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

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Abstract

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.

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References

  1. Wen D, Lin G, Vafaei S, Zhang K. Review of nanofluids for heat transfer applications. Particuology. 2009;7:141–50.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

  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.

    Article  CAS  Google Scholar 

  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.

  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.

    Article  CAS  Google Scholar 

  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. Chol S. Enhancing thermal conductivity of fluids with nanoparticles. ASME Publ Fed. 1995;231:99–106.

    Google Scholar 

  9. Chein R, Chuang J. Experimental microchannel heat sink performance studies using nanofluids. Int J Therm Sci. 2007;46:57–66.

    Article  CAS  Google Scholar 

  10. Maxwell JC. A treatise on electricity and magnetism. Oxford: Clarendon Press; 1881.

    Google Scholar 

  11. Murshed S, Leong K, Yang C. Investigations of thermal conductivity and viscosity of nanofluids. Int J Therm Sci. 2008;47:560–8.

    Article  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  13. Kleinstreuer C, Feng Y. Experimental and theoretical studies of nanofluid thermal conductivity enhancement: a review. Nanoscale Res Lett. 2011;6:1–13.

    CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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. 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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  33. Maxwell J. Electricity and magnetism. Oxford: Clarendon Press; 1873.

    Google Scholar 

  34. Hamilton R, Crosser O. Thermal conductivity of heterogeneous two-component systems. Ind Eng Chem Fundam. 1962;1:187–91.

    Article  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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. Koo J, Kleinstreuer C. A new thermal conductivity model for nanofluids. J Nanopart Res. 2004;6:577–88.

    Article  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

  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.

    Article  CAS  PubMed  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  49. Suykens JA, Vandewalle J. Least squares support vector machine classifiers. Neural Process Lett. 1999;9:293–300.

    Article  Google Scholar 

  50. Suykens JA, Vandewalle J. Recurrent least squares support vector machines. IEEE Trans Circuits Syst I Fundam Theory Appl. 2000;47:1109–14.

    Article  Google Scholar 

  51. Suykens JA, Van Gestel T, De Brabanter J. Least squares support vector machines. Singapore: World Scientific; 2002.

    Book  Google Scholar 

  52. Guo Z, Bai G. Application of least squares support vector machine for regression to reliability analysis. Chin J Aeronaut. 2009;22:160–6.

    Article  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  57. Murshed SS. Simultaneous measurement of thermal conductivity, thermal diffusivity, and specific heat of nanofluids. Heat Transf Eng. 2012;33:722–31.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  62. Thang BH, Khoi PH, Minh PN. A modified model for thermal conductivity of carbon nanotube-nanofluids. Phys Fluids. 2015;27:032002.

    Article  CAS  Google Scholar 

  63. Das SK, Putra N, Thiesen P, Roetzel W. Temperature dependence of thermal conductivity enhancement for nanofluids. J Heat Transf. 2003;125:567–74.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  73. Halelfadl S, Maré T, Estellé P. Efficiency of carbon nanotubes water based nanofluids as coolants. Exp Therm Fluid Sci. 2014;53:104–10.

    Article  CAS  Google Scholar 

  74. Chen L, Xie H, Li Y, Yu W. Nanofluids containing carbon nanotubes treated by mechanochemical reaction. Thermochim Acta. 2008;477:21–4.

    Article  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  PubMed  Google Scholar 

  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.

  81. Corcione M. Empirical correlating equations for predicting the effective thermal conductivity and dynamic viscosity of nanofluids. Energy Convers Manag. 2011;52:789–93.

    Article  CAS  Google Scholar 

  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.

  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.

    Article  CAS  Google Scholar 

  84. Jang SP, Choi SU. Role of Brownian motion in the enhanced thermal conductivity of nanofluids. Appl Phys Lett. 2004;84:4316–8.

    Article  CAS  Google Scholar 

  85. Rousseeuw PJ, Leroy AM. Robust regression and outlier detection. New York: Wiley; 2005.

    Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Amirkabir University of Technology (Tehran Polytechnic), Mahshahr Campus, Mahshahr, Iran

    Alireza Baghban & Sajjad Habibzadeh

  2. Chemical Engineering Department, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

    Sajjad Habibzadeh & Farzin Zokaee Ashtiani

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  1. Alireza Baghban
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  2. Sajjad Habibzadeh
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  3. Farzin Zokaee Ashtiani
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Correspondence to Alireza Baghban or Sajjad Habibzadeh.

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Appendix: Program

Appendix: Program

I have developed a graphical user interface (GUI) version of the model as illustrated in Fig. 15. This program is an exe file presented in supplementary content, and it needs Matlab software version 2012 (64bit) before running. As indicated, three input parameters (temperature, diameter, and volume fraction) should be given and by choosing one of nanofluid in the panel and then clicking on calculate button, the thermal conductivity of nanofluid is obtained.

Fig. 15
figure 15

GUI version of developed model for estimation of thermal conductivity of nanofluid

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Baghban, A., Habibzadeh, S. & Ashtiani, F.Z. Toward a modeling study of thermal conductivity of nanofluids using LSSVM strategy. J Therm Anal Calorim 135, 507–522 (2019). https://doi.org/10.1007/s10973-018-7074-5

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