- Nano Review
- Open Access
Thermal conductivity and viscosity measurements of ethylene glycol-based Al2O3 nanofluids
© Pastoriza-Gallego et al; licensee Springer. 2011
Received: 30 October 2010
Accepted: 15 March 2011
Published: 15 March 2011
The dispersion and stability of nanofluids obtained by dispersing Al2O3 nanoparticles in ethylene glycol have been analyzed at several concentrations up to 25% in mass fraction. The thermal conductivity and viscosity were experimentally determined at temperatures ranging from 283.15 K to 323.15 K using an apparatus based on the hot-wire method and a rotational viscometer, respectively. It has been found that both thermal conductivity and viscosity increase with the concentration of nanoparticles, whereas when the temperature increases the viscosity diminishes and the thermal conductivity rises. Measured enhancements on thermal conductivity (up to 19%) compare well with literature values when available. New viscosity experimental data yield values more than twice larger than the base fluid. The influence of particle size on viscosity has been also studied, finding large differences that must be taken into account for any practical application. These experimental results were compared with some theoretical models, as those of Maxwell-Hamilton and Crosser for thermal conductivity and Krieger and Dougherty for viscosity.
Improving the efficiency of energy production and consumption has undoubtedly become one of the most important global problems that will have to be faced during the next decades. Some of the particular concerns related with this main problem include the quantification and control of global climate change due to the emissions of greenhouse gases, or the expected decline in global oil production . Considering the rapid increase in energy demand worldwide, intensifying heat transfer processes and reducing energy losses due to ineffective use have become increasingly important tasks. Nanoscience and nanotechnology are expected to play a significant role in revitalizing the traditional energy industries and stimulating the emerging renewable energy industries [2, 3]. Nanofluids, in which nano-sized particles are suspended in liquids, have emerged as a potential candidate for the tailoring and production of heat transfer fluids. It is known that these new fluids enhance thermal conductivity of the base liquid, although the underlying nature of this effect still remains controversial. Moreover, nanofluids were found to be very stable due to the small size of the particles and the small volume fraction of the particles needed for heat transfer enhancement .
When the nanoparticles are properly dispersed, nanofluids can offer numerous benefits [5–7] besides the anomalously high effective thermal conductivity, such as improved heat transfer and stability, microchannel cooling without clogging, the possibility of miniaturizing systems scalings, or reduction in pumping power, among others. Thus, nanofluids have a wide range of industrial, engineering, and medical applications in fields ranging from transportation, micromechanics, heating, ventilating and air-conditioning systems, biomolecules trapping, or enhanced drug delivery [3, 8].
When studying this type of systems, one of the variables that must be considered carefully in first place is the sample polydispersity because usually, the average particle size values declared to characterize samples are only rough approximations, and definitely, a non-negligible size distribution is always present for real samples, producing noticeable changes in thermal behavior. Once the dry nanoparticles are well characterized, the stability of the suspensions must then be ensured. The measurement of zeta potential and the use of UV/Vis spectrophotometry represent reliable probes to quantify stability [9–11]. Usually, the dispersion in the base fluid is obtained using techniques such as mechanical stirring, ultrasound probes, or the combination of both, but also in this case, there are no clear guidelines about the most reliable method to achieve stability and avoid sedimentation. The recommended sonication times vary for the same nanofluid according to different authors, and the effect on the size and distribution of aggregates is seldom discussed [12, 13]. Visual technique controls may be discarded in this context for their lack of reproducibility.
