Journal of Thermal Analysis and Calorimetry

, Volume 135, Issue 1, pp 271–281 | Cite as

A proposed model to predict thermal conductivity ratio of Al2O3/EG nanofluid by applying least squares support vector machine (LSSVM) and genetic algorithm as a connectionist approach

  • Mohammad Hossein AhmadiEmail author
  • Mohammad Ali Ahmadi
  • Mohammad Alhuyi Nazari
  • Omid MahianEmail author
  • Roghayeh Ghasempour


In this study, a model is proposed by applying the least squares support vector machine (LSSVM). In addition, genetic algorithm is used for selection and optimization of hyperparameters that are embedded in the LSSVM model. In addition to temperature and concentration of nanoparticles, the parameters which are used in most of the modeling procedures for thermal conductivity, the effect of particle size is considered. By considering the size of nanoparticles as one of the input variables, a more comprehensive model is obtained which is applicable for wider ranges of influential factor on the thermal conductivity of the nanofluid. The coefficient of determination (R2) for the introduced model is equal to 0.9902, and the mean squared error is 8.64 × 10−4 for the thermal conductivity ratio of Al2O3/EG.


Nanofluid Ethylene glycol Thermal conductivity ratio Least squares support vector machine 


  1. 1.
    Parvin S, Chamkha AJ. An analysis on free convection flow, heat transfer and entropy generation in an odd-shaped cavity filled with nanofluid. Int Commun Heat Mass Transf. 2014;54:8–17. Scholar
  2. 2.
    Parvin S, Nasrin R, Alim MA, Hossain NF, Chamkha AJ. Thermal conductivity variation on natural convection flow of water–alumina nanofluid in an annulus. Int J Heat Mass Transf. 2012;55:5268–74. Scholar
  3. 3.
    Eshghi AT, Ghasempour R, Razi F, Pourfayaz F. Evaluation of nanoparticle shape effect on a nanofluid based flat-plate solar collector efficiency. Energy Explor Exploit. 2015;33:659–76. Scholar
  4. 4.
    Nazari MA, Ghasempour R, Ahmadi MH, Heydarian G, Shafii MB. Experimental investigation of graphene oxide nanofluid on heat transfer enhancement of pulsating heat pipe. Int Commun Heat Mass Transf. 2018;91:90–4. Scholar
  5. 5.
    Tawfik MM. Experimental studies of nanofluid thermal conductivity enhancement and applications: a review. Renew Sustain Energy Rev. 2017;75:1239–53. Scholar
  6. 6.
    Ponmani S, William JKM, Samuel R, Nagarajan R, Sangwai JS. Formation and characterization of thermal and electrical properties of CuO and ZnO nanofluids in xanthan gum. Colloids Surf A Physicochem Eng Asp. 2014;443:37–43. Scholar
  7. 7.
    Alawi OA, Sidik NAC, Xian HW, Kean TH, Kazi SN. Thermal conductivity and viscosity models of metallic oxides nanofluids. Int J Heat Mass Transf. 2018;116:1314–25. Scholar
  8. 8.
    Cui W, Shen Z, Yang J, Wu S. Molecular dynamics simulation on flow behaviors of nanofluids confined in nanochannel. Case Stud Therm Eng. 2015;5:114–21. Scholar
  9. 9.
    Chamkha AJ, Abbasbandy S, Rashad AM, Vajravelu K. Radiation effects on mixed convection about a cone embedded in a porous medium filled with a nanofluid. Meccanica. 2013;48:275–85. Scholar
  10. 10.
    Gandomkar A, Saidi MH, Shafii MB, Vandadi M, Kalan K. Visualization and comparative investigations of pulsating ferro-fluid heat pipe. Appl Therm Eng. 2017;116:56–65. Scholar
  11. 11.
    Kahani M, Heris SZ, Mousavi SM. Effects of curvature ratio and coil pitch spacing on heat transfer performance of Al2O3/water nanofluid laminar flow through helical coils. J Dispers Sci Technol. 2013;34:1704–12. Scholar
  12. 12.
