A model for temperature and particle volume fraction effect on nanofluid viscosity Marziehsadat Hosseini, Sattar Ghader ⁎ Department of Chemical Engineering, College of Engineering, Shahid Bahonar University of Kerman, Jomhoori blvd., Post Code 76175, Kerman, Iran abstract article info Article history: Received 19 December 2009 Accepted 9 February 2010 Available online 14 February 2010 Keywords: Nanofluid Viscosity Local composition theory Eyring's theory A theory based model is presented for viscosity of nanofluids and evaluated over the entire range of temperature and volume fraction of nanoparticles. The model is based on Eyring's viscosity model and the nonrandom two liquid (NRTL) model for describing deviations from ideality (Eyring-NRTL model). The equation for viscosity is composed of a contribution due to nonrandom mixing on the local level and another energetic section related to the strength of intercomponent interactions which inhibit components from being removed from their most favorable equilibrium position in the mixture. The experimental data were used to evaluate existing models which do not contain adjustable parameters and Eyring-NRTL model. The Eyring-NRTL model was found to agree well with the experimental data with the restriction that contains adjustable parameters which were interactions in the form of NRTL constants. However, the agreement was even better if temperature dependent interaction parameters were used. Comparisons of predicted and actual viscosity over the entire temperature and volume fraction range illustrate an improvement over the conventional nanofluid viscosity models with 2.91% AAD. © 2010 Elsevier B.V. All rights reserved. 1. Introduction An innovative technique has been studied extensively in recent years in which nanoparticles are dispersed in a base fluid (nanofluid) for enhancing physical properties. In spite of their promising features, there are only few published results on nanofluids. A review of relevant works on nanofluid's viscosity may be found in [1–3]. Viscosity is important in designing nanofluids for flow and heat transfer applications because the pressure drop and the resulting pumping power depend on the viscosity. Some of the experimental research for nanofluid's viscosity includes viscosity of carbon nanotubes [4] and graphite nanofluids [5], BaZrO 3 suspensions [6], BaTiO 3 suspensions [7], nickel-terpineol suspensions [8] and TiO 2 nanoparticles in water [9–11]. Other investigations have focused on the rheology and viscosity of Al 2 O 3 nanoparticles in water [12–14], copper oxide in EG at room temperature [15] and CuO nanoparticles in water and ethylene glycol mixture [16]. In spite of increasing interest for experimental report of nanofluids viscosity [4–16], researchers find that experimental results are larger than theoretical predictions of conventional models of nanofluids viscosity (shown in Table 1) especially at high nanoparticle volume fraction. It is very interesting to note that many of the existing formulas are derived based on the Einstein's pioneering work. Notice that all seven correlations in Table 1 are developed to relate viscosity to volume fraction only and there is no account of temperature dependence. Generally, fluids have higher viscosity near their freezing point and fairly low viscosity near their boiling temperature, showing that viscosity is a strong function of the temperature. A correlation that relates viscosity of copper oxide nanoparticles suspended in water in temperature range of 5–50 °C is given in [16]: ln μ = A 1 T  -B ð1Þ where A and B are the functions of volume percentage. A formula has been proposed for calculating viscosity of nanofluids at particle concentrations of 1% and 4% by Nguyen et al. [14]: μ nf = μ bf 1:1250-0:0007T ð Þ ð2Þ in which μ nf and μ bf are viscosity of nano and base fluids. Unfortunately, for higher particle volume fractions, it was not possible for authors to provide any correlations that could take into consideration the combined effects of temperature and particle concentration [14]. In a recent work Abu-Nada [17] performed a two-dimensional regression on experimental data of Nguyen et al. [14] and developed the following relation including temperature T and volume fraction φ: μ Al2O3 = -0:155- 19:582 T +0:794ϕ + 2094:47 T 2 -0:192ϕ 2 -8:11 ϕ T - 27463:863 T 3 + +0:0127ϕ 3 +1:6044 ϕ 2 T +2:1754 ϕ T 2 ð3Þ which had maximum error of 5%. Journal of Molecular Liquids 153 (2010) 139–145 ⁎ Corresponding author. E-mail address: sattarghader@yahoo.com (S. Ghader). 0167-7322/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2010.02.003 Contents lists available at ScienceDirect Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq