Skip to main content
Log in

Viscosity of carbon nanotube suspension using artificial neural networks with principal component analysis

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

This paper applies the model including back-propagation network (BPN) and principal component analysis (PCA) to estimate the effective viscosity of carbon nanotubes suspension. The effective viscosities of multiwall carbon nanotubes suspension are examined as a function of the temperature, nanoparticle volume fraction, effective length of nanoparticle and the viscosity of base fluids using artificial neural network. The obtained results by BPN–PCA model have good agreement with the experimental data.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Eastman JA, Choi SUS, Li S, Yu W, Thompson LJ (2001) Anoma-lously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Appl Phys Lett 78:718–720

    Article  Google Scholar 

  2. Xuan Y, Li Q (2000) Heat transfer enhancement of nanofluids. Int J Heat Fluid Flow 21:58–64

    Article  Google Scholar 

  3. Jang SP, Choi SUS (2004) Role of brownian motion in the enhanced thermal conductivity of nanofluids. Appl Phys Lett 84:4316–4318

    Article  Google Scholar 

  4. Maxwell JC (1904) A treatise on electricity and magnetism, 3rd edn. Clarendon Press, Oxford

    MATH  Google Scholar 

  5. Sohn CW, Chen MM (1981) Microconvective thermal conductivity in disperse two phase mixture as observed in a low velocity Couette flow experiment. J Heat Transf Trans ASME 103:47–51

    Article  Google Scholar 

  6. Nguyen CT, Desgranges F, Roy G, Galanis N, Maré T (2007) Temperature and particles-size dependent viscosity data for water-based nanofluids—Hysteresis phenomenon. Int J Heat Fluid Flow 28:1492–1506

    Article  Google Scholar 

  7. Maré T, Halelfadl S, Sow O, Estellé P, Duret S, Bazantay F (2011) Comparison of the thermal performances of three nanofluids at low temperature in a plate heat exchanger. Exp Therm Fluid Sci 35:1535–1543

    Article  Google Scholar 

  8. Ferrouillat S, Bontemps A, Ribeiro JP, Gruss JA, Soriano O (2011) Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature boundry conditions. Int J Heat Fluid Flow 32:424–439

    Article  Google Scholar 

  9. Wang X, Choi SUS (1999) Thermal conductivity of nanoparticle–fluid mixture. J Thermophys Heat Transf 13:474–480

    Article  Google Scholar 

  10. Chevalier J, Tillement O, Ayela F (2007) Rheogical properties of nanofluids flowing through microchannels. Appl Phys Lett 91:233103

    Article  Google Scholar 

  11. Chen HS, Ding YL, Tan CQ (2007) Rheological behaviour of nanofluids. New J Phys 9:1–25

    Article  Google Scholar 

  12. Chen HS, Ding YL, Lapkin A, Fan X (2009) Rheological behavior of ethylene glycol-titanate nanotube nanofluids. J Nanopart Res 11:1513–1520

    Article  Google Scholar 

  13. Kulkarni DP, Debendra KD, Ravikanth SV (2009) Application of nanofluids in heating buildings and reducing pollution. Appl Energy 86:2566–2573

    Article  Google Scholar 

  14. Kole M, Dey TK (2010) Thermal conductivity and viscosity of Al2O3 nanofluid based on car engine coolant. J Phys D Appl Phys 43:315501

    Article  Google Scholar 

  15. Einstein A (1906) Einene uebestimmung der molekul dimensionen. Ann Phys 19:289–306

    Article  Google Scholar 

  16. Batchelor GK (1977) The effect of Brownian motion on the bulk stress in the suspension of spherical particles. J Fluid Mech 83:97–117

    Article  MathSciNet  Google Scholar 

  17. Masoumi N, Sohrabi N, Behzadmehr A (2009) A new model for calculating the effective viscosity of nanofluids. J Phys D Appl Phys 42:055501–055507

    Article  Google Scholar 

  18. Hosseini MS, Mohebbi A, Ghader S (2010) Correlation of shear viscosity of nanofluids using the local composition theory. Chin J Chem Eng 18:102–110

    Article  Google Scholar 

  19. Nguyen CT, Desgranges F, Galanis N, Roy G, Mare T, Boucher S, Angue Mintsa H (2008) Viscosity data for Al2O3–water nanofluid-hysteresis: is heat transfer enhancement using nanofluids reliable. Int J Therm Sci 47:103–111

    Article  Google Scholar 

  20. Maiga SEB, Nguyen CT, Galanis N, Roy G (2004) Heat transfer behaviors of nanofluids in a uniformly heated tube. Superlattices Microstruct 35:543–557

