Journal of Thermal Analysis and Calorimetry

, Volume 135, Issue 1, pp 507–522 | Cite as

Toward a modeling study of thermal conductivity of nanofluids using LSSVM strategy

  • Alireza BaghbanEmail author
  • Sajjad HabibzadehEmail author
  • Farzin Zokaee Ashtiani


In the present study, a comprehensive model based on least square support vector machine algorithm (LSSVM) was developed to estimate thermal conductivity of nanofluids. The model assessed the thermal conductivity of 29 different nanofluids. The representative nanofluids were composed of nine base fluids, including water, ethylene glycol, transformer oil, engine oil, R113, DI Water, monoethylene glycol, paraffin, and oil. Al2O3, TiO2, CuO, ZnO, Al, and Cu nanoparticles were employed in the corresponding nanofluids. A collection of 1109 experimental samples from reliable sources was used. In addition, the present model can estimate the thermal conductivity of nanofluids as a function of temperature, diameter, nanoparticle volume fraction as well as the thermal conductivity of the nanoparticles and the base fluid. The proposed LSSVM structure was optimized by particle swarm optimization technique where the outcomes proved great accuracy of the model for estimating the thermal conductivity of nanofluids. Moreover, statistical observations showed superior predictive ability of LSSVM model than other previous available correlations. Namely, the average relative deviation percent of 2.46 and 3.10%, and R-squared values of 0.9954 and 0.9914 were resulted for training and testing stages of LSSVM model, respectively.


Nanofluid Thermal conductivity Least square support vector machine algorithm Particle swarm optimization Sensitivity analysis Outlier analysis 

Supplementary material

10973_2018_7074_MOESM1_ESM.rar (212 kb)
Supplementary material 1 (RAR 212 kb)


