Dynamic viscosity and thermal conductivity modeling of nanofluids based on Eyring’s absolute rate theory and modified Flory-Huggins equation

Fazlali, Alireza; Mahdavi Nik, Mohammad

doi:10.66224/CNJ.3.3.652

Dynamic viscosity and thermal conductivity modeling of nanofluids based on Eyring’s absolute rate theory and modified Flory-Huggins equation

Document Type : Original Article

Authors

Alireza Fazlali

Mohammad Mahdavi Nik

Department of Chemical Engineering, Faculty of Engineering, Arak University, Arak, Iran

10.66224/CNJ.3.3.652

Abstract

Using the concept of dimensionality, a new model based on the presented relationship for dynamic viscosity is presented to calculate the thermal conductivity of nanofluids based on the thermal conductivity of the base fluid and nanoparticles, molar volume of the base fluid and nanoparticles, temperature volume fraction, and interaction parameter. The presented model is developed to calculate the thermal conductivity of water-based nanofluids with Al2O3, CuO, Fe3O4, TiO2, and Ag nanoparticles, and also for ethylene glycol-based nanofluids with Al2O3, CuO, and ZnO nanoparticles. To develop the Eyring-mFH (Eyring-modified Flory-Huggins) model, experimental dynamic viscosity data of nanofluids with Newtonian behavior from different references in the temperature range of 10-90 oC and the volume fraction range of 0.2-9.4% were used to calculate the interaction parameters between the base fluid and nanoparticles in the viscosity model and experimental thermal conductivity data of different nanofluids in the temperature range of 10-90 oC and the volume fraction range of 0.3-8.6% were used to calculate the interaction parameter in the thermal conductivity model. The maximum and minimum errors of the model optimization on tentative data based on AARD% are 5.94% and 0.04% for the viscosity model, and 0.7% and 0.16% for the thermal conductivity model, respectively. The presented models are compared with various models of other researchers, and results show that the Eyring-mFH model is very accurate compared to them in calculating the thermophysical properties of viscosity and thermal conductivity of nanofluids.

Graphical Abstract

Keywords

Nanofluids

Viscosity

Thermal conductivity

Modeling

Eyring’ s absolute rate theory

modified Flory-Huggins

[1] J. Li, X. Zhang, B. Xu, M. Yuan, Nanofluid research and applications: A review, Int. Commun. Heat Mass Transf. 127 (2021) 105543.
https://doi.org/10.1016/j.icheatmasstransfer.2021.105543

[2] S.U. Choi, Enhancing thermal conductivity of fluids with nanoparticles, Proc. ASME Int. Mech. Eng. Congr. Expo. 17421 (1995) 99–105.
https://doi.org/10.1115/IMECE1995-0926

[3] F. Garoosi, Presenting two new empirical models for calculating the effective dynamic viscosity and thermal conductivity of nanofluids, Powder Technol. 366 (2020) 788–820.
https://doi.org/10.1016/j.powtec.2020.03.032

[4] S. Hassani, R. Saidur, S. Mekhilef, A. Hepbasli, A new correlation for predicting the thermal conductivity of nanofluids using dimensional analysis, Int. J. Heat Mass Transf. 90 (2015) 121–130.
https://doi.org/10.1016/j.ijheatmasstransfer.2015.06.040

[5] R. Powell, W. Roseveare, H. Eyring, Diffusion, thermal conductivity, and viscous flow of liquids, Ind. Eng. Chem. 33 (1941) 430–435.
https://doi.org/10.1021/ie50376a003

[6] R.J. Martins, M.J.D.M. Cardoso, O.E. Barcia, Excess Gibbs free energy model for calculating the viscosity of binary liquid mixtures, Ind. Eng. Chem. Res. 39 (2000) 849–854.
https://doi.org/10.1021/ie990398b

[7] J.M. Prausnitz, R.N. Lichtenthaler, E.G. Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd ed., Prentice Hall PTR, 1998.

