Skip to main content
SpringerLink
Log in

Optimization of turbulent convective heat transfer of CuO/water nanofluid in a square duct

An artificial neural network analysis

  • Published:
Journal of Thermal Analysis and Calorimetry Aims and scope Submit manuscript

Abstract

Analysis of the turbulent forced convective heat transfer of CuO/water nanofluid has been conducted employing an artificial neural network. A backpropagation network with two hidden layers has been used to investigate and optimize the effects of the Reynolds number, volume fraction and nanoparticle diameter on heat transfer, pressure drop and entropy generation. In order to train the network, the Levenberg–Marquardt algorithm has been applied. The results of a total of 168 sample models, considering the extended range of input data, have been prepared as the training data for the network. The precision of the network based on the mean squared error for a set of random experimental data has been approximately 0.05. The obtained results of the artificial neural network are presented in an extended range of Re, \(\varphi\) and particle diameter. Results indicate that heat transfer enhancement is achieved by increasing Re and volume fraction. While augmenting Re reduces the friction factor, it is increased at higher volume fractions. The optimum conditions concerning Nusselt number, friction factor and entropy generation have been investigated. For instance, at low volume fractions, the ratio \(Nu/f^{1/3} S^{2}\) has the highest value in the range \(5 \times 10^{4} < Re < 6 \times 10^{4}\), which is a proper range of performance for the nanofluid.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Abbreviations

a :

Activation function

ANN:

Artificial neural network

c p :

Specific heat (J kg−1 K−1)

d p :

Particle diameter (nm)

D h :

Hydraulic diameter (m)

e :

Error vector

E :

Mean squared error

f :

Peripherally averaged friction Factor \(( = 2\Delta PD_{\text{h}} /(l u^{2} ))\)

g :

Gradient matrix

H :

Hessian matrix

h :

Peripherally averaged convective heat transfer coefficient (W m−2 K−1) \(( = q^{\prime \prime } /(\hat{T}_{\text{wall}} - T_{\text{bulk}} ))\))

J :

Jacobian matrix

l :

Duct length (m)

N :

Number of training data

Nu :

Peripherally averaged Nusselt number \(( = hD_{\text{h}} /\lambda )\)

\(q^{\prime \prime }\) :

Heat flux (W m−2)

Re :

Reynolds number based on hydraulic diameter \(( = uD_{\text{h}} /\nu )\)

S gen :

Entropy generation

S :

Ratio of total entropy generation

t :

Network target

T :

Temperature (K)

\(\hat{T}_{\text{wall}}\) :

Peripherally averaged wall temperature (K)

u, v, w :

Velocity along x, y, z (m s−1)

V :

Volume of flow domain (m3)

w ij :

Network mass

X :

Network input

x :

Variable

y :

Network output

η :

Learning rate

κ :

Boltzmann constant (= 1.3807 × 1023 J K−1)

λ :

Thermal conductivity (W m−1 K−1)

μ :

Dynamic viscosity (N s m−2)

ρ :

Density (kg m−3)

ν :

Kinematic viscosity (m2 s−1)

φ :

Particle volume fraction

bf:

Base fluid

bulk:

Bulk

nf:

Nanofluid

p:

Particle

w:

Water

References

  1. Mahian O, Kianifar A, Heris SZ, Wen D, Sahin AZ, Wongwises S. Nanofluids effects on the evaporation rate in a solar still equipped with a heat exchanger. Nano Energy. 2017;36:134–55.

    Article  CAS  Google Scholar 

  2. Bazdidi-Tehrani F, Khabazipur A, Vasefi SI. Flow and heat transfer analysis of TiO2/water nanofluid in a ribbed flat-plate solar collector. Renew Energy. 2018;122:406–18.

    Article  CAS  Google Scholar 

  3. Mahian O, Kolsi L, Amani M, Estellé P, Ahmadi G, Kleinstreuer C, et al. Recent advances in modeling and simulation of nanofluid flows—part I: fundamental and theory. Phys Rep. 2018;790:1–48.

    Article  Google Scholar 

  4. Mahian O, Kolsi L, Amani M, Estellé P, Ahmadi G, Kleinstreuer C, et al. Recent advances in modeling and simulation of nanofluid flows—part II: applications. Phys Rep. 2018;791:1–59.

    Article  Google Scholar 

  5. Bahiraei M, Rahmani R, Yaghoobi A, Khodabandeh E, Mashayekhi R, Amani M. Recent research contributions concerning use of nanofluids in heat exchangers: a critical review. Appl Therm Eng. 2018;133:137–59.

    Article  CAS  Google Scholar 

  6. Das SK, Choi SU, Patel HE. Heat transfer in nanofluids—a review. Heat Transf Eng. 2006;27(10):3–19.

    Article  CAS  Google Scholar 

  7. Pandey SD, Nema V. Experimental analysis of heat transfer and friction factor of nanofluid as a coolant in a corrugated plate heat exchanger. Exp Therm Fluid Sci. 2012;38:248–56.

