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Connectionist intelligent model estimates of convective heat transfer coefficient of nanofluids in circular cross-sectional channels

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Abstract

Nanofluids are kind of fluids, which have a wide range of applications in different fields such as industry or engineering systems. The present study efforts to find accurate relationships between the convective heat transfer coefficient of the nanofluids containing the silica nanoparticles as a function of Reynolds number, Prandtl number, and mass fraction nanofluid. To that end, a number of seven different models including adaptive neuro-fuzzy inference system (ANFIS), artificial neural network (ANN), support vector machine (SVM), least square support vector machine (LSSVM), genetic programming (GP), principal component analysis (PCA), and committee machine intelligent system (CMIS) have been implemented according to experimental databases designed for measuring the convective heat transfer coefficient of nanofluid in circular cross-sectional channels. Results indicated the satisfactory capability of suggested models, especially CMIS model in order to estimate the convective heat transfer coefficient of nanofluid. The obtained statistical analyses such as the mean square error and R-squared (R 2) for the ANFIS, ANN, SVM, LSSVM, PCA, GP, and CMIS were 380.6671 and 0.9946, 215.062 and 0.9969, 335.748 and 0.9951, 298.88 and 0.9959, 1601.336 and 0.977, 1891.861 and 0.973, and 205.366 and 0.9970 correspondingly. We expect that these suggested models can help engineers who deal with heat transfer phenomenon to have great predictive tools for estimating convective heat transfer coefficient of nanofluid.

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References

  1. Khanjari Y, Pourfayaz F, Kasaeian A. Numerical investigation on using of nanofluid in a water-cooled photovoltaic thermal system. Energy Convers Manag. 2016;122:263–78.

    Article  CAS  Google Scholar 

  2. Amin TE, Roghayeh G, Fatemeh R, Fatollah P. Evaluation of nanoparticle shape effect on a nanofluid based flat-plate solar collector efficiency. Energy Explor Exploit. 2015;33(5):659–76.

    Article  Google Scholar 

  3. Lee S, Choi S-S, Li S, Eastman J. Measuring thermal conductivity of fluids containing oxide nanoparticles. J Heat Transfer. 1999;121(2):280–9.

    Article  CAS  Google Scholar 

  4. Das SK, Putra N, Thiesen P, Roetzel W. Temperature dependence of thermal conductivity enhancement for nanofluids. J Heat Transfer. 2003;125(4):567–74.

    Article  CAS  Google Scholar 

  5. Masuda H, Ebata A, Teramae K. Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles: dispersion of Al2O3, SiO2 and TiO2 ultra-fine particles. Netsu Bussei. 1993;7(4):227–33.

    Article  CAS  Google Scholar 

  6. Oh D-W, Jain A, Eaton JK, Goodson KE, Lee JS. Thermal conductivity measurement and sedimentation detection of aluminum oxide nanofluids by using the 3ω method. Int J Heat Fluid Flow. 2008;29(5):1456–61.

    Article  CAS  Google Scholar 

  7. Hung T-C, Yan W-M, Wang X-D, Chang C-Y. Heat transfer enhancement in microchannel heat sinks using nanofluids. Int J Heat Mass Transf. 2012;55(9):2559–70.

    Article  CAS  Google Scholar 

  8. Öztop HF, Estellé P, Yan W-M, Al-Salem K, Orfi J, Mahian O. A brief review of natural convection in enclosures under localized heating with and without nanofluids. Int Commun Heat Mass Transfer. 2015;60:37–44.

    Article  Google Scholar 

  9. Nasiri M, Etemad SG, Bagheri R. Experimental heat transfer of nanofluid through an annular duct. Int Commun Heat Mass Transfer. 2011;38(7):958–63.

    Article  CAS  Google Scholar 

  10. Nasrin R, Alim M. Semi-empirical relation for forced convective analysis through a solar collector. Sol Energy. 2014;105:455–67.

    Article  Google Scholar 

  11. Sahin B, Gültekin GG, Manay E, Karagoz S. Experimental investigation of heat transfer and pressure drop characteristics of Al2O3–water nanofluid. Exp Thermal Fluid Sci. 2013;50:21–8.

    Article  CAS  Google Scholar 

  12. Saeedinia M, Akhavan-Behabadi M, Nasr M. Experimental study on heat transfer and pressure drop of nanofluid flow in a horizontal coiled wire inserted tube under constant heat flux. Exp Thermal Fluid Sci. 2012;36:158–68.

    Article  CAS  Google Scholar 

  13. Moghadassi A, Masoud Hosseini S, Henneke D, Elkamel A. A model of nanofluids effective thermal conductivity based on dimensionless groups. J Therm Anal Calorim. 2009;96(1):81–4.

    Article  CAS  Google Scholar 

  14. Barbés B, Páramo R, Blanco E, Pastoriza-Gallego MJ, Pineiro MM, Legido JL, et al. Thermal conductivity and specific heat capacity measurements of Al2O3 nanofluids. J Therm Anal Calorim. 2013;111(2):1615–25.