    Akilu S, Baheta AT, Sharma KV. Experimental measurements of thermal conductivity and viscosity of ethylene glycol-based hybrid nanofluid with TiO2–CuO/C inclusions. J Mol Liq. 2017;246:396–405. Scholar
  13. 13.
    Bahiraei M, Hosseinalipour SM. Thermal dispersion model compared with Euler–Lagrange approach in simulation of convective heat transfer for nanoparticle. J Dispers Sci Technol. 2013. Scholar
  14. 14.
    Chamkha AJ, Rashad AM. Natural convection from a vertical permeable cone in a nanofluid saturated porous media for uniform heat and nanoparticles volume fraction fluxes. Int J Numer Methods Heat Fluid Flow. 2012;22:1073–85. Scholar
  15. 15.
    Shanbedi M, Heris SZ, Amiri A, Baniadam M. Improvement in heat transfer of a two-phased closed thermosyphon using silver-decorated MWCNT/water. J Dispers Sci Technol. 2014;35:1086–96. Scholar
  16. 16.
    Aramesh M, Pourfayaz F, Kasaeian A. Numerical investigation of the nanofluid effects on the heat extraction process of solar ponds in the transient step. Sol Energy. 2017;157:869–79. Scholar
  17. 17.
    Tabari ZT, Heris SZ. Heat transfer performance of milk pasteurization plate heat exchangers using MWCNT/water nanofluid. J Dispers Sci Technol. 2015;36:196–204. Scholar
  18. 18.
    Salimpour MR, Abdollahi A, Afrand M. An experimental study on deposited surfaces due to nanofluid pool boiling: comparison between rough and smooth surfaces. Exp Therm Fluid Sci. 2017;88:288–300. Scholar
  19. 19.
    Fang X, Chen Y, Zhang H, Chen W, Dong A, Wang R. Heat transfer and critical heat flux of nanofluid boiling: a comprehensive review. Renew Sustain Energy Rev. 2016;62:924–40. Scholar
  20. 20.
    Minakov AV, Pryazhnikov MI, Guzei DV, Zeer GM, Rudyak VY. The experimental study of nanofluids boiling crisis on cylindrical heaters. Int J Therm Sci. 2017;116:214–23. Scholar
  21. 21.
    Dadjoo M, Etesami N, Esfahany MN. Influence of orientation and roughness of heater surface on critical heat flux and pool boiling heat transfer coefficient of nanofluid. Appl Therm Eng. 2017;124:353–61. Scholar
  22. 22.
    Hong T-K, Yang H-S, Choi CJ. Study of the enhanced thermal conductivity of Fe nanofluids. J Appl Phys. 2005;97:64311. Scholar
  23. 23.
    Poudel B, Chiesa M, Gordon JB, Ma JJ, Garg J, et al. Enhanced thermal conductivity and viscosity of copper nanoparticles in ethylene glycol nanofluid. J Appl Phys. 2012. Scholar
  24. 24.
    Kannaiyan S, Boobalan C, Umasankaran A, Ravirajan A, Sathyan S, Thomas T. Comparison of experimental and calculated thermophysical properties of alumina/cupric oxide hybrid nanofluids. J Mol Liq. 2017. Scholar
  25. 25.
    Zadkhast M, Toghraie D, Karimipour A. Developing a new correlation to estimate the thermal conductivity of MWCNT–CuO/water hybrid nanofluid via an experimental investigation. J Therm Anal Calorim. 2017;129:859–67. Scholar
  26. 26.
    Sheikholeslami M, Ganji DD. Numerical modeling of magnetohydrodynamic CuO–water transportation inside a porous cavity considering shape factor effect. Colloids Surf A Physicochem Eng Asp. 2017;529:705–14. Scholar
  27. 27.
    Esfe MH, Hajmohammad MH. Thermal conductivity and viscosity optimization of nanodiamond-Co3O4/EG (40: 60) aqueous nanofluid using NSGA-II coupled with RSM. J Mol Liq. 2017;238:545–52. Scholar
  28. 28.
    Abdullah AA, Althobaiti SA, Lindsay KA. Marangoni convection in water–alumina nanofluids: dependence on the nanoparticle size. Eur J Mech B Fluids. 2018;67:259–68. Scholar
  29. 29.
