Abstract
Solar energy technologies represent a viable alternative to fossil fuels for meeting increasing global energy demands. However, to increase the production of solar technologies in the global energy mix, the cost of production should be as competitive as other sources. This study focuses on the implementation of machine learning for estimating the thermophysical properties of nanofluids for nanofluid-based solar energy technologies as this would make the synthesis of nanofluids cost-effective. The prediction of thermal conductivity has gained a lot of research attention, whereas, the viscosity of nanofluids has less concentration of studies. The accurate prediction of the viscosity of hybrid nanofluids is important in estimating the heat transfer performance of nanofluids as regards their pump power requirements and convective heat transfer coefficient in several applications. The rigor of experimentations of hybrid nanofluids has necessitated the need for developing efficient and robust machine learning models for accurately estimating the viscosity of hybrid nanofluids for solar applications. Several studies were aimed at developing a predictive model for the viscosity of nanofluids; however, these models are limited to specific types of nanofluids. This study is aimed at developing a robust machine learning algorithm for predicting the viscosity of several hybrid nanofluids from reliable experimental data (700 datasets) culled from literature. This study implements a novel optimizable Gaussian process regression (O-GPR), which have not been previously used in this area, and compares the result with other commonly used machine learning algorithms like, Boosted tree regression (BTR), Artificial neural network (ANN), support vector regression (SVR), to accurately predict the viscosity of a wide range of Newtonian-based hybrid nanofluid. The input parameters used in training the machine learning models were temperature (T), volume fraction (VF), the acentric factor of the base fluid (ACF), nanoparticle size (NS), and nanoparticle density (ND). The prediction performance of the machine learning algorithms was tested using statistical metrics and was compared with theoretical models. The O-GPR model showed superior predictive performance with an R2 of 0.999998 and an MSE of 0.0002552. The study conclusively states that the high accuracy prediction of thermophysical properties of nanofluid using robust machine learning models makes the design of nanofluid-based solar energy technologies more cost-effective.













Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Che Sidik NA, Mahmud Jamil M, Aziz Japar WMA, Muhammad Adamu I (2017) A review on preparation methods, stability and applications of hybrid nanofluids. Renew Sustain Energy Rev 80:1112–1122
Salari A, Kazemian A, Ma T, Hakkaki-Fard A, Peng J (2020) Nanofluid based photovoltaic thermal systems integrated with phase change materials: numerical simulation and thermodynamic analysis. Energy Convers Manag 205:112384
Das L, Habib K, Saidur R, Aslfattahi N, Yahya SM, Rubbi F (2020) Improved thermophysical properties and energy efficiency of aqueous ionic liquid/mxene nanofluid in a hybrid pv/t solar system. Nanomaterials 10(7):1–26
Asadi M, Asadi A (2016) Dynamic viscosity of MWCNT/ZnO-engine oil hybrid nanofluid: an experimental investigation and new correlation in different temperatures and solid concentrations. Int Commun Heat Mass Transf 76:41–45
Sarafraz M, Safaei MR, Leon A, Tlili I, Alkanhal T, Tian Z, Goodarzi M, Arjomandi M (2019) Experimental investigation on thermal performance of a PV/T-PCM (photovoltaic/thermal) system cooling with a PCM and nanofluid. Energies 12:2572
