Application of nano-quantitative structure–property relationship paradigm to develop predictive models for thermal conductivity of metal oxide-based ethylene glycol nanofluids


In this work, the relatively thermal conductivity of metal oxide-based ethylene glycol nanofluids is being predicted by using quantitative structure–property relationship methodology. The structural features of studied nanoparticles are represented by quasi-SMILES which is a coded linear structure. The gathered dataset includes ten types of nanoparticles (including Al2O3, MgO, TiO2, ZnO, Co3O4, CeO2, CuO, Fe2O3, Fe3O4, and SnO2) suspended in the same base fluid, ethylene glycol. The calculated optimal descriptors acquired by applying the Monte Carlo method in the free software available on the Web (named CORAL) and four random splits into the training, invisible, calibration, and validation sets were appraised. The statistical characteristics confirmed the predictive power and reliability of the developed models; all splits had \( \overline{{R_{\text{m}}^{2} }} \) more than 0.5 and \( \Delta R_{\text{m}}^{2} \) less than 0.2, and also the validation set showed the correlation coefficient (R2) in ranges 0.8611–0.6816 and cross-validated correlation coefficient (Q2) in ranges 0.8518–0.6668. The presented models accurately predicted the thermal conductivity of all considered nanofluids, and the technique is expected to provide a novel way for future theoretical projects.

This is a preview of subscription content, log in to check access.

Fig. 1


  1. 1.

    Memon AG, Memon RA. Thermodynamic analysis of a trigeneration system proposed for residential application. Energy Convers Manag. 2017;145:182–203.

    CAS  Article  Google Scholar 

  2. 2.

    Coco-Enríquez L, Munoz-Antón J, Martínez-Val JM, Muñoz-Antón J, Martínez-Val JM. New text comparison between CO2 and other supercritical working fluids (ethane, Xe, CH4 and N2) in line-focusing solar power plants coupled to supercritical Brayton power cycles. Int J Hydrog Energy. 2017;42:17611–31.

    CAS  Article  Google Scholar 

  3. 3.

    Yue C, Han D, Pu W, He W. Parametric analysis of a vehicle power and cooling/heating cogeneration system. Energy. 2016;115:800–10.

    CAS  Article  Google Scholar 

  4. 4.

    Das SK, Choi SU, Yu W, Pradeep T. Nanofluids: science and technology. Hoboken: Wiley; 2007.

    Google Scholar 

  5. 5.

    Yang J-CC, Li F-CC, Zhou W-WW, He Y-RR, Jiang B-CC. Experimental investigation on the thermal conductivity and shear viscosity of viscoelastic-fluid-based nanofluids. Int J Heat Mass Transf. 2012;55:3160–6.

    CAS  Article  Google Scholar 

  6. 6.

    Mahian O, Kianifar A, Kalogirou SA, Pop I, Wongwises S. A review of the applications of nanofluids in solar energy. Int J Heat Mass Transf. 2013;57:582–94.

    CAS  Article  Google Scholar 

  7. 7.

    Taylor R, Coulombe S, Otanicar T, Phelan P, Gunawan A, Lv W, Rosengarten G, Prasher R, Tyagi H. Small particles, big impacts: a review of the diverse applications of nanofluids. J Appl Phys. 2013;113:1.

    CAS  Article  Google Scholar 

  8. 8.

    Witharana S, Palabiyik I, Musina Z, Ding Y. Stability of glycol nanofluids—the theory and experiment. Powder Technol. 2013;239:72–7.

    CAS  Article  Google Scholar 

  9. 9.

    Ghadimi A, Saidur R, Metselaar HSCC. A review of nanofluid stability properties and characterization in stationary conditions. Int J Heat Mass Transf. 2011;54:4051–68.

    CAS  Article  Google Scholar 

  10. 10.

    Hachey M-AA, Nguyen CT, Galanis N, Popa CV. Experimental investigation of Al2O3 nanofluids thermal properties and rheology—effects of transient and steady-state heat exposure. Int J Therm Sci. 2014;76:155–67.

    CAS  Article  Google Scholar 

  11. 11.

    Li Y, Zhou J, Tung S, Schneider E, Xi S. A review on development of nanofluid preparation and characterization. Powder Technol. 2009;196:89–101.