[8] Y.G. Wang, D.X. Chen, X.K. OuYang, Viscosity calculations for ionic liquid–cosolvent mixtures based on Eyring’s absolute rate theory, J. Chem. Eng. Data 55 (2010) 4878–4884.
https://doi.org/10.1021/je100487m

[9] C. Qian, S.J. Mumby, B. Eichinger, Phase diagrams of binary polymer solutions and blends, Macromolecules 24 (1991) 1655–1661.
https://doi.org/10.1021/ma00007a031

[10] Y. Bae, J. Shim, D. Soane, J.M. Prausnitz, Representation of vapor–liquid and liquid–liquid equilibria for polymer systems, J. Appl. Polym. Sci. 47 (1993) 1193–1206.
https://doi.org/10.1002/app.1993.070470707

[11] L. Godson, B. Raja, D.M. Lal, S. Wongwises, Experimental investigation on thermal conductivity and viscosity of silver nanofluid, Exp. Heat Transf. 23 (2010) 317–332.
https://doi.org/10.1080/08916150903564796

[12] U. Rea, T. McKrell, L.W. Hu, J. Buongiorno, Laminar convective heat transfer of nanofluids, Int. J. Heat Mass Transf. 52 (2009) 2042–2048.
https://doi.org/10.1016/j.ijheatmasstransfer.2008.10.025

[13] C. Nguyen et al., Temperature and particle-size dependent viscosity data, Int. J. Heat Fluid Flow 28 (2007) 1492–1506.
https://doi.org/10.1016/j.ijheatfluidflow.2007.02.004

[14] A. Turgut et al., Thermal conductivity and viscosity of TiO₂ nanofluids, Int. J. Thermophys. 30 (2009) 1213–1226.
https://doi.org/10.1007/s10765-009-0594-2

[15] I. Tavman et al., Viscosity and thermal conductivity of nanosuspensions, Arch. Mater. Sci. 100 (2008) 99–104.

[16] L.S. Sundar et al., Thermal conductivity and viscosity of Fe₃O₄ nanofluid, Int. Commun. Heat Mass Transf. 44 (2013) 7–14.
https://doi.org/10.1016/j.icheatmasstransfer.2013.02.014

[17] M.J. Pastoriza-Gallego et al., Al₂O₃–EG nanofluids, Nanoscale Res. Lett. 6 (2011) 221.
https://doi.org/10.1186/1556-276X-6-221

[18] M. Pastoriza-Gallego et al., ZnO–EG nanofluids, J. Chem. Thermodyn. 73 (2014) 23–30.
https://doi.org/10.1016/j.jct.2013.07.002

[19] M. Akbari et al., Rheological behavior of EG-based nanofluids, J. Mol. Liq. 233 (2017) 352–357.
https://doi.org/10.1016/j.molliq.2017.03.020

[20] D. Kwek et al., Thermal property measurements of nanofluids, J. Chem. Eng. Data 55 (2010) 5690–5695.
https://doi.org/10.1021/je1006407

[21] H.E. Patel et al., Thermal conductivity enhancement, J. Nanopart. Res. 12 (2010) 1015–1031.
https://doi.org/10.1007/s11051-009-9658-2

[22] W. Duangthongsuk, S. Wongwises, TiO₂–water nanofluids, Exp. Therm. Fluid Sci. 33 (2009) 706–714.
https://doi.org/10.1016/j.expthermflusci.2009.01.005

[23] I. Akande et al., Dispersion factor model for nanofluids, J. Mol. Liq. 380 (2023) 121644.
https://doi.org/10.1016/j.molliq.2023.121644

[24] M. Klazly, G. Bognár, Empirical equation for nanofluid viscosity, Int. Commun. Heat Mass Transf. 135 (2022) 106054.
https://doi.org/10.1016/j.icheatmasstransfer.2022.106054

[25] S.M. Hosseini et al., Dimensionless group model, J. Therm. Anal. Calorim. 100 (2010) 873–877.
https://doi.org/10.1007/s10973-010-0721-0

[26] G.K. Batchelor, Effect of Brownian motion, J. Fluid Mech. 83 (1977) 97–117.
https://doi.org/10.1017/S0022112077001062

[27] R.L. Hamilton, O. Crosser, Thermal conductivity of heterogeneous systems, Ind. Eng. Chem. Fundam. 1 (1962) 187–191.
https://doi.org/10.1021/i160003a005

[28] R. Prasher et al., Brownian-motion-based model, J. Heat Transf. 128 (2006) 588–595.
https://doi.org/10.1115/1.2188509

[29] A. Moghadassi et al., Dimensionless thermal conductivity model, J. Therm. Anal. Calorim. 96 (2009) 81–84.
https://doi.org/10.1007/s10973-008-9843-z

[30] M. Hosseini et al., Local composition theory for nanofluids, J. Heat Transf. 133 (2011) 052401.
https://doi.org/10.1115/1.4003042