Although the determination of thermal conductivity has focused most efforts, it is believed that viscosity is as critical as thermal conductivity in engineering systems that entail fluid flow [8, 14–16]. Pumping power is proportional to the pressure drop, which in turn is related to fluid viscosity. In laminar flow, the pressure drop is directly proportional to the viscosity. Both viscosity and thermal conductivity of nanofluids are known to undergo anomalous enhancements, but more thorough investigations should be carried out on these properties because a good deal of controversy and remarkable inconsistencies have been reported in this emerging subject . The monograph published by Das et al.  represents a reference study about nanofluids, including a wide literature survey, which is indicative of the efforts done in the last few years. A recent collective study  intended to establish a benchmark for thermal conductivity measurements by comparing the results obtained from a common sample delivered to many reference laboratories. The results yielded differences between 5% and 10% for data of water and PAO-based samples from different sources. In other recent studies concerning thermophysical characterization of nanofluids, Das et al.  and Eastman et al.  presented a good account about nanotubes and the role of the contact resistance in the thermal transport of nanofluids, besides addressing the issues about thermal conductivity and viscosity of oxide nanoparticle-based and metallic nanofluids. Wang and Mujumdar  presented an overview focused on heat transfer characteristics using nanofluids, and Murshed et al.  remarked that it is imperative to conduct detailed research in order to confirm the effects of particle size, shapes, clustering of particles, and temperature on the effective thermal conductivity of a wide range of nanofluids and added that it is necessary to develop more comprehensive models, based on first principles, with the aim of accounting for the enhanced thermal conductivity of nanofluids. Li et al.  also discussed the preparation and characterization of nanofluids, a subject that unfortunately has not received the necessary attention so far but plays a key role. Wen et al.  and Murshed et al.  insisted on the need of studies about other properties such as viscosity, wetting behavior, thermal diffusivity, convective heat transfer coefficients, and viscosity; finally, Özerinç et al.  summarized the research in nanofluid thermal conductivity from experimental and theoretical investigations.
In this general context, the objective of this article was to study nanofluids composed by alumina (Al2O3) nanoparticles dispersed in ethylene glycol in a concentration ranging up to 25% in weight fraction. Two different sets of samples were considered, one of them obtained from dispersion of different brands of commercial dry nanopowder and the second obtained from dispersion of a dry nanopowder obtained by centrifuged and dried of a commercial dispersion. The characteristics of the dry powder, stability, size distribution, and Z potential are discussed in each case. Then, the thermal conductivity and viscosity of the nanofluids have been determined experimentally between 283.15 K and up to 323.15 K.
From a theoretical point of view, it was Maxwell  who first proposed a theory to account for the enhancement produced in the thermal conductivity of a fluid by the presence of suspended colloidal particles. Unfortunately, the classical models on suspensions give an insufficient understanding of the formulation and thermophysical profile of nanofluids, thus limiting their potential applications. Although it is widely agreed now that the initial thermal conductivity enhancements reported were by far too optimistic, a reliable theory connecting the molecular structure and the macroscopic transport properties of nanofluids is not available yet, so a considerable effort for the determination of accurate and reproducible experimental data for this type of suspensions is essential. The results presented in this work have been compared with other reported experimental values and with various theoretical models proposed for the prediction of the thermal conductivity and viscosity of nanofluids. Concerning experimental and theoretical studies on alumina nanoparticles dispersed in ethylene glycol, the works studying the effect of temperature by Timofeeva et al.  and Beck et al. [25–27] must be cited. Alternatively, Beck et al.  have studied the effect of particle size on thermal conductivity and Timofeeva et al. [24, 29] considered the effect of particle shape and pH on this property and also on viscosity, from both experimental and theoretical perspectives. Timofeeva et al. have drawn attention on the fact that evaluation of nanofluids for a particular application requires proper understanding of all their characteristics and thermophysical properties of nanoparticle suspensions.
Sample preparation and characterization
Two sets of different samples of ethylene glycol-based Al2O3 nanofluids were used. The first of them, S1, was prepared by dispersing dry Al2O3 nanoparticles in ethylene glycol (Aldrich, St. Louis, MO, USA, 99%). The nanoparticles were supplied by Nanophase, with a declared diameter distribution D = 40-50 nm and a crystal phase composition of 70:30 γ and δ phases, respectively. Samples S2 were prepared using Al2O3 nanoparticles supplied by Aldrich dispersed in water (10% weight fraction), with a limiting value of D < 20 nm. This original dispersion was centrifuged and washed repeatedly with absolute ethanol, and the obtained solid was dried and redispersed in ethylene glycol. The powder sample was in every case dispersed into a predetermined volume of the base fluid to obtain the desired weight fraction. Values up to 20 wt.% for viscosity, and up to 25% for thermal conductivity measurements were prepared using a Mettler AE-240 electronic balance (Mettler-Toledo, Columbus, OH, USA), whose accuracy is 5 × 10-5 g.