    Toghraie D, Chaharsoghi VA, Afrand M. Measurement of thermal conductivity of ZnO–TiO2/EG hybrid nanofluid. J Therm Anal Calorim. 2016;125:527–35. Scholar
  30. 30.
    Heris SZ, Shokrgozar M, Poorpharhang S, Shanbedi M, Noie SH. Experimental study of heat transfer of a car radiator with CuO/ethylene glycol-water as a coolant. J Dispers Sci Technol. 2014;35:677–84. Scholar
  31. 31.
    Esfe MH, Rostamian H, Sarlak MR, Rejvani M, Alirezaie A. Rheological behavior characteristics of TiO2-MWCNT/10w40 hybrid nano-oil affected by temperature, concentration and shear rate: an experimental study and a neural network simulating. Phys E Low Dim Syst Nanostructures. 2017;94:231–40. Scholar
  32. 32.
    Esfe MH, Ahangar MRH, Rejvani M, Toghraie D, Hajmohammad MH. Designing an artificial neural network to predict dynamic viscosity of aqueous nanofluid of TiO2 using experimental data. Int Commun Heat Mass Transf. 2016;75:192–6. Scholar
  33. 33.
    Esfe MH, Ahangar MRH, Toghraie D, Hajmohammad MH, Rostamian H, Tourang H. Designing artificial neural network on thermal conductivity of Al2O3–water–EG (60–40%) nanofluid using experimental data. J Therm Anal Calorim. 2016;126:837–43. Scholar
  34. 34.
    Nadooshan AA, Esfe MH, Afrand M. Prediction of rheological behavior of SiO2-MWCNTs/10W40 hybrid nanolubricant by designing neural network. J Therm Anal Calorim. 2017. Scholar
  35. 35.
    Alirezaie A, Saedodin S, Esfe MH, Rostamian SH. Investigation of rheological behavior of MWCNT (COOH-functionalized)/MgO - engine oil hybrid nanofluids and modelling the results with artificial neural networks. J Mol Liq. 2017;241:173–81. Scholar
  36. 36.
    Esfe MH, Esfande S, Rostamian SH. Experimental evaluation, new correlation proposing and ANN modeling of thermal conductivity of ZnO-DWCNT/EG hybrid nanofluid for internal combustion engines applications. Appl Therm Eng. 2017. Scholar
  37. 37.
    Esfe MH, Esfandeh S, Saedodin S, Rostamian H. Experimental evaluation, sensitivity analyzation and ANN modeling of thermal conductivity of ZnO-MWCNT/EG-water hybrid nanofluid for engineering applications. Appl Therm Eng. 2017;125:673–85. Scholar
  38. 38.
    Afrand M, Esfe MH, Abedini E, Teimouri H. Predicting the effects of magnesium oxide nanoparticles and temperature on the thermal conductivity of water using artificial neural network and experimental data. Phys E Low Dim Syst Nanostructures. 2017;87:242–7. Scholar
  39. 39.
    Esfe MH, Rejvani M, Karimpour R, Arani AAA. Estimation of thermal conductivity of ethylene glycol-based nanofluid with hybrid suspensions of SWCNT–Al2O3 nanoparticles by correlation and ANN methods using experimental data. J Therm Anal Calorim. 2017;128:1359–71. Scholar
  40. 40.
    Shamaeil M, Firouzi M, Fakhar A. The effects of temperature and volume fraction on the thermal conductivity of functionalized DWCNTs/ethylene glycol nanofluid. J Therm Anal Calorim. 2016;126:1455–62. Scholar
  41. 41.
    Esfe MH, Esfandeh S, Rejvani M. Modeling of thermal conductivity of MWCNT-SiO2 (30:70%)/EG hybrid nanofluid, sensitivity analyzing and cost performance for industrial applications. J Therm Anal Calorim. 2017. Scholar
  42. 42.
    Esfe MH, Arani AAA, Badi RS, Rejvani M. ANN modeling, cost performance and sensitivity analyzing of thermal conductivity of DWCNT–SiO2/EG hybrid nanofluid for higher heat transfer. J Therm Anal Calorim. 2017. Scholar
  43. 43.