    Article  CAS  Google Scholar 

  8. Zarringhalam M, Karimipour A, Toghraie D. Experimental study of the effect of solid volume fraction and Reynolds number on heat transfer coefficient and pressure drop of CuO–water nanofluid. Exp Therm Fluid Sci. 2016;76:342–51.

    Article  CAS  Google Scholar 

  9. Williams W, Buongiorno J, Hu L-W. Experimental investigation of turbulent convective heat transfer and pressure loss of alumina/water and zirconia/water nanoparticle colloids (nanofluids) in horizontal tubes. J Heat Transf. 2008;130(4):042412–9.

    Article  Google Scholar 

  10. Mojarrad MS, Keshavarz A, Ziabasharhagh M, Raznahan MM. Experimental investigation on heat transfer enhancement of alumina/water and alumina/water–ethylene glycol nanofluids in thermally developing laminar flow. Exp Therm Fluid Sci. 2014;53:111–8.

    Article  CAS  Google Scholar 

  11. Heris SZ, Edalati Z, Noie SH, Mahian O. Experimental investigation of Al2O3/water nanofluid through equilateral triangular duct with constant wall heat flux in laminar flow. Heat Transf Eng. 2014;35(13):1173–82.

    Article  CAS  Google Scholar 

  12. Jafaryar M, Sheikholeslami M, Li Z, Moradi R. Nanofluid turbulent flow in a pipe under the effect of twisted tape with alternate axis. J Therm Anal Calorim. 2018;135:305–23.

    Article  Google Scholar 

  13. Mehrjou B, Heris SZ, Mohamadifard K. Experimental study of CuO/water nanofluid turbulent convective heat transfer in square cross-section duct. Exp Heat Transf. 2015;28(3):282–97.

    Article  CAS  Google Scholar 

  14. Bahiraei M, Jamshidmofid M, Goodarzi M. Efficacy of a hybrid nanofluid in a new microchannel heat sink equipped with both secondary channels and ribs. J Mol Liq. 2019;273:88–98.

    Article  CAS  Google Scholar 

  15. Vasefi SI, Bazdidi-Tehrani F, Reyhani L. Assessment of mean and fluctuating velocity and temperature of CuO/water nanofluid in a horizontal channel: large eddy simulation. Numer Heat Transf Part A Appl. 2018;74(9):1520–38.

    Article  CAS  Google Scholar 

  16. Bazdidi-Tehrani F, Vasefi SI, Khabazipur A. Scale-adaptive simulation of turbulent mixed convection of nanofluids in a vertical duct. J Therm Anal Calorim. 2018;131(3):3011–23.

    Article  CAS  Google Scholar 

  17. Zadeh AD, Toghraie D. Experimental investigation for developing a new model for the dynamic viscosity of silver/ethylene glycol nanofluid at different temperatures and solid volume fractions. J Therm Anal Calorim. 2018;131(2):1449–61.

    Article  CAS  Google Scholar 

  18. Bahiraei M, Vasefi SI. A novel thermal dispersion model to improve prediction of nanofluid convective heat transfer. Adv Powder Technol. 2014;25(6):1772–9.

    Article  CAS  Google Scholar 

  19. Siavashi M, Jamali M. Heat transfer and entropy generation analysis of turbulent flow of TiO2–water nanofluid inside annuli with different radius ratios using two-phase mixture model. Appl Therm Eng. 2016;100:1149–60.

    Article  CAS  Google Scholar 

  20. Buongiorno J. Convective transport in nanofluids. J Heat Transf. 2006;128(3):240–50.

    Article  Google Scholar 

  21. Bazdidi-Tehrani F, Sedaghatnejad M, Vasefi SI, Jolandan NE. Investigation of mixed convection and particle dispersion of nanofluids in a vertical duct. Proc Inst Mech Eng Part C J Mech Eng Sci. 2016;230(20):3691–705.

    Article  CAS  Google Scholar 

  22. Bazdidi-Tehrani F, Vasefi SI, Anvari AM. Analysis of particle dispersion and entropy generation in turbulent mixed convection of CuO–water nanofluid. Heat Transf Eng. 2019;40(1–2):81–94.

    Google Scholar 

  23. Fausett L. Fundamentals of neural networks. 1st ed. Upper Saddle River: Prentice Hall; 1994.

    Google Scholar 

  24. Gurney K. An introduction to neural networks. 1st ed. Abingdon: Taylor & Francis; 2003.

    Google Scholar 

  25. Hassoun MH. Fundamentals of artificial neural networks. 1st ed. Cambridge: MIT Press; 1995.

    Google Scholar 

  26. Ertunc H, Hosoz M. Artificial neural network analysis of a refrigeration system with an evaporative condenser. Appl Therm Eng. 2006;26(5):627–35.

    Article  CAS  Google Scholar 

  27. Jambunathan K, Hartle S, Ashforth-Frost S, Fontama V. Evaluating convective heat transfer coefficients using neural networks. Int J Heat Mass Transf. 1996;39(11):2329–32.