As described in a previous work , the use of an ultrasonic homogenizer improves nanofluid stability over other alternatives available to disperse the nanoparticles, and so a (U.S.int) BandelinSonoplus HD 2200 was used (Bandelin Electronic, Berlin, Germany), with typical sonication times of 16 min. In order to check the morphology and size distribution of the fluid samples, transmission electron microscope technique was used . An estimate of the size distribution in each case was obtained using ImageTool freeware software http://www.digitalimagetool.com. The volume-weighted average diameter values computed were D = 43 ± 23 nm for S1 and D = 8 ± 3 nm for S2 . More details about sample preparation and characterizations are given in [10, 30].
Thermal conductivity and viscosity measurements of nanofluids
Once both samples have been adequately characterized, the following step is to determine the thermal conductivity and viscosity of the nanofluids. The transient hot-wire method was first suggested in 1931 to measure the absolute thermal conductivity, and ever since many authors have contributed to improve the method, making it more accurate. With the development of modern electronic instrumentation and use of a proper theoretical basis, this method has evolved to be one of the most accurate techniques of determining the thermal conductivity of fluids, including nanofluids [8, 31]. The advantage of this method is connected with its success to nearly completely avoid natural convection effects. In addition, this method is fast and its conceptual design is simple when compared to other techniques. Thermal conductivity data were measured in this case using the Decagon devices KD2 Pro Thermal Properties Analyzer (Decagon Devices Inc., Pullman, WA, USA). This apparatus meets the standards of ASTM D5334 and IEEE 442-1981 regulations. Its principle of measurement is based on the transient hot-wire source approach, and it has been used successfully for nanofluids by several authors [29, 32–34]. It basically comprises a readout unit and a single-needle sensor that is inserted into the fluid sample. The thermal probe (1.27-mm diameter, 60-mm length), containing a heating element and a thermoresistor, should be inserted into the sample vertically, rather than horizontally, with the aim of minimizing the possibility of inducing convection. The measurement is made by heating the probe within the sample while simultaneously monitoring the temperature change of the probe. A single reading generally takes 2 min. The first 90 s are used to ensure temperature stability, after which the probe is heated for 30 s using a controlled current intensity. The thermistor measures the changing temperature while the microprocessor stores the data. At the end of the reading, the thermal conductivity of the fluid is computed using the temperature difference versus time data based on a parameter-corrected version of the temperature model given by Carslaw and Jaeger  for an infinite line heat source with constant heat output and zero mass in an infinite medium. Before and after analysis of the nanofluid samples, the accuracy of the probe was carefully checked on pure water, ethylene glycol, and a standard sample of glycerol of well-known thermal conductivity. Approximately 15 cm3 of the sample to be analyzed was sealed in a glass sample vial. The probe was then inserted vertically into the sample via a purpose-made port in the lid of the vial. The sealed vial was then fully immersed in a temperature-controlled water bath, model Grant GD200, (Grant Instruments, Cambridge, UK), and allowed to thermostatize. Once the sample reached the required temperature, 15 more minutes were allowed to go before carrying out the measurement to ensure complete thermal equilibration. At least four measurements were taken at each temperature, with a delay of at least 15 min between each other, to ensure reproducibility. The uncertainty of the thermal conductivity was estimated from the standard deviations of experimental data and departures from literature values of the cited reference fluids, and was estimated to be lower than 3%.
Viscosity measurements of alumina nanofluids were performed using a Schott rotational viscometer (Cole Parmer, Vernon Hills, IL, USA), equipped with a spindle of coaxial cylindrical geometry (LCP) equipped with a stainless steel flow jacket. This viscometer is a controlled shear rate instrument. By using a multiple-speed transmission and interchangeable spindles, a variety of viscosity ranges can be measured, enhancing device versatility. Flow behavior of nanofluids was tested at a shear rate of 123 s-1. The LCP adaptor holds a sample volume of 16-18 ml and is connected to a PolyScience fluid circulation bath (PolyScience, Niles, IL, USA), that controls temperature measured inside the cell with a PT100 probe that ensures an uncertainty of 0.05 K. The estimated uncertainty in viscosity using this device is guaranteed to within ± 1%.
Results and discussion
Experimental thermal conductivity for ethylene glycol and water
k (W m-1 K-1)
k (W m-1 K-1)
Experimental values of the thermal conductivity of nanofluids based on EG (S1 samples)
knf (W m-1 K-1)
where knf, kp, and k0 stand for the thermal conductivity of the nanofluid, solid particles, and bulk liquid, respectively, and ϕ is the particle volume fraction (vol.%). For the thermal conductivity of the particles, we used tabulated values  for the bulk solid, kAl2O3 = 36 W m-1 K-1 (polycrystalline).