Ekiciler R, Arslan K, Turgut O, Kurşun B (2020) Effect of hybrid nanofluid on heat transfer performance of parabolic trough solar collector receiver. J Therm Anal Calorim 143(2):1637–1654
Murshed SMS, Estellé P (2017) A state of the art review on viscosity of nanofluids. Renew Sustain Energy Rev 76:1134–1152
Bashirnezhad K, Bazri S, Safaei MR, Goodarzi M, Dahari M, Mahian O, Dalkiliça AS, Wongwises S (2016) Viscosity of nanofluids: a review of recent experimental studies. Int Commun Heat Mass Transf 73:114–123
Duangthongsuk W, Wongwises S (2009) Measurement of temperature-dependent thermal conductivity and viscosity of TiO2-water nanofluids. Exp Therm Fluid Sci 33(4):706–714
Chandrasekar M, Suresh S, Chandra Bose A (2010) Experimental investigations and theoretical determination of thermal conductivity and viscosity of Al2O3/water nanofluid. Exp Therm Fluid Sci 34(2):210–216
Mahbubul IM, Saidur R, Amalina MA (2012) Latest developments on the viscosity of nanofluids. Int J Heat Mass Transf 55(4):874–885
Corcione M (2011) Empirical correlating equations for predicting the effective thermal conductivity and dynamic viscosity of nanofluids. Energy Convers Manag 52(1):789–793
Okonkwo EC, Wole-Osho I, Almanassra IW, Abdullatif YM, Al-Ansari T (2020) An updated review of nanofluids in various heat transfer devices. J Therm Anal Calorim 145(6):2817–2872
Almanassra IW, Okonkwo EC, Alhassan O, Ali M, Kochkodan V, Al-ansari T (2021) Stability and thermophysical properties test of carbide-derived carbon thermal fluid; a comparison between functionalized and emulsified suspensions. Powder Technol 377:415–428
Afrand M, Nazari Najafabadi K, Akbari M (2016) Effects of temperature and solid volume fraction on viscosity of SiO2-MWCNTs/SAE40 hybrid nanofluid as a coolant and lubricant in heat engines. Appl Therm Eng 102:45–54
Giwa SO, Sharifpur M, Goodarzi M, Alsulami H, Meyer JP (2021) Influence of base fluid, temperature, and concentration on the thermophysical properties of hybrid nanofluids of alumina–ferrofluid: experimental data, modeling through enhanced ANN, ANFIS, and curve fitting. J Therm Anal Calorim 143(6):4149–4167
Goodarzi M, Toghraie D, Reiszadeh M, Afrand M (2019) Experimental evaluation of dynamic viscosity of ZnO–MWCNTs/engine oil hybrid nanolubricant based on changes in temperature and concentration. J Therm Anal Calorim 136(2):513–525
Einstein A (1906) Eine neue Bestimmung der Molekuldimensionen. Ann Phys 19:289–306
Chen H, Ding Y, Tan C (2007) Rheological behaviour of nanofluids. New J Phys 9:367
Okonkwo EC, Wole-Osho I, Kavaz D, Abid M, Al-Ansari T (2020) Thermodynamic evaluation and optimization of a flat plate collector operating with alumina and iron mono and hybrid nanofluids. Sustain Energy Technol Assess 37:100636
Wole-Osho I, Okonkwo EC, Kavaz D, Abbasoglu S (2020) An experimental investigation into the effect of particle mixture ratio on specific heat capacity and dynamic viscosity of Al2O3-ZnO hybrid nanofluids. Powder Technol 363:699–716
Eshgarf H, Sina N, Esfe MH, Izadi F, Afrand M (2018) Prediction of rheological behavior of MWCNTs–SiO2/EG–water non-Newtonian hybrid nanofluid by designing new correlations and optimal artificial neural networks. J Therm Anal Calorim 132(2):1029–1038
Alarifi IM, Nguyen HM, Bakhtiyari AN, Asadi A (2019) Feasibility of ANFIS-PSO and ANFIS-GA models in predicting thermophysical properties of Al2O3-MWCNT/Oil hybrid nanofluid. Materials (Basel) 12(21):3628
Karimipour A, Bagherzadeh SA, Taghipour A, Abdollahi A, Safaei MR (2019) A novel nonlinear regression model of SVR as a substitute for ANN to predict conductivity of MWCNT-CuO/water hybrid nanofluid based on empirical data. Phys A Stat Mech Appl 521:89–97