    CAS  Article  Google Scholar 

  12. 12.

    Ahmadi MH, Mirlohi A, Nazari MA, Ghasempour R, Nazari MA, Ghasempour R. A review of thermal conductivity of various nanofluids. J Mol Liq. 2018;265:181–8.

    CAS  Article  Google Scholar 

  13. 13.

    Żyła G, Fal J, Estellé P. Thermophysical and dielectric profiles of ethylene glycol based titanium nitride (TiN–EG) nanofluids with various size of particles. Int J Heat Mass Transf. 2017;113:1189–99.

    CAS  Article  Google Scholar 

  14. 14.

    Żyła G, Fal J, Estellé P. The influence of ash content on thermophysical properties of ethylene glycol based graphite/diamonds mixture nanofluids. Diam Relat Mater. 2017;74:81–9.

    CAS  Article  Google Scholar 

  15. 15.

    Mahian O, Kolsi L, Amani M, Estellé P, Ahmadi G, Kleinstreuer C, Marshall JS, Siavashi M, Taylor RA, Niazmand H, Wongwises S, Hayat T, Kolanjiyil A, Kasaeian A, Pop I. Recent advances in modeling and simulation of nanofluid flows-Part I: fundamentals and theory. Phys Rep. 2019;790:1–48.

    CAS  Article  Google Scholar 

  16. 16.

    Ansari HR, Zarei MJ, Sabbaghi S, Keshavarz P. A new comprehensive model for relative viscosity of various nanofluids using feed-forward back-propagation MLP neural networks. Int Commun Heat Mass Transf. 2018;91:158–64.

    CAS  Article  Google Scholar 

  17. 17.

    Rabiee F, Akbari V, Taheri A. Preparation and characterization of nitrofurantoin nanoemulsions to increase cisplatin sensitivity in ALDH overexpressed non-small lung carcinoma cells. 2018.

    Article  Google Scholar 

  18. 18.

    Aminian A. Predicting the effective viscosity of nanofluids for the augmentation of heat transfer in the process industries. J Mol Liq. 2017;229:300–8.

    CAS  Article  Google Scholar 

  19. 19.

    Longo GA, Zilio C, Ortombina L, Zigliotto M. Application of artificial neural network (ANN) for modeling oxide-based nanofluids dynamic viscosity. Int Commun Heat Mass Transf. 2017;83:8–14.

    CAS  Article  Google Scholar 

  20. 20.

    Esfe MH, Rostamian H, Toghraie D, Yan WM. Using artificial neural network to predict thermal conductivity of ethylene glycol with alumina nanoparticle: effects of temperature and solid volume fraction. J Therm Anal Calorim. 2016;126:643–8.

    CAS  Article  Google Scholar 

  21. 21.

    Esfe MH, Afrand M, Wongwises S, Naderi A, Asadi A, Rostami S, Akbari M, Esfe MH, Afrand M, Wongwises S, Naderi A, Asadi A, Rostami S, Akbari M. Applications of feedforward multilayer perceptron artificial neural networks and empirical correlation for prediction of thermal conductivity of Mg (OH)2–EG using experimental data. Int Commun Heat Mass Transf. 2015;67:46–50.

    CAS  Article  Google Scholar 

  22. 22.

    Yousefinejad S, Hemmateenejad B. Chemometrics tools in QSAR/QSPR studies: a historical perspective. Chemom Intell Lab Syst. 2015;149:177–204.

    CAS  Article  Google Scholar 

  23. 23.

    Sizochenko N, Jagiello K, Leszczynski J, Puzyn T. How the “liquid drop” approach could be efficiently applied for quantitative structure–property relationship modeling of nanofluids. J Phys Chem C. 2015;119:25542–7.

    CAS  Article  Google Scholar 

  24. 24.

    Puzyn T, Leszczynska D, Leszczynski J. Toward the development of “nano-QSARs”: advances and challenges. Small. 2009;5:2494–509.

    CAS  Article  PubMed  Google Scholar 

  25. 25.

    Chen G, Vijver MG, Xiao Y, Peijnenburg WJGM. A review of recent advances towards the development of (quantitative) structure-activity relationships for metallic nanomaterials. Materials. 2017;10:1013.

    CAS  Article  PubMed Central  Google Scholar 

  26. 26.