    Vakili M, Karami M, Delfani S, Khosrojerdi S, Kalhor K. Experimental investigation and modeling of thermal conductivity of CuO–water/EG nanofluid by FFBP-ANN and multiple regressions. J Therm Anal Calorim. 2017;129:629–37. Scholar
  44. 44.
    Esfahani MR, Languri EM, Nunna MR. Effect of particle size and viscosity on thermal conductivity enhancement of graphene oxide nanofluid. Int Commun Heat Mass Transf. 2016;76:308–15. Scholar
  45. 45.
    Li CH, Peterson GP. The effect of particle size on the effective thermal conductivity of Al2O3–water nanofluids. J Appl Phys. 2007;101:44312. Scholar
  46. 46.
    Chopkar M, Sudarshan S, Das PK, Manna I. Effect of particle size on thermal conductivity of nanofluid. Metall Mater Trans A. 2008;39:1535–42. Scholar
  47. 47.
    Ahmadi MA, Mahmoudi B. Development of robust model to estimate gas–oil interfacial tension using least square support vector machine: experimental and modeling study. J Supercrit Fluids. 2016;107:122–8. Scholar
  48. 48.
    Ahmadi MA, Ebadi M, Hosseini SM. Prediction breakthrough time of water coning in the fractured reservoirs by implementing low parameter support vector machine approach. Fuel. 2014;117:579–89. Scholar
  49. 49.
    Ahmadi MA. Connectionist approach estimates gas–oil relative permeability in petroleum reservoirs: application to reservoir simulation. Fuel. 2015;140:429–39. Scholar
  50. 50.
    Ahmadi M-A, Bahadori A. A LSSVM approach for determining well placement and conning phenomena in horizontal wells. Fuel. 2015;153:276–83. Scholar
  51. 51.
    Hemmat Esfe M, Karimipour A, Yan W-M, Akbari M, Safaei MR, Dahari M. Experimental study on thermal conductivity of ethylene glycol based nanofluids containing Al2O3 nanoparticles. Int J Heat Mass Transf. 2015;88:728–34. Scholar
  52. 52.
    Beck MP, Yuan Y, Warrier P, Teja AS. The effect of particle size on the thermal conductivity of alumina nanofluids. J Nanoparticle Res. 2009;11:1129–36. Scholar
  53. 53.
    Agarwal R, Verma K, Kumar N, Singh R. Sensitivity of thermal conductivity for Al2O3 nanofluids. Exp Therm Fluid Sci. 2017;80:19–26. Scholar
  54. 54.
    Ahmadi MA. Toward reliable model for prediction drilling fluid density at wellbore conditions: a LSSVM model. Neurocomputing. 2016;211:143–9. Scholar
  55. 55.
    Ahmadi MH, Ahmadi MA, Sadatsakkak SA, Feidt M. Connectionist intelligent model estimates output power and torque of stirling engine. Renew Sustain Energy Rev. 2015;50:871–83. Scholar
  56. 56.
    Ahmadi M-A, Bahadori A, Shadizadeh SR. A rigorous model to predict the amount of dissolved calcium carbonate concentration throughout oil field brines: side effect of pressure and temperature. Fuel. 2015;139:154–9. Scholar
  57. 57.
    Suykens JAK. Least squares support vector machines. Singapore: World Scientific; 2002.CrossRefGoogle Scholar
  58. 58.
    Vong C-M, Wong P-K, Li Y-P. Prediction of automotive engine power and torque using least squares support vector machines and Bayesian inference. Eng Appl Artif Intell. 2006;19:277–87. Scholar
  59. 59.
    Mehdizadeh B, Movagharnejad K. A comparative study between LS-SVM method and semi empirical equations for modeling the solubility of different solutes in supercritical carbon dioxide. Chem Eng Res Des. 2011;89:2420–7. Scholar
  60. 60.
    Pelckmans K, Suykens JA, Van Gestel T, De Brabanter J, Lukas L, Hamers B, De Moor B, Vandewalle J. LS-SVMlab: a matlab/c toolbox for least squares support vector machines. Tutorial. Leuven: KULeuven-ESAT. 2002;142, p. 1–2.Google Scholar
  61. 61.