Many other models were proposed based on the traditional Maxwell formulation, considering the influence of factors as particle diameter, surface area, shape, Brownian motion, or solid/fluid interfacial effects. Wang and Mujumdar  extensively reviewed different nanofluid thermal conductivity theories, beginning with the adaptation by Hamilton and Crosser  of the classical Maxwell model.
The effects of solid/fluid interface are very important in suspensions. The nanolayer between the nanoparticles and the base fluid may be a dominant factor influencing the thermal conductivity of nanofluids. Current research on nanofluids indicates that the enhancement of thermal conductivity might be due to the ordered layering of liquid molecules near the solid particles, and some models taking this effect into account have been developed . Nevertheless, it is beyond the goal of this work to compare our experimental data with an extensive review of models. Moreover, as was pointed out elsewhere  for dilute concentrations, there is little difference between the classical Maxwell model and other more sophisticated theories.
Experimental viscosity values, η (mPa·s), for nanofluids based on EG constituted by S1 and S2 samples
Coefficients A, B, T0, and standard deviation, s, from Vogel-Fulcher-Tammann equation for S1 Al2O3/EG nanofluids at different volume concentration, ϕ
s (mPa s(
Coefficients A, B, T0, and standard deviation, s, from Vogel-Fulcher-Tammann equation for S2 Al2O3/EG nanofluids at different volume concentration, ϕ
s (mPa s)
where aa and a represent the average radius of the aggregates and single particles, respectively. This theory attributes the viscosity enhancement of a nanofluid only to the aggregation state of the nanoparticles. Assuming as Chen et al.  Newtonian behavior for EG-based nanofluids and the enhancement of the viscosity depending on particle concentration in a nonlinear manner but independent of temperature, we considered the size of the aggregates dependent on nanofluid concentration. Thus, a value of the ratio aa/a was computed in Equation 5 for each nanofluid concentration. This calculation offers ratio values from 3 to 4 for S1 samples, whereas these fitted parameters goes from 5.2 to 6.5 for S2 samples. The value of this parameter is always higher in S2 than in S1 sample, but this difference decreases when concentration rises. The goodness of this Equation is plotted in Figure 6, and deviations lower than experimental uncertainties are obtained, showing the suitability of the proposed theory to describe the viscosity for these EG-based nanofluids.
Finally, Equation 5 was applied using the size of the aggregates as independent of the nanofluid concentration. This way, when this equation is fitted to experimental viscosities of this work, ratios of aa/a of 3.2 and 5.5 are found for S1 and S2, respectively, yielding viscosity absolute average deviations of 3% and 2% for both fluids. According to this theory, the aggregation phenomenon is more relevant for smaller particles dispersions as it has been found to occur as the result of this calculation. The results from Equation 5 using only one parameter for all S1 and S2 samples are also plotted in Figure 6. With this model, aggregation alone might not be enough to describe as well the behavior of viscosity at higher concentrations, so in this case, other variables should be taken into account.
Thermal conductivities and viscosities of Al2O3 in ethylene glycol nanofluids have been determined experimentally as a function of volume concentration and temperature. Two different types of samples were considered for viscosity, with nominal particle sizes of 43 and 8 nm, denoted here as S1 and S2, respectively, while S1 samples were considered for thermal conductivity studies. It has been found that the thermal conductivity and the viscosity increase with the concentration of nanoparticles, whereas when the temperature increases the viscosity diminishes and the thermal conductivity rises. Enhancements up to 19% and more than twice the value of the base fluid were found for thermal conductivity and viscosity, respectively. Viscosity increases as particle size decreases, following the expected classical behavior for dispersions. These large differences on viscosity depending on particle size must be taken into account for any practical application. We have used the Maxwell model to predict the thermal conductivities, finding that the Maxwell method overpredicts these experimental values. The Vogel-Tammann-Fulcher method was applied to the experimental viscosity data, finding good agreements and showing that this correlation with temperature is suitable also for nanofluids. Among the methods to describe the viscosity trend with the volume fraction of nanofluids, that from Krieger and Dougherty, which attributes the viscosity enhancement of a nanofluid only to the aggregation state of the nanoparticles, gives excellent results in this particular case, so here there is no need to consider the influence of other variables, as for instance sample polydispersity.