    Tantra R, Oksel C, Puzyn T, Wang J, Robinson KN, Wang XZ, Ma CY, Wilkins T. Nano (Q) SAR: challenges, pitfalls and perspectives. Nanotoxicology. 2015;9:636–42.

    CAS  Article  PubMed  Google Scholar 

  27. 27.

    Sizochenko N, Syzochenko M, Gajewicz A, Leszczynski J, Puzyn T. Predicting physical properties of nanofluids by computational modeling. J Phys Chem C. 2017;121:1910–7.

    CAS  Article  Google Scholar 

  28. 28.

    Toropov A, Sizochenko N, Toropova A, Leszczynski J. Towards the development of global nano-quantitative structure–property relationship models: zeta potentials of metal oxide nanoparticles. Nanomaterials. 2018;8:243.

    CAS  Article  PubMed Central  Google Scholar 

  29. 29.

    Weininger D. SMILES, a chemical language and information system. 1. Introduction to methodology and encoding rules. J Chem Inf Comput Sci. 1988;28:31–6.

    CAS  Article  Google Scholar 

  30. 30.

    Lubinski L, Urbaszek P, Gajewicz A, Cronin MTDD, Enoch SJ, Madden JC, Leszczynska D, Leszczynski J, Puzyn T. Evaluation criteria for the quality of published experimental data on nanomaterials and their usefulness for QSAR modelling. SAR QSAR Environ Res. 2013;24:995–1008.

    CAS  Article  PubMed  Google Scholar 

  31. 31.

    Esfe MH, Saedodin S, Bahiraei M, Toghraie D, Mahian O, Wongwises S. Thermal conductivity modeling of MgO/EG nanofluids using experimental data and artificial neural network. J Therm Anal Calorim. 2014;118:287–94.

    CAS  Article  Google Scholar 

  32. 32.

    Tertsinidou GJ, Tsolakidou CM, Pantzali M, Assael MJ, Colla L, Fedele L, Bobbo S, Wakeham WA. New measurements of the apparent thermal conductivity of nanofluids and investigation of their heat transfer capabilities. J Chem Eng Data. 2016;62:491–507.

    CAS  Article  Google Scholar 

  33. 33.

    Esfe MH, Saedodin S, Naderi A, Alirezaie A, Karimipour A, Wongwises S, Goodarzi M, bin Dahari M. Modeling of thermal conductivity of ZnO-EG using experimental data and ANN methods. Int Commun Heat Mass Transf. 2015;63:35–40.

    CAS  Article  Google Scholar 

  34. 34.

    Keyvani M, Afrand M, Toghraie D, Reiszadeh M. An experimental study on the thermal conductivity of cerium oxide/ethylene glycol nanofluid: developing a new correlation. J Mol Liq. 2018;266:211–7.

    CAS  Article  Google Scholar 

  35. 35.

    Khedkar RS, Shrivastava N, Sonawane SS, Wasewar KL. Experimental investigations and theoretical determination of thermal conductivity and viscosity of TiO2–ethylene glycol nanofluid. Int Commun Heat Mass Transf. 2016;73:54–61.

    CAS  Article  Google Scholar 

  36. 36.

    Mariano A, Pastoriza-Gallego MJ, Lugo L, Camacho A, Canzonieri S, Piñeiro MM. Thermal conductivity, rheological behaviour and density of non-Newtonian ethylene glycol-based SnO2 nanofluids. Fluid Phase Equilib. 2013;337:119–24.

    CAS  Article  Google Scholar 

  37. 37.

    Mariano A, Pastoriza-Gallego MJ, Lugo L, Mussari L, Piñeiro MM. Co3O4 ethylene glycol-based nanofluids: thermal conductivity, viscosity and high pressure density. Int J Heat Mass Transf. 2015;85:54–60.

    CAS  Article  Google Scholar 

  38. 38.

    Pastoriza-Gallego MJ, Lugo L, Cabaleiro D, Legido JL, Piñeiro MM. Thermophysical profile of ethylene glycol-based ZnO nanofluids. J Chem Thermodyn. 2014;73:23–30.

    CAS  Article  Google Scholar 

  39. 39.