    Suykens JAK, Vandewalle J. Training multilayer perceptron classifiers based on a modified support vector method. IEEE Trans Neural Netw. 1999;10:907–11. Scholar
  62. 62.
    Suykens JAK, Vandewalle J. Recurrent least squares support vector machines. IEEE Trans Circuits Syst I Fundam Theory Appl. 2000;47:1109–14. Scholar
  63. 63.
    Suykens JAK, Vandewalle J. Multiclass least squares support vector machines. In: IJCNN’99. International Joint Conference on Neural Network Proceedings (Cat. No. 99CH36339), vol. 2, IEEE; n.d. p. 900–3.
  64. 64.
    Yu W, France DM, Routbort JL, Choi SUS. Review and comparison of nanofluid thermal conductivity and heat transfer enhancements. Heat Transf Eng. 2008;29:432–60. Scholar
  65. 65.
    Arani JB, Narooei A, Branch CT, Faculty S, Branch A. Nanofluid thermal conductivity prediction model based on artificial neural network. Trans Phenom Nano Micro Scales. 2016;4:41–6. Scholar
  66. 66.
    Maheshwary PB, Handa CC, Nemade KR. A comprehensive study of effect of concentration, particle size and particle shape on thermal conductivity of titania/water based nanofluid. Appl Therm Eng. 2017;119:79–88. Scholar
  67. 67.
    Darvanjooghi MHK, Esfahany MN. Experimental investigation of the effect of nanoparticle size on thermal conductivity of in situ prepared silica–ethanol nanofluid. Int Commun Heat Mass Transf. 2016;77:148–54. Scholar
  68. 68.
    Mintsa HA, Roy G, Nguyen CT, Doucet D. New temperature dependent thermal conductivity data for water-based nanofluids. Int J Therm Sci. 2009;48:363–71. Scholar
  69. 69.
    Khedkar RS, Sonawane SS, Wasewar KL. Influence of CuO nanoparticles in enhancing the thermal conductivity of water and monoethylene glycol based nanofluids. Int Commun Heat Mass Transf. 2012;39:665–9. Scholar
  70. 70.
    Zhang X, Gu H, Fujii M. Effective thermal conductivity and thermal diffusivity of nanofluids containing spherical and cylindrical nanoparticles. Exp Therm Fluid Sci. 2007;31:593–9. Scholar
  71. 71.
    Yang L, Xu J, Du K, Zhang X. Recent developments on viscosity and thermal conductivity of nanofluids. Powder Technol. 2017;317:348–69. Scholar
  72. 72.
    Lugo L, Legido JL, Piñeiro MM, Lugo L, Legido JL, Pin MM. Enhancement of thermal conductivity and volumetric behavior of FexOy nanofluids. J Appl Phys. 2011. Scholar
  73. 73.
    Jiang W, Wang L. Monodisperse magnetite nanofluids: synthesis, aggregation, and thermal conductivity. J Appl Phys. 2012;108:114311. Scholar
  74. 74.
    Gharagozloo PE, Goodson KE, Gharagozloo PE, Goodson KE. Aggregate fractal dimensions and thermal conduction in nanofluids. J Appl Phys. 2014. Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  • Mohammad Hossein Ahmadi
    • 1
    Email author
  • Mohammad Ali Ahmadi
    • 2
  • Mohammad Alhuyi Nazari
    • 3
  • Omid Mahian
    • 4
    Email author
  • Roghayeh Ghasempour
    • 3
  1. 1.Faculty of Mechanical EngineeringShahrood University of TechnologyShahroodIran
  2. 2.Department of Petroleum Engineering, Ahwaz Faculty of Petroleum EngineeringPetroleum University of Technology (PUT)AhwazIran
  3. 3.Renewable Energy and Environmental Engineering DepartmentUniversity of TehranTehranIran
  4. 4.Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Laboratory (FUTURE Laboratory), Department of Mechanical EngineeringKing Mongkut’s University of Technology ThonburiBangkokThailand

Personalised recommendations