The authors acknowledge CACTI (Universidade de Vigo) for the technical assistance in microscopy techniques and the Ministerio de Educación y Ciencia (CTQ2006-15537-C02/PPQ) and Xunta de Galicia (PGIDIT07PXIB314181PR), Spain, for financial support. L.L. would like to acknowledge the financial support of the Ramon y Cajal Program from the Ministerio de Ciencia e Innovación (Spain).
- Smalley RE: Future global energy prosperity: The terawatt challenge. MRS Bull 2005, 30: 412. 10.1557/mrs2005.124View ArticleGoogle Scholar
- Wen DS, Lin G, Vafaei S, Zhang K: Review of nanofluids for heat transfer applications. Particuology 2009, 7: 141. 10.1016/j.partic.2009.01.007View ArticleGoogle Scholar
- Wen DS: Nanofuel as a potential secondary energy carrier. Energy Environ Sci 2010, 3: 591. 10.1039/b906384fView ArticleGoogle Scholar
- Das SK, Choi SUS, Yu W, Pradeep T: Nanofluids: Science and Technology. New York: Wiley; 2008.Google Scholar
- Choi SUS, Zhang ZG, Keblinski P: Nanofluids. In Encyclopedia of Nanoscience and Nanotechnology, 6. Edited by: Nalwa SH. New York: Scientific Publishers; 2004:757–773.Google Scholar
- Zussman S: New Nanofluids Increase Heat Transfer Capability. USA: Argonne National Laboratory; 1997:4.Google Scholar
- Wang L, Fan J: Nanofluids Research: Key Issues. Nanoscale Res Lett 2010, 5: 1241. 10.1007/s11671-010-9638-6View ArticleGoogle Scholar
- Murshed SMS, Leong KC, Yang C: Thermophysical and electrokinetic properties of nanofluids - A critical review. Appl Thermal Eng 2008, 28: 2109. 10.1016/j.applthermaleng.2008.01.005View ArticleGoogle Scholar
- Li X, Zhu D, Wang X: J Evaluation on dispersion behavior of the aqueous copper nano-suspensions. Colloid Interface Sci 2007, 310: 456. 10.1016/j.jcis.2007.02.067View ArticleGoogle Scholar
- Pastoriza-Gallego MJ, Casanova C, Páramo R, Barbés B, Legido JL, Piñeiro MM: A study on stability and thermophysical properties (density and viscosity) of Al2O3 in water nanofluid. J Appl Phys 2009, 106: 064301. 10.1063/1.3187732View ArticleGoogle Scholar
- Wang XQ, Mujumdar AS: Heat transfer characteristics of nanofluids: a review. Int J Therm Sci 2007, 46: 1. 10.1016/j.ijthermalsci.2006.06.010View ArticleGoogle Scholar
- Gharagozloo PE, Eaton JK, Goodson KE: Diffusion, aggregation, and the thermal conductivity of nanofluids. Appl Phys Lett 2008, 93: 103110. 10.1063/1.2977868View ArticleGoogle Scholar
- Prasher R, Evans W, Meakin P, Fish J, Phelan P, Keblinski P: Effect of aggregation on thermal conduction in colloidal nanofluids. Appl Phys Lett 2006, 89: 143119. 10.1063/1.2360229View ArticleGoogle Scholar
- Keblinski P, Eastman JA, Cahill DG: Nanofluids for thermal transport. Materials Today 2005, 8: 36. 10.1016/S1369-7021(05)70936-6View ArticleGoogle Scholar
- Eastman JA, Phillpot SR, Choi SUS, Keblinski P: Thermal transport in nanofluids. Annu Rev Mater Res 2004, 34: 219. 10.1146/annurev.matsci.34.052803.090621View ArticleGoogle Scholar
- Guo SZ, Li Y, Jiang JS, Xie HQ: Nanofluids Containing gamma-Fe(2)O(3) Nanoparticles and Their Heat Transfer Enhancements. Nanoscale Res Lett 2010, 5: 1222. 10.1007/s11671-010-9630-1View ArticleGoogle Scholar
- Keblinski P, Prasher R, Eapen J: Thermal conductance of nanofluids: is the controversy over? J Nanopart Res 2008, 10: 1089. 10.1007/s11051-007-9352-1View ArticleGoogle Scholar
- Buongiorno J, et al.: A benchmark study on the thermal conductivity of nanofluids. J Appl Phys 2009, 106: 094312. 10.1063/1.3245330View ArticleGoogle Scholar