  1. 1.
    Wen D, Lin G, Vafaei S, Zhang K. Review of nanofluids for heat transfer applications. Particuology. 2009;7:141–50.Google Scholar
  2. 2.
    Zalba B, Marín JM, Cabeza LF, Mehling H. Review on thermal energy storage with phase change: materials, heat transfer analysis and applications. Appl Therm Eng. 2003;23:251–83.Google Scholar
  3. 3.
    Tomlinson HL, Manning W, Schaefer W, Record T (2016) Process for increasing the efficiency of heat removal from a Fischer–Tropsch slurry reactor, Google Patents.Google Scholar
  4. 4.
    Ebrahimnia-Bajestan E, Moghadam MC, Niazmand H, Daungthongsuk W, Wongwises S. Experimental and numerical investigation of nanofluids heat transfer characteristics for application in solar heat exchangers. Int J Heat Mass Transf. 2016;92:1041–52.Google Scholar
  5. 5.
    Mazumdar A, Spencer SJ, Hobart C, Kuehl M, Brunson G, Coleman N, Buerger SP. Improving robotic actuator torque density and efficiency through enhanced heat transfer. In: ASME 2016 Dynamic Systems and Control Conference. American Society of Mechanical Engineers; 2016, p. V002T026A004.Google Scholar
  6. 6.
    Eiamsa-Ard S, Wongcharee K. Experimental study of TiO2–water nanofluid flow in corrugated tubes mounted with semi-circular wing tapes. Heat Transf Eng. 2018;39:1–14.Google Scholar
  7. 7.
    Zeeshan A, Shehzad N, Ellahi R, Alamri SZ. Convective Poiseuille flow of Al2O3–EG nanofluid in a porous wavy channel with thermal radiation. Neural Comput Appl. 2017;28:1–12.Google Scholar
  8. 8.
    Chol S. Enhancing thermal conductivity of fluids with nanoparticles. ASME Publ Fed. 1995;231:99–106.Google Scholar
  9. 9.
    Chein R, Chuang J. Experimental microchannel heat sink performance studies using nanofluids. Int J Therm Sci. 2007;46:57–66.Google Scholar
  10. 10.
    Maxwell JC. A treatise on electricity and magnetism. Oxford: Clarendon Press; 1881.Google Scholar
  11. 11.
    Murshed S, Leong K, Yang C. Investigations of thermal conductivity and viscosity of nanofluids. Int J Therm Sci. 2008;47:560–8.Google Scholar
  12. 12.
    Lee J-H, Lee S-H, Choi C, Jang S, Choi S. A review of thermal conductivity data, mechanisms and models for nanofluids. Int J Micro Nano Scale Transp. 2011;1:269–322.Google Scholar
  13. 13.
    Kleinstreuer C, Feng Y. Experimental and theoretical studies of nanofluid thermal conductivity enhancement: a review. Nanoscale Res Lett. 2011;6:1–13.Google Scholar
  14. 14.
    Keblinski P, Phillpot S, Choi S, Eastman J. Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids). Int J Heat Mass Transf. 2002;45:855–63.Google Scholar
  15. 15.
    Vatani A, Woodfield PL, Dao DV. A survey of practical equations for prediction of effective thermal conductivity of spherical-particle nanofluids. J Mol Liq. 2015;211:712–33.Google Scholar
  16. 16.
    Ariana M, Vaferi B, Karimi G. Prediction of thermal conductivity of alumina water-based nanofluids by artificial neural networks. Powder Technol. 2015;278:1–10.Google Scholar
  17. 17.
    Baghban A, Pourfayaz F, Ahmadi MH, Kasaeian A, Pourkiaei SM, Lorenzini G. Connectionist intelligent model estimates of convective heat transfer coefficient of nanofluids in circular cross-sectional channels. J Therm Anal Calorim. 2017;130:1–27.Google Scholar
  18. 18.
    Baghban A, Ahmadi MA, Shahraki BH. Prediction carbon dioxide solubility in presence of various ionic liquids using computational intelligence approaches. J Supercrit Fluids. 2015;98:50–64.Google Scholar
  19. 19.
    Baghban A, Bahadori A, Mohammadi AH, Behbahaninia A. Prediction of CO2 loading capacities of aqueous solutions of absorbents using different computational schemes. Int J Greenh Gas Control. 2017;57:143–61.Google Scholar
  20. 20.
    Baghban A, Bahadori M, Rozyn J, Lee M, Abbas A, Bahadori A, Rahimali A. Estimation of air dew point temperature using computational intelligence schemes. Appl Therm Eng. 2016;93:1043–52.Google Scholar
  21. 21.
    Baghban A, Mohammadi AH, Taleghani MS. Rigorous modeling of CO2 equilibrium absorption in ionic liquids. Int J Greenh Gas Control. 2017;58:19–41.Google Scholar
  22. 22.
