Developing free-volume models for nanofluid viscosity modeling
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Developing free‑volume models for nanofluid viscosity modeling Roghayeh Bardool1 · Ali Bakhtyari1 · Feridun Esmaeilzadeh1 · Xiaopo Wang2 Received: 9 June 2020 / Accepted: 17 October 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
Abstract Developing simple theoretical models that are capable of estimating the physical properties of nanofluids such as viscosity in a broad range is currently a major trend. Following this necessity, the present contribution is devoted to applying the free-volume model for the calculation of nanofluids’ viscosity. To do so, the combination of the free-volume model and the Esmaeilzadeh–Roshanfekr equation of state was applied. A simple modification was also developed to enhance the performance of the model. Results were additionally compared with the empirical equations extracted from the literature. In this regard, a broad data bank including 932 experimental viscosity data of various nanofluids was gathered. The collected nanofluids include different base fluids (water, methanol, ethylene glycol, and propylene glycol) and various nanoparticles [Al2O3, SiO2, TiO2, Ag, Fe, ZnO, MgO, and functionalized multiwalled nanotube (FMWNT)]. The overall errors in calculations (AARD%) for 26 nanofluids are 19.83% and 2.99% for the original and modified models, respectively. The R-squared values are 0.14 and 0.99 for the original and modified models, respectively, revealing the superiority of the modified model. The largest deviations of the modified model were found to be 8.25% and 6.47% for ethylene glycol/MgO and water/ZnO systems, respectively. A comparison of the modified model developed in the present study with the empirical models of the literature revealed that the modified model results in an 11.3–16.4% improvement of the precision of nanofluids viscosity calculations. Keywords Nano · Nanoparticle · Viscosity · Esmaeilzadeh–Roshanfekr · Physical property Abbreviations AARD% Average absolute relative deviation a Equation of state parameter/m6 mol−2 α Parameter of free-volume model/J m3 kg−1 mol−1 A, B, C Equation of state parameters/dimensionless b Co-volume parameter/m3 mol−1 Ɓ Parameter of free-volume model/ dimensionless Ɓ1, Ɓ2, Ɓ3 Parameter of free-volume model/ dimensionless c Equation of state parameter/m3 mol−1 ℓ Parameter of free-volume model/m ℓ1, ℓ2, ℓ3 Parameter of free-volume model/m * Xiaopo Wang [email protected] 1
Chemical Engineering Department, Shiraz University, Shiraz, Iran
Key Laboratory of Thermo‑Fluid Science and Engineering, Ministry of Education, Xi’an Jiaotong University, Xi’an, People’s Republic of China
2
MW Molecular mass/kg mol−1 NDP Number of data points P Pressure/Pa Pc Critical pressure/Pa R Universal gas constant/J mol−1 K−1 T Temperature/K Tc Critical temperature/K Tr, T’r Reduced temperature/dimensionless v Volume/m3 mol−1 μ Viscosity/Pa s μbf Viscosity of base fluid/Pa s μnf Viscosity of nanofluid/Pa s ρ Density/kg m−3 φ Volume percent ω Acentric factor
Introduction The increasing need for energy, as wel
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