Tian Z, Arasteh H, Parsian A, Karimipour A, Safaei MR, Nguyen TK (2019) Estimate the shear rate & apparent viscosity of multi-phased non-Newtonian hybrid nanofluids via new developed support vector machine method coupled with sensitivity analysis. Phys A Stat Mech Appl 535:122456
Alrashed AAAA, Gharibdousti MS, Goodarzi M, de Oliveira LR, Safaei MR, Bandarra Filho EP (2018) Effects on thermophysical properties of carbon based nanofluids: Experimental data, modelling using regression, ANFIS and ANN. Int J Heat Mass Transf 125:920–932
Bahrami M, Akbari M, Bagherzadeh SA, Karimipour A, Afrand M, Goodarzi M (2019) Develop 24 dissimilar ANNs by suitable architectures & training algorithms via sensitivity analysis to better statistical presentation: measure MSEs between targets & ANN for Fe–CuO/Eg–water nanofluid. Phys A Stat Mech Appl 519:159–168
Ahmadi MH, Mohseni-Gharyehsafa B, Ghazvini M, Goodarzi M, Jilte RD, Kumar R (2020) Comparing various machine learning approaches in modeling the dynamic viscosity of CuO/water nanofluid. J Therm Anal Calorim 139(4):2585–2599
Boyle, P. (2007) Gaussian processes for regression and optimisation. 190
Khalifeh A, Vaferi B (2019) Intelligent assessment of effect of aggregation on thermal conductivity of nanofluids—comparison by experimental data and empirical correlations. Thermochim Acta 681:1783
Wole-Osho I, Okonkwo EC, Adun H, Kavaz D, Abbasoglu S (2020) An intelligent approach to predicting the effect of nanoparticle mixture ratio, concentration and temperature on thermal conductivity of hybrid nanofluids. J Therm Anal Calorim 144(3):671–688
Wang X, Xu X, Choi SUS (1999) Thermal conductivity of nanoparticle-fluid mixture. J Thermophys Heat Transf 13:474–480
Okonkwo EC, Wole-Osho I, Kavaz D, Abid M (2019) Comparison of experimental and theoretical methods of obtaining the thermal properties of alumina/iron mono and hybrid nanofluids. J Mol Liq 292:111377
Afshari A, Akbari M, Toghraie D, Yazdi ME (2018) Experimental investigation of rheological behavior of the hybrid nanofluid of MWCNT–alumina/water (80%)–ethylene-glycol (20%): new correlation and margin of deviation. J Therm Anal Calorim 132(2):1001–1015
Hemmat Esfe M, Reiszadeh M, Esfandeh S, Afrand M (2018) Optimization of MWCNTs (10%) – Al2O3 (90%)/5W50 nanofluid viscosity using experimental data and artificial neural network. Phys A Stat Mech Appl 512:731–744
Soltani O, Akbari M (2016) Effects of temperature and particles concentration on the dynamic viscosity of MgO-MWCNT/ethylene glycol hybrid nanofluid: experimental study. Phys E Low-Dimens Syst Nanostruct 84:564–570
Dardan E, Afrand M, Meghdadi Isfahani AH (2016) Effect of suspending hybrid nano-additives on rheological behavior of engine oil and pumping power. Appl Therm Eng 109:524–534
Nabil MF, Azmi WH, Abdul Hamid K, Mamat R, Hagos FY (2017) An experimental study on the thermal conductivity and dynamic viscosity of TiO2-SiO2 nanofluids in water: ethylene glycol mixture. Int Commun Heat Mass Transf 86:181–189
Ruhani B, Toghraie D, Hekmatifar M, Hadian M (2019) Statistical investigation for developing a new model for rheological behavior of ZnO–Ag (50%–50%)/Water hybrid Newtonian nanofluid using experimental data. Phys A Stat Mech Appl 525:741–751
Hemmat Esfe M, Afrand M, Yan WM, Yarmand H, Toghraie D, Dahari M (2016) Effects of temperature and concentration on rheological behavior of MWCNTs/SiO2(20–80)-SAE40 hybrid nano-lubricant. Int Commun Heat Mass Transf 76:133–138
Hemmat Esfe M, Rostamian H, Reza Sarlak M (2018) A novel study on rheological behavior of ZnO-MWCNT/10w40 nanofluid for automotive engines. J Mol Liq 254:406–413
Afrand M, Nazari Najafabadi K, Sina N, Safaei MR, Kherbeet AS, Wongwises S, Dahari M (2016) Prediction of dynamic viscosity of a hybrid nano-lubricant by an optimal artificial neural network. Int Commun Heat Mass Transf 76:209–214