    Article  Google Scholar 

  15. Huminic G, Huminic A. Application of nanofluids in heat exchangers: a review. Renew Sustain Energy Rev. 2012;16(8):5625–38.

    Article  CAS  Google Scholar 

  16. Sarkar J. A critical review on convective heat transfer correlations of nanofluids. Renew Sustain Energy Rev. 2011;15(6):3271–7.

    Article  CAS  Google Scholar 

  17. Vajjha RS, Das DK, Kulkarni DP. Development of new correlations for convective heat transfer and friction factor in turbulent regime for nanofluids. Int J Heat Mass Transf. 2010;53(21):4607–18.

    Article  CAS  Google Scholar 

  18. Lu G, Wang X-D, Duan Y-Y. A critical review of dynamic wetting by complex fluids: from Newtonian fluids to non-Newtonian fluids and nanofluids. Adv Coll Interface Sci. 2016;236:43–62.

    Article  CAS  Google Scholar 

  19. Lu G, Duan Y-Y, Wang X-D. Surface tension, viscosity, and rheology of water-based nanofluids: a microscopic interpretation on the molecular level. J Nanopart Res. 2014;16(9):2564.

    Article  Google Scholar 

  20. Yang L, Du K, Zhang X. A theoretical investigation of thermal conductivity of nanofluids with particles in cylindrical shape by anisotropy analysis. Powder Technol. 2017;314:328–338.

    Article  CAS  Google Scholar 

  21. Valinataj-Bahnemiri P, Ramiar A, Manavi S, Mozaffari A. Heat transfer optimization of two phase modeling of nanofluid in a sinusoidal wavy channel using Artificial Bee Colony technique. Eng Sci Technol Int J. 2015;18(4):727–37.

    Article  Google Scholar 

  22. Islam M, Shabani B, Rosengarten G, Andrews J. The potential of using nanofluids in PEM fuel cell cooling systems: a review. Renew Sustain Energy Rev. 2015;48:523–39.

    Article  CAS  Google Scholar 

  23. Baghban A, Ahmadi MA, Pouladi B, Amanna B. Phase equilibrium modeling of semi-clathrate hydrates of seven commonly gases in the presence of TBAB ionic liquid promoter based on a low parameter connectionist technique. J Supercrit Fluids. 2015;101:184–92.

    Article  CAS  Google Scholar 

  24. 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 

  25. Baghban A, Bahadori M, Rozyn J, Lee M, Abbas A, Bahadori A, et al. Estimation of air dew point temperature using computational intelligence schemes. Appl Therm Eng. 2016;93:1043–52.

    Article  Google Scholar 

  26. Mohanraj M, Jayaraj S, Muraleedharan C. Applications of artificial neural networks for refrigeration, air-conditioning and heat pump systems—a review. Renew Sustain Energy Rev. 2012;16(2):1340–58.

    Article  Google Scholar 

  27. Kurt H, Kayfeci M. Prediction of thermal conductivity of ethylene glycol–water solutions by using artificial neural networks. Appl Energy. 2009;86(10):2244–8.

    Article  CAS  Google Scholar 

  28. Durairaj M, Thamilselvan P. Applications of artificial neural network for IVF data analysis and prediction. J Eng Comput Appl Sci (JEC and AS). 2013;2(9):11–5.

    Google Scholar 

  29. Kalogirou SA. Applications of artificial neural-networks for energy systems. Appl Energy. 2000;67(1):17–35.

    Article  Google Scholar 

  30. Bhoopal RS, Sharma P, Singh R, Beniwal R. Applicability of artificial neural networks to predict effective thermal conductivity of highly porous metal foams. J Porous Media. 2013;7:585–96.

    Article  Google Scholar 

  31. Jang J-S, Sun C-T. Neuro-fuzzy modeling and control. Proc IEEE. 1995;83(3):378–406.

    Article  Google Scholar 

  32. Jang J-SR, Sun C-T. Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence. Upper Saddle River: Prentice-Hall Inc; 1996.

    Google Scholar 

  33. Buragohain M, Mahanta C. A novel approach for ANFIS modelling based on full factorial design. Appl Soft Comput. 2008;8(1):609–25.

    Article  Google Scholar 

  34. Ying L-C, Pan M-C. Using adaptive network based fuzzy inference system to forecast regional electricity loads. Energy Convers Manag. 2008;49(2):205–11.

    Article  Google Scholar 

  35. Ozturk A, Arslan A, Hardalac F. Comparison of neuro-fuzzy systems for classification of transcranial Doppler signals with their chaotic invariant measures. Expert Syst Appl. 2008;34(2):1044–55.

    Article  Google Scholar 

  36. Wang S-C. Artificial neural network. Interdisciplinary computing in java programming. Berlin: Springer; 2003. p. 81–100.