- Das SK, Choi SUS, Patel HE: Heat transfer in nanofluids - A review. Heat Transfer Eng 2006, 27: 3. 10.1080/01457630600904593View ArticleGoogle Scholar
- Li Y, Zhou J, Tung S, Schneider E, Xi S: A review on development of nanofluid preparation and characterization. Powder Technology 2009, 196: 89. 10.1016/j.powtec.2009.07.025View ArticleGoogle Scholar
- Murshed SMS, Leong KC, Yang C: Investigations of thermal conductivity and viscosity of nanofluids. Int J Thermal Sci 2008, 47: 560. 10.1016/j.ijthermalsci.2007.05.004View ArticleGoogle Scholar
- Özerinç S, Kakaç S, Yazicioglu AG: Enhanced thermal conductivity of nanofluids: a state-of-the-art review. Microfluid Nanofluid 2010, 8: 145.View ArticleGoogle Scholar
- Maxwell JC: A Treatise on Electricity and Magnetism. 3rd edition. London: Oxford University Press; 1892.Google Scholar
- Timofeeva EV, Gavrilov AN, McCloskey JM, Tolmachev YV, Sprunt S, Lopatina LM, Selinger JV: Thermal conductivity and particle agglomeration in alumina nanofluids: Experiment and theory. Physical Review E 2007, 76: 061203. 10.1103/PhysRevE.76.061203View ArticleGoogle Scholar
- Beck MP, Sun T, Teja AS: The thermal conductivity of alumina nanoparticles dispersed in ethylene glycol. Fluid Phase Equilib 2007, 260: 275. 10.1016/j.fluid.2007.07.034View ArticleGoogle Scholar
- Beck MP, Yuan Y, Warrier P, Teja AS: The thermal conductivity of alumina nanofluids in water, ethylene glycol, and ethylene glycol + water mixtures. J Nanopart Res 2010, 12: 1469. 10.1007/s11051-009-9716-9View ArticleGoogle Scholar
- Teja AS, Beck MP, Yuan Y, Warrier P: The limiting behavior of the thermal conductivity of nanoparticles and nanofluids. J App Phys 2010, 107: 114319/1. 10.1063/1.3354094View ArticleGoogle Scholar
- Beck MP, Yuan Y, Warrier P, Teja AS: The effect of particle size on the thermal conductivity of alumina nanofluids. J Nanopart Res 2009, 11: 1129. 10.1007/s11051-008-9500-2View ArticleGoogle Scholar
- Timofeeva EV, Routbort JL, Singh D: Particle shape effects on thermophysical properties of alumina nanofluids. J App Phys 2009, 106: 014304. 10.1063/1.3155999View ArticleGoogle Scholar
- Pastoriza-Gallego MJ, Casanova C, Legido JL, Piñeiro MM: CuO in water nanofluid: influence of particle size and polydispersity on volumetric behaviour and viscosity. Fluid Phase Equilib 2010, 25: 188.Google Scholar
- Nagasaka Y, Nagashima A: Absolute measurement of the thermal conductivity of electrically conducting liquids by the transient hot-wire method. Journal of Physics E: Scientific Instruments 1981, 14: 1435. 10.1088/0022-3735/14/12/020View ArticleGoogle Scholar
- Mintsa HA, Roy G, Nguyen CT, Doucet D: New temperature dependent thermal conductivity data for water-based nanofluids. Int J Therm Sci 2009, 48: 363. 10.1016/j.ijthermalsci.2008.03.009View ArticleGoogle Scholar
- Wen D, Ding Y: Effective thermal conductivity of aqueous suspensions of carbon nanotubes (carbon nanotube nanofluids). J Thermophys Heat Transf 2004, 18: 481. 10.2514/1.9934View ArticleGoogle Scholar
- Nieto de Castro CA, Lourenço MJV, Ribeiro APC, Langa E, Vieira SIC, Goodrich P, Hardacre C: Thermal properties of ionic liquids and IoNanoFluids of imidazolium and pyrrolidinium liquids. J Chem Eng Data 2010, 55: 653. 10.1021/je900648pView ArticleGoogle Scholar
- Carslaw HS, Jaeger JC: Conduction of Heat in Solids. London: Oxford University Press; 1959:25.Google Scholar