    Article  Google Scholar 

  21. Kulkarni DP, Das DK, Chukwu G (2006) Temperature dependent rheological property of copper oxide nanoparticles suspension (Nanofluid). J Nanosci Nanotechnol 6:1150–1154

    Article  Google Scholar 

  22. Yousefi F, Karimi H, Papari MM (2012) Modeling viscosity of nanofluids using diffusional neural networks. J Mol Liq 175:85–90

    Article  Google Scholar 

  23. Karimi H, Yousefi F (2012) Application of artificial neural network–genetic algorithm (ANN–GA) to correlation of density in nanofluid. Fluid Phase Equilib 336:79–83

    Article  Google Scholar 

  24. Sablani SS, Kacimov A, Perret J, Mujumdar AS, Campo A (2005) Non-iterative estimation of heat transfer coefficients using neural network models. Int J Heat Mass Transf 48:665–790

    Article  MATH  Google Scholar 

  25. Kurt H, Atik K, Ozkaymak M, Binark AK (2006) The artificial neural network approach for evolution of temperature and density profiles of salt gradient solar pond. J Energy Inst 80:46–51

    Article  Google Scholar 

  26. Papari MM, Yousefi F, Moghadasi J, Karimi H, Campo A (2011) Modeling thermal conductivity augmentation of nanofluids using diffusion neural networks. Int J Therm Sci 50:44–52

    Article  Google Scholar 

  27. Yousefi F, Karimi H, Gomar M (2013) Ability of analytical and artificial approaches for prediction of the volumetric properties of some polymer blends. Fluid Phase Equilib 355:92–98

    Article  Google Scholar 

  28. Yousefi F, Karimi H (2013) Application of equation of state and artificial neural network to prediction of volumetric properties of polymer melts. J Ind Eng Chem 19:498–507

    Article  Google Scholar 

  29. Yousefi F, Karimi H (2012) P-V–T properties of polymer melts based on equation of state and neural network. Eur Polym J 48:1135–1143

    Article  Google Scholar 

  30. Yousefi F, Karimi H, Gandomkar Z (2014) Equation of state and artificial neural network to predict the thermodynamic properties of pure and mixture of liquid alkali metals. Fluid Phase Equilib 370:43–49

    Article  Google Scholar 

  31. Yousefi F, Karimi H, Alekasir E, Shishebor M (2015) Prediction of thermodynamic behavior of copolymers using equation of state and artificial neural network. Colloid Polym Sci 293:75–87

    Article  Google Scholar 

  32. Chauhan D, Singhvi N, Singh R (2013) Dependence of effective thermal conductivity of composite materials on the size of fillerparticles. J Reinf Plast Compos 32:1323–1330

    Article  Google Scholar 

  33. Ahadian S, Hiroshi M, Yoshiyuki K (2011) Effects of hydration level, temperature, side chain and backbone flexibility of the polymer on the proton transfer in short-side-chain perfluorosulfonic acid membranes at low humidity conditions. J Membr Sci 369:339–349

    Article  Google Scholar 

  34. Xinliang Y, Xueye W, Bo L (2010) Prediction of the Q-e parameters rom radical structures. Colloid Polym Sci 288:951–958

    Article  Google Scholar 

  35. Xinliang Y, Bing Y, Fang L et al (2008) Prediction of the dielectric dissipation factor tan delta of polymers with an ANN model based on the DFT calculation. React Funct Polym 68:1557–1562

    Article  Google Scholar 

  36. Zhang Z, Fried K (2003) Artificial neural networks applied to polymer composites: a review. Compos Sci Technol 63:2029–2044

    Article  Google Scholar 

  37. Khajeh A, Modarress H (2010) Prediction of solubility of gases in polystyrene by adaptive neuro-fuzzy inference system and radial basis function neural network. Expert Syst Appl 37:3070–3074

    Article  Google Scholar 

  38. Gharagheizi F, Salehi GR (2011) Prediction of enthalpy of fusion of pure compounds using an artificial neural network-group contribution method. Thermochim Acta 52137–40

  39. Sencan A, Ilke Köse I, Selbas R (2011) Prediction of thermophysical properties of mixed refrigerants using artificial neural network. Energy Convers Manag 52:958–974

    Article  Google Scholar 

  40. Poole CP, Owens FJ (2003) Introduction to Nanothechnology. Wiley, Hoboken

    Google Scholar 

  41. Iijima S (1991) Helical microtubules of graphitic carbon. Nature 354:56–58

    Article  Google Scholar 

  42. Dresselhaus MS, Dresselhaus G, Avouris P (2001) Carbon nanotubes: synthesis, properties, and applications. Springer, Berlin