    Bahadori A, Baghban A, Bahadori M, Lee M, Ahmad Z, Zare M, Abdollahi E. Computational intelligent strategies to predict energy conservation benefits in excess air controlled gas-fired systems. Appl Therm Eng. 2016;102:432–46.Google Scholar
  23. 23.
    Baghban A, Kardani MN, Habibzadeh S. Prediction viscosity of ionic liquids using a hybrid LSSVM and group contribution method. J Mol Liq. 2017;236:452–64.Google Scholar
  24. 24.
    Karimi H, Yousefi F, Rahimi MR. Correlation of viscosity in nanofluids using genetic algorithm-neural network (GA-NN). Heat Mass Transf. 2011;47:1417–25.Google Scholar
  25. 25.
    Atashrouz S, Pazuki G, Alimoradi Y. Estimation of the viscosity of nine nanofluids using a hybrid GMDH-type neural network system. Fluid Phase Equilib. 2014;372:43–8.Google Scholar
  26. 26.
    Sharifpur M, Adio SA, Meyer JP. Experimental investigation and model development for effective viscosity of Al2O3–glycerol nanofluids by using dimensional analysis and GMDH-NN methods. Int Commun Heat Mass Transf. 2015;68:208–19.Google Scholar
  27. 27.
    Karimi H, Yousefi F. Application of artificial neural network–genetic algorithm (ANN–GA) to correlation of density in nanofluids. Fluid Phase Equilib. 2012;336:79–83.Google Scholar
  28. 28.
    Hojjat M, Etemad SG, Bagheri R, Thibault J. Thermal conductivity of non-Newtonian nanofluids: experimental data and modeling using neural network. Int J Heat Mass Transf. 2011;54:1017–23.Google Scholar
  29. 29.
    Papari MM, Yousefi F, Moghadasi J, Karimi H, Campo A. Modeling thermal conductivity augmentation of nanofluids using diffusion neural networks. Int J Therm Sci. 2011;50:44–52.Google Scholar
  30. 30.
    Longo GA, Zilio C, Ceseracciu E, Reggiani M. Application of artificial neural network (ANN) for the prediction of thermal conductivity of oxide–water nanofluids. Nano Energy. 2012;1:290–6.Google Scholar
  31. 31.
    Esfe MH, Afrand M, Yan W-M, Akbari M. Applicability of artificial neural network and nonlinear regression to predict thermal conductivity modeling of Al2O3–water nanofluids using experimental data. Int Commun Heat Mass Transf. 2015;66:246–9.Google Scholar
  32. 32.
    Meybodi MK, Naseri S, Shokrollahi A, Daryasafar A. Prediction of viscosity of water-based Al2O3, TiO2, SiO2, and CuO nanofluids using a reliable approach. Chemom Intell Lab Syst. 2015;149:60–9.Google Scholar
  33. 33.
    Maxwell J. Electricity and magnetism. Oxford: Clarendon Press; 1873.Google Scholar
  34. 34.
    Hamilton R, Crosser O. Thermal conductivity of heterogeneous two-component systems. Ind Eng Chem Fundam. 1962;1:187–91.Google Scholar
  35. 35.
    Bruggeman VD. Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen. Ann Phys. 1935;416:636–64.Google Scholar
  36. 36.
    Yu W, Choi S. The role of interfacial layers in the enhanced thermal conductivity of nanofluids: a renovated Maxwell model. J Nanopart Res. 2003;5:167–71.Google Scholar
  37. 37.
    Leong K, Yang C, Murshed S. A model for the thermal conductivity of nanofluids—the effect of interfacial layer. J Nanopart Res. 2006;8:245–54.Google Scholar
  38. 38.
    Xie H, Fujii M, Zhang X. Effect of interfacial nanolayer on the effective thermal conductivity of nanoparticle-fluid mixture. Int J Heat Mass Transf. 2005;48:2926–32.Google Scholar
  39. 39.
    Sohrabi N, Masoumi N, Behzadmehr A, Sarvari S. A simple analytical model for calculating the effective thermal conductivity of nanofluids. Heat Transf Asian Res. 2010;39:141–50.Google Scholar
  40. 40.
    Koo J, Kleinstreuer C. A new thermal conductivity model for nanofluids. J Nanopart Res. 2004;6:577–88.Google Scholar
  41. 41.
    Xu J, Yu B, Zou M, Xu P. A new model for heat conduction of nanofluids based on fractal distributions of nanoparticles. J Phys D Appl Phys. 2006;39:4486.Google Scholar
  42. 42.
    Evans W, Prasher R, Fish J, Meakin P, Phelan P, Keblinski P. Effect of aggregation and interfacial thermal resistance on thermal conductivity of nanocomposites and colloidal nanofluids. Int J Heat Mass Transf. 2008;51:1431–8.Google Scholar
  43. 43.
    Schwartz LM, Garboczi EJ, Bentz DP. Interfacial transport in porous media: application to DC electrical conductivity of mortars. J Appl Phys. 1995;78:5898–908.Google Scholar
  44. 44.
