Latest developments on the viscosity of nanofluids
Introduction
Nanofluid is a new dimensional thermo fluid term emerged after the pioneering work by Choi [1]. Nanofluid is a solid–liquid mixture which consists of nanoparticles and a base liquid. Nanoparticles are basically metal (Cu, Ni, Al, etc.), oxides (Al2O3, TiO2, CuO, SiO2, Fe2O3, Fe3O4, BaTiO3, etc.) and some other compounds (AlN, SiC, CaCO3, graphene, etc.) and base fluids usually include water, ethylene glycol, propylene glycol, engine oil, etc. Due to very small sizes and large specific surface areas of the nanoparticles, nanofluids have superior properties like high thermal conductivity, minimal clogging in flow passages, long-term stability, and homogeneity [2]. Conventional fluids such as ethylene glycol (EG), water and oil have poor heat transfer properties but their vast applications in power generation, chemical processes, heating and cooling processes, transportation, electronics, automotive and other micro-sized applications make the re-processing of those thermo fluids to have better heat transfer properties quite essential.
Viscosity describes the internal resistance of a fluid to flow and it is an important property for all thermal applications involving fluids [3]. The pumping power is related with the viscosity of a fluid. In laminar flow, the pressure drop is directly proportional to the viscosity. Furthermore, convective heat transfer coefficient is influenced by viscosity. Hence, viscosity is as important as thermal conductivity in engineering systems involving fluid flow [4]. There has been a lot of research done about nanofluids recently but most of them are related with the heat transfer properties having different contents including heat transfer enhancement [5], [6], [7], thermal conductivity measurement [8], [9], [10], thermal conductivity enhancement [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], effective thermal conductivity [22], [23], [24], [25], [26], [27], [28], thermal conductivity of suspensions [29], [30], [31], thermal properties enhancement [32], thermal transport [33], thermal conductivity improvement [34], estimation of thermal conductivity [35], and others [36], [37], [38], [39], [40], [41], [42]. Some review papers [43], [44] emphasized only the thermal conductivity of nanofluids. Recently some new issues have been introduced in literatures like thermal diffusion coefficient of nanofluid [45], slip mechanisms in nanofluids [46], electrical conductivity of nanofluids [47], nanofluids for cooling of electronic devices [48]. Very few researches have been performed on the viscosity of nanofluids although viscosity seems to be a significant property and viscosity should be taken into consideration for heat transfer performance studies of a nanofluid [49], [50].
Some articles have been published considering rheological behavior of nanofluids such as viscosity. First, Masuda et al. [51] measured the viscosity of some water-based nanofluids for Al2O3, SiO2 and TiO2. Then Pak and Cho [52] presented some additional data for Al2O3/water nanofluid. Some parameters like, temperature, particle size and shape, volume concentrations have shown to have a great effect over viscosity of nanofluid. Murshed et al. [53] measured the volumetric effect on viscosity for Al2O3 and TiO2 with deionized water (DIW) and concluded that viscosity increases about 82% and 86%, respectively, for 5 vol.% of Al2O3 and TiO2. Chen et al. [54] measured the volume fraction and temperature effects on viscosity for multi walled carbon nanotubes (MWCNT’s) with distilled water for a temperature range of 5 °C to 65 °C. They reported that viscosity increases accordingly with nanoparticle loadings when the volume fraction is higher than 0.4 vol.%. Also, relative viscosity increases significantly with temperature after 55 °C. But, Prasher et al. [55] and Chen et al. [56], [57] have presented a contradictory report including that nanofluid viscosity is independent of temperature. He et al. [58] measured TiO2-distilled water nanofluid viscosity for different concentrations and for three different particle sizes and stated that viscosity increases with the increase of particle size as well as the increase in volume concentrations. However, some others [59], [60], [61] found that viscosity decreases with the increase of particle size. Prasher et al. [55] reported that, nanofluid viscosity is not a strong function of nanoparticle diameter. Table 1 shows a list including investigations about temperature, particle size and volume concentration effects over viscosity of nanofluids.
Available literature shows that most of the researches done mainly consider the volume concentration effect on viscosity and few literatures discussed these three effects for viscosity, yet along with some contradictions among them. No review paper is available that would include all temperature, particle size and volume concentration effects over viscosity of a nanofluid. Some review papers discussed the viscosity of nanofluid but actually emphasized the thermal conductivity of nanofluids plus they did not discuss all the aspects of viscosity of these fluids. Studies like that by Ghadimi et al. [62] discussed the analytical model, Daungthongsuk and Wongwises [63] and Keblinski et al. [64] emphasized viscosity for convective heat transfer, Das et al. [65] mentioned the importance of studying the viscosity of nanofluids, and Murshed et al. [66] emphasized the volumetric concentration effect on viscosity. In a review paper, Ramesh and Prabhu [67] summarize some papers in a single paragraph about viscosity of nanofluids. Also, Sridhara and Satapathy brief about the viscosity of some Al2O3 based nanofluids [68]. A comparison of viscosity enhancement for some nanofluids has been reported in literature [69], which are not sufficient. Therefore, a complete study considering all aspects of the viscosity of a nanofluid seems to be required in this field. The purpose of this article is to provide the available information about temperature, particle diameter and volume concentration effects over viscosity of a nanofluid.
In the subsequent sections preparation methods used by the researchers, experimental results concerning temperature, particle size and volume fraction effects on viscosity, theoretical models (including conventional model of viscosity for suspensions) and correlations for volume concentrations, temperature and particle diameter for viscosity have been described consecutively.
Section snippets
Preparation methods
Preparation of nanofluids is quite of importance to be known for measuring viscosity of nanofluids since particle agglomeration depends on the preparation method of a nanofluid. Nanofluids preparation is not as simple as mixing some solid nanoparticles in a base fluid. There are two techniques mainly used for synthesizing nanofluids: single step method and two step method.
In a single step method [27], [98], both preparation of nanoparticles and synthesis of nanofluids are done in a combined
Effect of temperature
Some literature is available about the temperature effect over nanofluids viscosity. Yang et al. [77] experimentally measured temperature effect of viscosity with four temperatures (35, 43, 50 and 70 °C) for four nanofluid solutions taking graphite as nanoparticles. They experimentally showed that kinematic viscosity decreases with the increase of temperature and interesting observations were made such as: the corresponding viscosity of 2 wt% graphite with ATF at 35 and 70 °C is found to be 41.4
Theoretical investigations
There are some existing theoretical formulas to estimate the particle suspension viscosities. Among them equation suggested by Einstein [110] could be labeled the pioneer one and most of other derivations have been basically established from this relation. His assumptions are based on linear viscous fluid containing dilute, suspended, spherical particles and low particle volume fractions (ϕ < 0.02). The suggested formula is as follows:Here, μnf is the viscosity of suspension; μbf
Discussion
In this study, attempt has been made to cover all the investigations performed on the viscosity of nanofluids available in the literature. Through this study it is found that temperature, particle size & shape and volume fractions have significant effects over viscosity of nanofluids. Results indicate that viscosity increases as the particle volume fractions increase, and nanofluids behave in a Newtonian way for low particle volume concentrations. No existing model or correlation is capable of
Acknowledgements
The authors would like to acknowledge University of Malaya for financial support. This work is supported by Fundamental Research Grant Scheme (FRGS) fund (Project No. FP017/2010B, FRGS) and Postgraduate Research Grant (PPP) (No. PV013/2011A).
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