.98
2.9%
[11]
Cu- Gear oil, 0.11% Vol. T= 20 oC
1.02
0.139
0.99
2.9%
[11]
Cu- Gear oil, 0.11% Vol. T= 30 oC
1.03
0.139
1.02
1%
[11]
Cu- Gear oil, 0.11% Vol. T= 40 oC
1.04
0.138
1.04
0
[11]
Cu- Gear oil, 0.11% Vol. T= 50 oC
1.05
0.137
1.06
0.9%
[11]
Cu- Gear oil, 0.11% Vol. T= 60 oC
1.053
0.136
1.08
3.1%
[11]
Cu- Gear oil, 0.57% Vol. T= 10 oC
1.08
0.14
1.17
8.3%
[11]
Cu- Gear oil, 0.57% Vol. T= 20 oC
1.09
0.139
1.19
9.2%
[11]
Cu- Gear oil, 0.57% Vol. T= 30 oC
1.11
0.139
1.21
9%
[11]
Cu- Gear oil, 0.57% Vol. T= 40 oC
1.11
0.138
1.23
10.8%
[11]
Cu- Gear oil, 0.57% Vol. T= 50 oC
1.12
0.137
1.26
12.5%
[11]
Cu- Gear oil, 0.57% Vol. T= 60 oC
1.13
0.136
1.28
13.3%
[11]
Cu- Gear oil, 2% Vol. T= 10 oC
1.2
0.14
1.24
3.3%
[11]
Cu- Gear oil, 2% Vol. T= 20 oC
1.22
0.139
1.25
4%
[11]
Cu- Gear oil, 2% Vol. T= 30 oC
1.24
0.139
1.27
2.4%
[11]
Cu- Gear oil, 2% Vol. T= 40 oC
1.25
0.138
1.29
3.2%
[11]
Cu- Gear oil, 2% Vol. T= 50 oC
1.26
0.137
1.31
4%
[11]
Cuo- Gear oil, 0.005% Vol. T= 10 oC
1.01
0.14
1.003
0.7%
[31]
Page 30 of 33
Cuo- Gear oil, 0.005% Vol. T= 20 oC
1.02
0.139
1.03
1%
[31]
Cuo- Gear oil, 0.005% Vol. T= 30 oC
1.021
0.139
1.06
3.2%
[31]
Cuo- Gear oil, 0.005% Vol. T= 40 oC
1.022
0.138
1.08
4.7%
[31]
Cuo- Gear oil, 0.005% Vol. T= 50 oC
1.028
0.137
1.11
8.1%
[31]
Cuo- Gear oil, 0.005% Vol. T= 60 oC
1.025
0.136
1.13
10.2%
[31]
Cuo- Gear oil, 0.005% Vol. T= 70 oC
1.03
0.134
1.15
11.6%
[31]
Cuo- Gear oil, 0.015% Vol. T= 10 oC
1.05
0.14
1.01
3.8%
[31]
Cuo- Gear oil, 0.015% Vol. T= 20 oC
1.052
0.139
1.04
1.4%
[31]
Cuo- Gear oil, 0.015% Vol. T= 30 oC
1.058
0.139
1.06
0.2%
[31]
Cuo- Gear oil, 0.015% Vol. T= 40 oC
1.063
0.138
1.09
2.5%
[31]
Cuo- Gear oil, 0.015% Vol. T= 50 oC
1.066
0.137
1.12
5%
[31]
Cuo- Gear oil, 0.015% Vol. T= 60 oC
1.069
0.136
1.15
7.6%
[31]
Cuo- Gear oil, 0.015% Vol. T= 70 oC
1.074
0.134
1.17
8.9%
[31]
Cuo- Gear oil, 0.025% Vol. T= 10 oC
1.08
0.14
1.02
5.5%
[31]
Cuo- Gear oil, 0.025% Vol. T= 20 oC
1.09
0.139
1.05
3.7%
[31]
Cuo- Gear oil, 0.025% Vol. T= 30 oC
1.1
0.139
1.07
2.7%
[31]
Cuo- Gear oil, 0.025% Vol. T= 40 oC
1.105
0.138
1.10
0.4%
[31]
Cuo- Gear oil, 0.025% Vol. T= 50 oC
1.108
0.137
1.13
2%
[31]
Cuo- Gear oil, 0.025% Vol. T= 60 oC
1.112
0.136
1.16
4.3%
[31]
Cuo- Gear oil, 0.025% Vol. T= 70 oC
1.12
0.134
1.18
5.3%
[31]
Cuo- oil, 0.13% Vol. T= 24 oC
1.02
0.141
1.023
0.3%
[10]
Cuo- oil, 0.13% Vol. T= 30 oC
1.04
0.139
1.046
0.6%
[10]
Cuo- oil, 0.13% Vol. T= 38 oC
1.08
0.138
1.086
0.5%
[10]
Page 31 of 33
Cuo- oil, 0.13% Vol. T= 48 oC
1.10
0.137
1.114
1.3%
[10]
Cuo- oil, 0.13% Vol. T= 60 oC
1.13
0.136
1.15
1.8%
[10]
Cuo- oil, 0.13% Vol. T= 70 oC
1.15
0.135
1.18
2.6%
[10]
Cuo- oil, 0.27% Vol. T= 24 oC
1.04
1.06
1.9%
[10]
Cuo- oil, 0.27% Vol. T= 30 oC
1.06
0.139
1.07
0.9%
[10]
Cuo- oil, 0.27% Vol. T= 38 oC
1.095
0.138
1.09
0.4%
[10]
Cuo- oil, 0.27% Vol. T= 48 oC
1.12
0.137
1.137
1.5%
[10]
Cuo- oil, 0.27% Vol. T= 60 oC
1.15
0.136
1.18
2.6%
[10]
Cuo- oil, 0.27% Vol. T= 70 oC
1.17
0.135
1.196
2.2%
[10]
0.141
Table 6. The most popular models for predicting viscosity of nanofluids in literature. Model n f b f (1 2 .5 )
nf
1906
Einstein [21]
1952
Brinkman [22]
1972
Lundgren [24]
1999
Wang et al. [25]
2007
Chen et al. [23]
2010
Abedian et al.
2 .5
(11)
n f b f (1 2 .5 6 .2 5 ) 2
n f b f (1 7 .3 1 2 3 )
(12)
2
(13)
n f b f (1 1 0 .6 (1 0 .6 ) ) 2
nf
Ref.
(10)
bf (1 )
Year
bf (1 2 .5 ) (15)
(14)
[26]
Page 32 of 33
Page 33 of 33