Hemmat Esfe M, Afrand M, Rostamian SH, Toghraie D (2017) Examination of rheological behavior of MWCNTs/ZnO-SAE40 hybrid nano-lubricants under various temperatures and solid volume fractions. Exp Therm Fluid Sci 80:384–390
Ramezanizadeh M, Ahmadi MH, Nazari MA, Sadeghzadeh M, Chen L (2019) A review on the utilized machine learning approaches for modeling the dynamic viscosity of nanofluids. Renew Sustain Energy Rev 114:109345
Hamid KA, Azmi WH, Nabil MF, Mamat R, Sharma KV (2018) Experimental investigation of thermal conductivity and dynamic viscosity on nanoparticle mixture ratios of TiO2-SiO2 nanofluids. Int J Heat Mass Transf 116:1143–1152
Wanatasanapan VV, Abdullah MZ, Gunnasegaran P (2020) Effect of TiO2-Al2O3nanoparticle mixing ratio on the thermal conductivity, rheological properties, and dynamic viscosity of water-based hybrid nanofluid. J Mater Res Technol 9(6):13781–13792
Wole-Osho I, Adun H, Adedeji M, Okonkwo EC, Kavaz D, Dagbasi M (2020) Effect of hybrid nanofluids mixture ratio on the performance of a photovoltaic thermal collector. Int J Energy Res 44(11):9064–9081
Mohammed A, Burhan L, Ghafor K, Sarwar W, Mahmood W (2021) Artificial neural network (ANN), M5P-tree, and regression analyses to predict the early age compression strength of concrete modified with DBC-21 and VK-98 polymers. Neural Comput Appl 33(13):7851–7873
Jamei M, Ahmadianfar I, Olumegbon IA, Karbasi M, Asadi A (2021) On the assessment of specific heat capacity of nanofluids for solar energy applications: application of Gaussian process regression (GPR) approach. J Energy Storage 33:102067
Cao C, Liao J, Hou Z, Wang G, Feng W, Fang Y (2020) Parametric uncertainty analysis for CO2 sequestration based on distance correlation and support vector regression. J Nat Gas Sci Eng 77:103237
Daneshfar R, Bemani A, Hadipoor M, Sharifpur M, Ali HM, Mahariq I, Abdeljawad T (2020) Estimating the heat capacity of non-Newtonian ionanofluid systems using ANN, ANFIS, and SGB tree algorithms. Appl Sci 10(18):6432
Wu H, Bagherzadeh SA, D’Orazio A, Habibollahi N, Karimipour A, Goodarzi M, Bach QV (2019) Present a new multi objective optimization statistical Pareto frontier method composed of artificial neural network and multi objective genetic algorithm to improve the pipe flow hydrodynamic and thermal properties such as pressure drop and heat transfer. Phys A Stat Mech Appl 535:122409
Cheng K, Lu Z, Zhou Y, Shi Y, Wei Y (2017) Global sensitivity analysis using support vector regression. Appl Math Model 49:587–598
Alade IO, Rahman MAA, Saleh TA (2020) An approach to predict the isobaric specific heat capacity of nitrides/ethylene glycol-based nanofluids using support vector regression. J. Energy Storage 29:101313
Chen H, Ding Y, Tan C (2007) Rheological behaviour of nanofluids. New J Phys 9(10):367
Meybodi MK, Naseri S, Shokrollahi A, Daryasafar A (2015) Prediction of viscosity of water-based Al2O3, TiO2, SiO2, and CuO nanofluids using a reliable approach. Chemom Intell Lab Syst 149:60–69
Friedman JH, Meulman JJ (2003) Multiple additive regression trees with application in epidemiology. Stat Med 22(9):1365–1381
Landwehr N, Hall M, Frank E (2005) Logistic model trees. Mach Learn 59(1–2):161–205
Hemmat Esfe M, Abbasian Arani AA, Rezaie M, Yan WM, Karimipour A (2015) Experimental determination of thermal conductivity and dynamic viscosity of Ag-MgO/water hybrid nanofluid. Int Commun Heat Mass Transf 66:189–195
Yan, S.R., Kalbasi, R., Nguyen, Q., and Karimipour, A. (2020) Rheological behavior of hybrid MWCNTs-TiO2/EG nanofluid: A comprehensive modeling and experimental study. J. Mol. Liq., 308, 113058.