    Book  Google Scholar 

  43. Huang JY, Chen S, Wang ZQ, KempaK Wang YM, Jo SH, Chen G, Dresselhaus MS, Ren ZF (2006) Superplastic single-walled carbon nanotubes. Nature 439:281

    Article  Google Scholar 

  44. Van der SmagtP P (1994) Minimization methods for training feed forward neural network. Neural Netw 7:1994

    Google Scholar 

  45. Huang CF, Moraga C (2004) A diffusion-neural-network for learning from small samples. Int J Approx Reason 35:137–161

    Article  MathSciNet  MATH  Google Scholar 

  46. Lanouette R, Thibault J, Valade JL (1999) Process modeling with neural networks using small experimental datasets. Comput Chem Eng 23:1167–1176

    Article  Google Scholar 

  47. http://en.wikipedia.org/wiki/Principal_component_analysis

  48. Wang X, Paliwal KK (2003) Feature extraction and dimensionality reduction algorithms and their applications in vowel recognition. J Pattern RecognSoc 36:2429–2439

    Article  MATH  Google Scholar 

  49. Smith Lindsay I (2002) A tutorial on principal components analysis. http://kybele.psych.cornell.edu/~edelman/Psych-465Spring-2003/PCA-tutorial

  50. Kumaresan V, Velraj R (2012) Experimental investigation of the thermo-physical properties of water–ethylene glycol mixture based CNT nanofluids. Thermochim Acta 545:180–186

    Article  Google Scholar 

  51. Chen Lifei, Xie Huaqing, Li Yang, Wei Yu (2008) Nanofluids containing carbon nanotubes treated by mechanochemical reaction. Thermochim Acta 477:21–24

    Article  Google Scholar 

  52. Halelfadl S, Estellé P, Aladag B, Doner N, Maré Th (2013) Viscosity of carbon nanotubes water based nanofluids: influence of concentration and temperature. Int J Therm Sci 71:111–117

    Article  Google Scholar 

  53. Liu ZH, Yang XF, Xiong JG (2010) Boiling characteristics of carbon nanotube suspensions under sub-atmospheric pressures. Int J Therm Sci 49:1156–1164

    Article  Google Scholar 

  54. Jyothirmayee Aravind SS, Baskar P, Th Baby T, Sabareesh RK, Das S, Ramaprabhu S (2011) Investigation of structural stability, dispersion, viscosity, and conductive heat transfer properties of functionalized carbon nanotube based nanofluids. J Phys Chem C 115(34):6737–6744

    Google Scholar 

  55. Einstein A (1906) Einenen uebestimmung der moleküldimensionen. Ann Phys 324(2):289–306

    Article  Google Scholar 

  56. Brinkman HC (1952) The viscosity of concentrated suspensions and solutions. J Chem Phys 20:571–581

    Article  Google Scholar 

  57. Batchelor G (1977) The effect of Brownian motion on the bulk stress in a suspension of spherical particles. J Fluid Mech 83:97–117

    Article  MathSciNet  Google Scholar 

  58. Cheng NS, Wing-Keung Law A (2003) Experimental formula for computing effecttive viscosity. J Powder Technol 129:156–160

    Article  Google Scholar 

  59. Krieger IM, Dougherty TJ (1959) A mechanism for non-Newtonian flow in suspension of rigid spheres. J Trans Soc Rheol 3:137–152

    Article  MATH  Google Scholar 

  60. Vand V (1948) Viscosity of solutions and suspensions. J Phys Colloid Chem Theory 52:277–299

    Article  Google Scholar 

  61. Saito N (1950) Concentration dependence of the viscosity of high polymer solutions. J Phys Soc Jpn I 5:4–8

    Article  Google Scholar 

  62. Lundgren TS (1972) Slow flow through stationary random beds and suspensions of spheres. J Fluid Mech 51(2):273–299

    Article  MATH  Google Scholar 

  63. Karimi H, Yousefi F, Rahimi MR (2011) Correlation of viscosity in nanofluids using geneticalgorithm-neural network (GA-NN). Heat Mass Transf 47:1417–1425

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fakhri Yousefi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yousefi, F., Karimi, H. & Mohammadiyan, S. Viscosity of carbon nanotube suspension using artificial neural networks with principal component analysis. Heat Mass Transfer 52, 2345–2355 (2016). https://doi.org/10.1007/s00231-015-1745-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-015-1745-6

Keywords

Navigation