    Pastoriza-Gallego MJ, Lugo L, Legido JL, Piñeiro MM. Enhancement of thermal conductivity and volumetric behavior of FexOy nanofluids. J Appl Phys. 2011;110:14309.

    CAS  Article  Google Scholar 

  40. 40.

    Patel HE, Sundararajan T, Das SK. An experimental investigation into the thermal conductivity enhancement in oxide and metallic nanofluids. J Nanoparticle Res. 2010;12:1015–31.

    CAS  Article  Google Scholar 

  41. 41.

    Toropov AA, Toropova AP, Benfenati E, Gini G, Leszczynska D, Leszczynski J. CORAL: QSPR model of water solubility based on local and global SMILES attributes. Chemosphere. 2013;90:877–80.

    CAS  Article  PubMed  Google Scholar 

  42. 42.

    Toropov AA, Toropova AP. Quasi-SMILES and nano-QFAR: united model for mutagenicity of fullerene and MWCNT under different conditions. Chemosphere. 2015;139:18–22.

    CAS  Article  PubMed  Google Scholar 

  43. 43.

    Toropova AP, Achary PGR, Toropov AA. Quasi-SMILES for Nano-QSAR prediction of toxic effect of Al2O3 nanoparticles. J Nanotoxicol Nanomed. 2016;1:17–28.

    Article  Google Scholar 

  44. 44.

    R. Todeschini, V. Consonni, P. Gramatica, M. Descriptors, H. Approach, G.C. Methods, C.S. Analysis, R. Approach, M. Descriptors, M.D. Selection, V. Reduction, V.S. Selection, C. Modeling, U.M. Algorithm, A. Domain, M.D. Interpretability, Chemometrics in QSAR, in: Comprehensive Chemometrics, 2009, pp. 129–172.

  45. 45.

    Toropov AA, Toropova AP. QSAR as a random event: criteria of predictive potential for a chance model. Struct Chem. 2019.

    Article  Google Scholar 

  46. 46.

    Toropova AP, Toropov AA. Quasi-SMILES: quantitative structure–activity relationships to predict anticancer activity. Mol Divers. 2018.

    Article  PubMed  Google Scholar 

  47. 47.

    Leone C, Bertuzzi EE, Toropova AP, Toropov AA, Benfenati E. CORAL: predictive models for cytotoxicity of functionalized nanozeolites based on quasi-SMILES. Chemosphere. 2018;210:52–6.

    CAS  Article  PubMed  Google Scholar 

  48. 48.

    Toropova AP, Toropov AA. QSPR and nano-QSPR: What is the difference? J Mol Struct. 2019;1182:141–9.

    CAS  Article  Google Scholar 

  49. 49.

    Toropov AA, Toropova AP. Quasi-QSAR for mutagenic potential of multi-walled carbon-nanotubes. Chemosphere. 2015;124:40–6.

    CAS  Article  PubMed  Google Scholar 

  50. 50.

    Roy K, Mitra I, Ojha PK, Kar S, Das RN, Kabir H. Introduction of rm2 (rank) metric incorporating rank-order predictions as an additional tool for validation of QSAR/QSPR models. Chemom Intell Lab Syst. 2012;118:200–10.

    CAS  Article  Google Scholar 

  51. 51.

    Lin LI. A concordance correlation coefficient to evaluate reproducibility. Biometrics. 1989;45:255–68.

    CAS  Article  Google Scholar 

  52. 52.

    Ojha PK, Mitra I, Das RN, Roy K. Further exploring rm2 metrics for validation of QSPR models. Chemom Intell Lab Syst. 2011;107:194–205.

    CAS  Article  Google Scholar 

  53. 53.

    OECD (Organisation for Economic Co‐operation Development), Guidance Document on the Validation of (Quantitative) Structure Activity Relationship [(Q) SAR] Models, (2007).

Download references

Author information



Corresponding author

Correspondence to Mohammad Hossein Fatemi.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (DOCX 112 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Jafari, K., Fatemi, M.H. Application of nano-quantitative structure–property relationship paradigm to develop predictive models for thermal conductivity of metal oxide-based ethylene glycol nanofluids. J Therm Anal Calorim 142, 1335–1344 (2020).

Download citation


  • Nanofluids
  • Thermal conductivity
  • Nano-QSPR
  • Quasi-SMILES
  • Molecular features