- Lemmon EW, Huber ML, McLinden MO: REFPROP: NIST Reference Fluid Thermodynamic and Transport Properties. Version 8.0 (NIST, Gaithersburg) 2007.Google Scholar
- Wagner W, Pruss A: The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. J Phys Chem Ref Data 2002, 31: 387. 10.1063/1.1461829View ArticleGoogle Scholar
- Peñas JRV, Ortiz de Zárate JM, Khayet M: Measurement of the thermal conductivity of nanofluids by the multicurrent hot-wire method. J Appl Phys 2008, 104: 044314.View ArticleGoogle Scholar
- Sun T, Teja AS: Density, viscosity, and thermal conductivity of aqueous ethylene, diethylene, and triethylene glycol mixtures between 290 K and 450 K. J Chem Eng Data 2003, 48: 198. 10.1021/je025610oView ArticleGoogle Scholar
- DiGuilio R, Teja AS: Thermal conductivity of poly(ethylene glycols) and their binary mixtures. J Chem Eng Data 1990, 35: 117. 10.1021/je00060a005View ArticleGoogle Scholar
- LienhardIV JH, LienhardV JH: A Heat transfer textbook. Phlogiston Press Massachusetts; 2008.Google Scholar
- Assael MJ, Charitidou E, Avgoustiniatos S, Wakeham WA: Absolute measurements of the thermal conductivity of mixtures of alkene-glycols with water. Int J Thermophys 1989, 10: 1127. 10.1007/BF00500567View ArticleGoogle Scholar
- Wang X, Xu X, Choi SUS: Thermal conductivity of nanoparticle-fluid mixture. J Thermophys Heat Transfer 1999, 13: 474. 10.2514/2.6486View ArticleGoogle Scholar
- Hamilton RL, Crosser OK: Thermal conductivity of heterogeneous two-component systems. Ind Eng Chem Fundam 1962, 1: 187. 10.1021/i160003a005View ArticleGoogle Scholar
- Chen H, Ding Y, Tan C: Rheological behaviour of nanofluids. New J Phys 2007, 9: 367. 10.1088/1367-2630/9/10/367View ArticleGoogle Scholar
- Comuñas MJP, Bazile JP, Lugo L, Baylaucq A, Fernández J, Boned C: Influence of the molecular structure on the volumetric properties and viscosities of dialkyl adipates (dimethyl, diethyl, and diisobutyl adipates). J Chem Eng Data 2010, 55: 3697.View ArticleGoogle Scholar
- Prasher R, Song D, Wang J, Phelan P: Measurements of nanofluid viscosity and its implications for thermal applications. App Phys Lett 2006, 89: 133108. 10.1063/1.2356113View ArticleGoogle Scholar
- Lee DI: Packing of spheres and its effect on the viscosity of suspensions. J Paint Technol 1970, 42: 579.Google Scholar
- Einstein A: Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann Phys 1905, 17: 549. Eine neue Bestimmung der Moleküldimensionen Ann Phys 1906, 19:289; Berichtigung zu meiner Arbeit: "Eine neue Bestimmung der Moleküldimensionen" Ann Phys 1911, 34:591 Eine neue Bestimmung der Moleküldimensionen Ann Phys 1906, 19:289; Berichtigung zu meiner Arbeit: "Eine neue Bestimmung der Moleküldimensionen" Ann Phys 1911, 34:591 10.1002/andp.19053220806View ArticleGoogle Scholar
- Chow TS: Viscosities of concentrated dispersions. Phys Rev E 1993, 48: 1977. 10.1103/PhysRevE.48.1977View ArticleGoogle Scholar
- Krieger IM, Dougherty TJ: A Mechanism for Non-Newtonian Flow in Suspensions of Rigid Spheres. Trans Soc Rheol 1959, 3: 137. 10.1122/1.548848View ArticleGoogle Scholar
- Khayet M, Ortiz de Zárate JM: Application of the multi-current transient hot-wire technique for absolute measurements of the thermal conductivity of glycols. Int J Thermophys 2005, 26: 637. 10.1007/s10765-005-5568-4View ArticleGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.