Brinkman HC (1952) The viscosity of concentrated suspensions and solutions. J Chem Phys 20(4):571
Lundgren T (1972) Slow flow through stationary random beds and suspensions of spheres. J Fluid Mech 51:273–299
Li L, Zhai Y, Jin Y, Wang J, Wang H, Ma M (2020) Stability, thermal performance and artificial neural network modeling of viscosity and thermal conductivity of Al2O3-ethylene glycol nanofluids. Powder Technol 363:360–368
Ma M, Zhai Y, Wang J, Yao P, Wang H (2020) Statistical image analysis of uniformity of hybrid nanofluids and prediction models of thermophysical parameters based on artificial neural network (ANN). Powder Technol 362:257–266
Hemmati-Sarapardeh A, Varamesh A, Husein MM, Karan K (2017) (2018) On the evaluation of the viscosity of nanofluid systems: modeling and data assessment. Renew Sustain Energy Rev 81:313–329
Gholizadeh M, Jamei M, Ahmadianfar I, Pourrajab R (2020) Prediction of nanofluids viscosity using random forest (RF) approach. Chemom Intell Lab Syst 201:104010
Jamei M, Ahmadianfar I (2020) A rigorous model for prediction of viscosity of oil-based hybrid nanofluids. Physica A 556:124827
Doan CHID, Liong S (2004) Generalization for multilayer neural network Bayesian regularization or early stopping. Network 119260:1–8
Alade IO, Abd Rahman MA, Saleh TA (2019) Modeling and prediction of the specific heat capacity of Al2O3/water nanofluids using hybrid genetic algorithm/support vector regression model. Nano-Struct Nano-Objects 17:103–111
Elith J, Leathwick JR, Hastie T (2008) A working guide to boosted regression trees. J Anim Ecol 77(4):802–813
Heidari E, Sobati MA, Movahedirad S (2016) Accurate prediction of nanofluid viscosity using a multilayer perceptron artificial neural network (MLP-ANN). Chemom Intell Lab Syst 155:73–85
Kayri M (2016) Predictive abilities of Bayesian regularization and Levenberg-Marquardt algorithms in artificial neural networks: a comparative empirical study on social data. Math Comput Appl 21(2):20
Chaipimonplin T (2016) The efficiency of using different of learning algorithms in artificial neural network model for flood forecasting at Upper River Ping catchment. J Civi Eng 20(1):478–484
Karimi H, Yousefi F, Rahimi MR (2011) Correlation of viscosity in nanofluids using genetic algorithm-neural network (GA-NN). Heat Mass Transf und Stoffuebertragung 47(11):1417–1425
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The authors declare the following financial interests/personal relationships which may be considered as potential competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Adun, H., Wole-Osho, I., Okonkwo, E.C. et al. Estimation of thermophysical property of hybrid nanofluids for solar Thermal applications: Implementation of novel Optimizable Gaussian Process regression (O-GPR) approach for Viscosity prediction. Neural Comput & Applic 34, 11233–11254 (2022). https://doi.org/10.1007/s00521-022-07038-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-022-07038-2