    Book  Google Scholar 

  37. Hagan MT, Demuth HB, Beale MH. Neural network design. Boston: PWS Publisher; 1996.

    Google Scholar 

  38. Harrington PdB. Sigmoid transfer functions in backpropagation neural networks. Anal Chem. 1993;65(15):2167–8.

    Article  CAS  Google Scholar 

  39. Buntine WL, Weigend AS. Bayesian back-propagation. Complex Syst. 1991;5(6):603–43.

    Google Scholar 

  40. Chauvin Y, Rumelhart DE. Backpropagation: theory, architectures, and applications. Hove: Psychology Press; 1995.

    Google Scholar 

  41. Suykens JA, Vandewalle J. Least squares support vector machine classifiers. Neural Process Lett. 1999;9(3):293–300.

    Article  Google Scholar 

  42. Steinwart I, Christmann A. Support vector machines. Berlin: Springer; 2008.

    Google Scholar 

  43. Suykens JA, Vandewalle J. Recurrent least squares support vector machines. IEEE Trans Circuits Syst I Fundam Theory Appl. 2000;47(7):1109–14.

    Article  Google Scholar 

  44. Bair E, Hastie T, Paul D, Tibshirani R. Prediction by supervised principal components. J Am Stat Assoc. 2006;101(473):119–137.

    Article  CAS  Google Scholar 

  45. Björck Ȧ, Pereyra V. Solution of Vandermonde systems of equations. Math Comput. 1970;24(112):893–903.

    Article  Google Scholar 

  46. Macon N, Spitzbart A. Inverses of Vandermonde matrices. Am Math Mon. 1958;65(2):95–100.

    Article  Google Scholar 

  47. Banzhaf W, Nordin P, Keller RE, Francone FD. Genetic programming: an introduction. San Francisco: Morgan Kaufmann Publishers; 1998.

    Book  Google Scholar 

  48. Poli R, Koza J. Genetic programming. Search methodologies. Berlin: Springer; 2014. p. 143–85.

    Book  Google Scholar 

  49. Nilsson NJ. Learning machines: foundations of trainable pattern-classifying systems. New York City: McGraw-Hill; 1965.

    Google Scholar 

  50. Can M. Committee machine networks to diagnose cardiovascular diseases. SouthEast Eur J Soft Comput. 2013;2(1):76-83.

    Google Scholar 

  51. Genest C, Zidek JV. Combining probability distributions: a critique and an annotated bibliography. Stat Sci. 1986;1(1):114–135.

    Article  Google Scholar 

  52. Xu L, Krzyzak A, Suen CY. Methods of combining multiple classifiers and their applications to handwriting recognition. IEEE Trans Syst Man Cybern. 1992;22(3):418–35.

    Article  Google Scholar 

  53. Hashem S, Schmeiser B. Approximating a function and its derivatives using MSE-optimal linear combinations of trained feedforward neural networks. CiteseerX. 1993.

  54. Pourfayaz F, Sanjarian N, Kasaeian A, Razi Astaraie F, Sameti M, Nasirivatan S. An experimental comparison of SiO2/water nanofluid heat transfer in square and circular cross-section channels. J Therm Anal Calorim. 2017. https://doi.org/10.1007/s10973-017-6500-4.

    Google Scholar 

  55. Levenberg K. A method for the solution of certain non-linear problems in least squares. Quart Appl Math. 1944;2:164–8.

    Article  Google Scholar 

  56. Marquardt DW. An algorithm for least-squares estimation of nonlinear parameters. J Soc Ind Appl Math. 1963;11(2):431–41.

    Article  Google Scholar 

  57. Rousseeuw PJ, Leroy AM. Robust regression and outlier detection. Hoboken: Wiley; 2005.

    Google Scholar 

  58. 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 

  59. 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 

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Acknowledgements

The authors would like to thank the reviewers for their valuable comments, which have been utilized in improving the quality of the paper.

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Authors and Affiliations

  1. Department of Chemical Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran

    Alireza Baghban

  2. Department of Renewable Energies, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran

    Fathollah Pourfayaz, Alibakhsh Kasaeian & Seyed Mohsen Pourkiaei

  3. Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran

    Mohammad Hossein Ahmadi

  4. Dipartimento di Ingegneria e Architettura, Università degli Studi di Parma, Parco Area delle Scienze 181/A, 43124, Parma, Italy

    Giulio Lorenzini

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  1. Alireza Baghban
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  2. Fathollah Pourfayaz
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  4. Alibakhsh Kasaeian
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  5. Seyed Mohsen Pourkiaei
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Correspondence to Fathollah Pourfayaz or Mohammad Hossein Ahmadi.

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Baghban, A., Pourfayaz, F., Ahmadi, M.H. et al. Connectionist intelligent model estimates of convective heat transfer coefficient of nanofluids in circular cross-sectional channels. J Therm Anal Calorim 132, 1213–1239 (2018). https://doi.org/10.1007/s10973-017-6886-z

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