    Article  CAS  Google Scholar 

  28. Parlak A, Islamoglu Y, Yasar H, Egrisogut A. Application of artificial neural network to predict specific fuel consumption and exhaust temperature for a diesel engine. Appl Therm Eng. 2006;26(8):824–8.

    Article  CAS  Google Scholar 

  29. Shokouhmand H, Ghazvini M, Shabanian J, editors. Performance analysis of using nanofluids in microchannel heat sink in different flow regimes and its simulation using artificial neural network. In: Proceedings of the World Congress on Engineering (WCE’08); 2008: Citeseer.

  30. Esfe MH, Bahiraei M, Hajmohammad MH, Afrand M. Rheological characteristics of MgO/oil nanolubricants: experimental study and neural network modeling. Int Commun Heat Mass Transf. 2017;86:245–52.

    Article  Google Scholar 

  31. Bahiraei M, Hosseinalipour SM, Zabihi K, Taheran E. Using neural network for determination of viscosity in water–TiO2 nanofluid. Adv Mech Eng. 2012;4:742680.

    Article  Google Scholar 

  32. Amani M, Amani P, Kasaeian A, Mahian O, Pop I, Wongwises S. Modeling and optimization of thermal conductivity and viscosity of MnFe2O4 nanofluid under magnetic field using an ANN. Sci Rep. 2017;7(1):17369.

    Article  Google Scholar 

  33. Pak BC, Cho YI. Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp Heat Transf Int J. 1998;11(2):151–70.

    Article  CAS  Google Scholar 

  34. Nazififard M, Nematollahi M, Jafarpur K, Suh KY. Numerical simulation of water-based alumina nanofluid in subchannel geometry. Sci Technol Nucl Install. 2012. https://doi.org/10.1155/2012/928406.

    Article  Google Scholar 

  35. Sundar LS, Singh MK. Convective heat transfer and friction factor correlations of nanofluid in a tube and with inserts: a review. Renew Sustain Energy Rev. 2013;20:23–35.

    Article  Google Scholar 

  36. Moraveji MK, Darabi M, Haddad SMH, Davarnejad R. Modeling of convective heat transfer of a nanofluid in the developing region of tube flow with computational fluid dynamics. Int Commun Heat Mass Transf. 2011;38(9):1291–5.

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  38. Nguyen C, Desgranges F, Roy G, Galanis N, Maré T, Boucher S, et al. Temperature and particle-size dependent viscosity data for water-based nanofluids—hysteresis phenomenon. Int J Heat Fluid Flow. 2007;28(6):1492–506.

    Article  CAS  Google Scholar 

  39. Patankar S. Numerical heat transfer and fluid flow. Abingdon: Taylor & Francis; 1980.

    Google Scholar 

  40. Cruz C. Understanding neural networks: a primer. 1st ed. Arlington: Cutter Information Corporation; 1991.

    Google Scholar 

  41. Han J, Moraga C, editors. The influence of the sigmoid function parameters on the speed of backpropagation learning. In: International workshop on artificial neural networks. Berlin: Springer; 1995. pp. 195–201.

  42. Bishop CM. Neural networks for pattern recognition. 1st ed. New York: Oxford University Press; 1995.

    Google Scholar 

  43. Haykin S. Neural networks: a comprehensive foundation. 2nd ed. Upper Saddle River: Prentice Hall; 1994.

    Google Scholar 

  44. Battiti R. First-and second-order methods for learning: between steepest descent and Newton’s method. Neural Comput. 1992;4(2):141–66.

    Article  Google Scholar 

  45. Bejan A. Entropy generation through heat and fluid flow. Hoboken: Wiley; 1982.

    Google Scholar 

  46. Chu P, He Y, Lei Y, Tian L, Li R. Three-dimensional numerical study on fin-and-oval-tube heat exchanger with longitudinal vortex generators. Appl Therm Eng. 2009;29(5–6):859–76.

    Article  Google Scholar 

  47. Karwa R, Sharma C, Karwa N. Performance evaluation criterion at equal pumping power for enhanced performance heat transfer surfaces. J Sol Energy. 2013. https://doi.org/10.1155/2013/370823.

    Article  Google Scholar 

  48. Ji Y, Zhang H-C, Yang X, Shi L. Entropy generation analysis and performance evaluation of turbulent forced convective heat transfer to nanofluids. Entropy. 2017;19(3):108.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Iran University of Science and Technology, Tehran, 16846-13114, Iran

    Seyed Iman Vasefi, Farzad Bazdidi-Tehrani, Mohammad Sedaghatnejad & Arash Khabazipur

Authors
  1. Seyed Iman Vasefi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Farzad Bazdidi-Tehrani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohammad Sedaghatnejad
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Arash Khabazipur
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Farzad Bazdidi-Tehrani.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vasefi, S.I., Bazdidi-Tehrani, F., Sedaghatnejad, M. et al. Optimization of turbulent convective heat transfer of CuO/water nanofluid in a square duct. J Therm Anal Calorim 138, 517–529 (2019). https://doi.org/10.1007/s10973-019-08128-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-019-08128-5

Keywords

Search

Navigation