    Tomotika S, Aoi T, Yosinobu H. On the forces acting on a circular cylinder set obliquely in a uniform stream at low values of Reynolds number. In: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, The Royal Society; 1953, p. 233–244.Google Scholar
  45. 45.
    Prasher R, Phelan PE, Bhattacharya P. Effect of aggregation kinetics on the thermal conductivity of nanoscale colloidal solutions (nanofluid). Nano Lett. 2006;6:1529–34.Google Scholar
  46. 46.
    He Y, Jin Y, Chen H, Ding Y, Cang D, Lu H. Heat transfer and flow behaviour of aqueous suspensions of TiO2 nanoparticles (nanofluids) flowing upward through a vertical pipe. Int J Heat Mass Transf. 2007;50:2272–81.Google Scholar
  47. 47.
    Wang B-X, Zhou L-P, Peng X-F. A fractal model for predicting the effective thermal conductivity of liquid with suspension of nanoparticles. Int J Heat Mass Transf. 2003;46:2665–72.Google Scholar
  48. 48.
    Nan C-W, Birringer R, Clarke DR, Gleiter H. Effective thermal conductivity of particulate composites with interfacial thermal resistance. J Appl Phys. 1997;81:6692–9.Google Scholar
  49. 49.
    Suykens JA, Vandewalle J. Least squares support vector machine classifiers. Neural Process Lett. 1999;9:293–300.Google Scholar
  50. 50.
    Suykens JA, Vandewalle J. Recurrent least squares support vector machines. IEEE Trans Circuits Syst I Fundam Theory Appl. 2000;47:1109–14.Google Scholar
  51. 51.
    Suykens JA, Van Gestel T, De Brabanter J. Least squares support vector machines. Singapore: World Scientific; 2002.Google Scholar
  52. 52.
    Guo Z, Bai G. Application of least squares support vector machine for regression to reliability analysis. Chin J Aeronaut. 2009;22:160–6.Google Scholar
  53. 53.
    Nan C-W, Shi Z, Lin Y. A simple model for thermal conductivity of carbon nanotube-based composites. Chem Phys Lett. 2003;375:666–9.Google Scholar
  54. 54.
    Rashmi W, Khalid M, Ismail AF, Saidur R, Rashid A. Experimental and numerical investigation of heat transfer in CNT nanofluids. J Exp Nanosci. 2015;10:545–63.Google Scholar
  55. 55.
    Jiang H, Li H, Zan C, Wang F, Yang Q, Shi L. Temperature dependence of the stability and thermal conductivity of an oil-based nanofluid. Thermochim Acta. 2014;579:27–30.Google Scholar
  56. 56.
    Kazemi-Beydokhti A, Heris SZ, Moghadam N, Shariati-Niasar M, Hamidi A. Experimental investigation of parameters affecting nanofluid effective thermal conductivity. Chem Eng Commun. 2014;201:593–611.Google Scholar
  57. 57.
    Murshed SS. Simultaneous measurement of thermal conductivity, thermal diffusivity, and specific heat of nanofluids. Heat Transf Eng. 2012;33:722–31.Google Scholar
  58. 58.
    Patel HE, Sundararajan T, Das SK. An experimental investigation into the thermal conductivity enhancement in oxide and metallic nanofluids. J Nanopart Res. 2010;12:1015–31.Google Scholar
  59. 59.
    Chon CH, Kihm KD, Lee SP, Choi SU. Empirical correlation finding the role of temperature and particle size for nanofluid (Al2O3) thermal conductivity enhancement. Appl Phys Lett. 2005;87:153107.Google Scholar
  60. 60.
    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.Google Scholar
  61. 61.
    Godson L, Raja B, Lal DM, Wongwises S. Experimental investigation on the thermal conductivity and viscosity of silver-deionized water nanofluid. Exp Heat Transf. 2010;23:317–32.Google Scholar
  62. 62.
    Thang BH, Khoi PH, Minh PN. A modified model for thermal conductivity of carbon nanotube-nanofluids. Phys Fluids. 2015;27:032002.Google Scholar
  63. 63.
    Das SK, Putra N, Thiesen P, Roetzel W. Temperature dependence of thermal conductivity enhancement for nanofluids. J Heat Transf. 2003;125:567–74.Google Scholar
  64. 64.
    Lee S, Choi S-S, Li S, Eastman J. Measuring thermal conductivity of fluids containing oxide nanoparticles. J Heat Transf. 1999;121:280–9.Google Scholar
  65. 65.
    Kim SH, Choi SR, Kim D. Thermal conductivity of metal-oxide nanofluids: particle size dependence and effect of laser irradiation. J Heat Transf. 2007;129:298–307.Google Scholar
  66. 66.
    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.Google Scholar
  67. 67.
    Zerradi H, Ouaskit S, Dezairi A, Loulijat H, Mizani S. New Nusselt number correlations to predict the thermal conductivity of nanofluids. Adv Powder Technol. 2014;25:1124–31.Google Scholar
  68. 68.
    Eastman JA, Choi S, Li S, Yu W, Thompson L. Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Appl Phys Lett. 2001;78:718–20.Google Scholar
  69. 69.
    Moghadassi A, Hosseini SM, Henneke DE. Effect of CuO nanoparticles in enhancing the thermal conductivities of monoethylene glycol and paraffin fluids. Ind Eng Chem Res. 2010;49:1900–4.Google Scholar
  70. 70.
    Fedele L, Colla L, Bobbo S. Viscosity and thermal conductivity measurements of water-based nanofluids containing titanium oxide nanoparticles. Int J Refrig. 2012;35:1359–66.Google Scholar
  71. 71.
    Pastoriza-Gallego M, Lugo L, Cabaleiro D, Legido J, Piñeiro M. Thermophysical profile of ethylene glycol-based ZnO nanofluids. J Chem Thermodyn. 2014;73:23–30.Google Scholar
  72. 72.
    Mondragón R, Segarra C, Martínez-Cuenca R, Juliá JE, Jarque JC. Experimental characterization and modeling of thermophysical properties of nanofluids at high temperature conditions for heat transfer applications. Powder Technol. 2013;249:516–29.Google Scholar
  73. 73.
    Halelfadl S, Maré T, Estellé P. Efficiency of carbon nanotubes water based nanofluids as coolants. Exp Therm Fluid Sci. 2014;53:104–10.Google Scholar
  74. 74.
    Chen L, Xie H, Li Y, Yu W. Nanofluids containing carbon nanotubes treated by mechanochemical reaction. Thermochim Acta. 2008;477:21–4.Google Scholar
  75. 75.
    Hwang Y, Ahn Y, Shin H, Lee C, Kim G, Park H, Lee J. Investigation on characteristics of thermal conductivity enhancement of nanofluids. Curr Appl Phys. 2006;6:1068–71.Google Scholar
  76. 76.
    Jiang W, Ding G, Peng H. Measurement and model on thermal conductivities of carbon nanotube nanorefrigerants. Int J Therm Sci. 2009;48:1108–15.Google Scholar
  77. 77.
    Choi S, Zhang Z, Yu W, Lockwood F, Grulke E. Anomalous thermal conductivity enhancement in nanotube suspensions. Appl Phys Lett. 2001;79:2252–4.Google Scholar
  78. 78.
    Godson L, Lal DM, Wongwises S. Measurement of thermo physical properties of metallic nanofluids for high temperature applications. Nanoscale Microscale Thermophys Eng. 2010;14:152–73.Google Scholar
  79. 79.
    Timofeeva EV, Moravek MR, Singh D. Improving the heat transfer efficiency of synthetic oil with silica nanoparticles. J Colloid Interface Sci. 2011;364:71–9.Google Scholar
  80. 80.
    Wasp EJ, Kenny JP, Gandhi RL. Solid–liquid flow: slurry pipeline transportation. [Pumps, valves, mechanical equipment, economics]. Ser Bulk Mater Handl U S 1977;1.Google Scholar
  81. 81.
    Corcione M. Empirical correlating equations for predicting the effective thermal conductivity and dynamic viscosity of nanofluids. Energy Convers Manag. 2011;52:789–93.Google Scholar
  82. 82.
    Azmi W, Sharma K, Mamat R, Alias A, Misnon II. Correlations for thermal conductivity and viscosity of water based nanofluids. In: IOP Conference Series: Materials Science and Engineering. IOP Publishing; 2012, p. 012029.Google Scholar
  83. 83.
    Vajjha RS, Das DK. Experimental determination of thermal conductivity of three nanofluids and development of new correlations. Int J Heat Mass Transf. 2009;52:4675–82.Google Scholar
  84. 84.
    Jang SP, Choi SU. Role of Brownian motion in the enhanced thermal conductivity of nanofluids. Appl Phys Lett. 2004;84:4316–8.Google Scholar
  85. 85.
    Rousseeuw PJ, Leroy AM. Robust regression and outlier detection. New York: Wiley; 2005.Google Scholar
  86. 86.
    Mohammadi AH, Gharagheizi F, Eslamimanesh A, Richon D. Evaluation of experimental data for wax and diamondoids solubility in gaseous systems. Chem Eng Sci. 2012;81:1–7.Google Scholar
  87. 87.
    Hosseinzadeh M, Hemmati-Sarapardeh A. Toward a predictive model for estimating viscosity of ternary mixtures containing ionic liquids. J Mol Liq. 2014;200:340–8.Google Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Amirkabir University of Technology (Tehran Polytechnic)MahshahrIran
  2. 2.Chemical Engineering DepartmentAmirkabir University of Technology (Tehran Polytechnic)TehranIran

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