Heat and Mass Transfer

, Volume 53, Issue 2, pp 673–685 | Cite as

Prediction of friction factor of pure water flowing inside vertical smooth and microfin tubes by using artificial neural networks

  • A. Çebi
  • E. Akdoğan
  • A. Celen
  • A. S. DalkilicEmail author


An artificial neural network (ANN) model of friction factor in smooth and microfin tubes under heating, cooling and isothermal conditions was developed in this study. Data used in ANN was taken from a vertically positioned heat exchanger experimental setup. Multi-layered feed-forward neural network with backpropagation algorithm, radial basis function networks and hybrid PSO-neural network algorithm were applied to the database. Inputs were the ratio of cross sectional flow area to hydraulic diameter, experimental condition number depending on isothermal, heating, or cooling conditions and mass flow rate while the friction factor was the output of the constructed system. It was observed that such neural network based system could effectively predict the friction factor values of the flows regardless of their tube types. A dependency analysis to determine the strongest parameter that affected the network and database was also performed and tube geometry was found to be the strongest parameter of all as a result of analysis.


Artificial Neural Network Hide Layer Mass Flow Rate Friction Factor Hydraulic Diameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols


Mass flow rate (kg/s)


Pressure drop (mbar)


Cross section of the pipe (m2)


Hydraulic diameter (mm)


Equivalent hydraulic diameter (mm)


Inner diameter (mm)


Outer diameter (mm)


Fin height (mm)


Friction factor (−)


Length of the pipe (m)


Number of fins around the inner perimeter (−)


Fin pitch (mm)


Pipe wall thickness (mm)


Average velocity (m/s)


Helix angle (°)


Average density (kg/m3)



Artificial intelligence


Artificial neural network


Bayesian regulation




Multi-layer perceptron


Mean square error


Particle swarm optimization


Correlation coefficient


Radial basis function


Resilient backpropagation


Scaled conjugate gradient



This study has been financially supported by Yildiz Technical University Scientific Research Projects Coordination Department, Project Number 2013-06-01-KAP01. The authors also wish to thank Wieland-Wilke AG (Ulm, Germany) for valuable donation of the microfin tube used in the present study.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • A. Çebi
    • 1
  • E. Akdoğan
    • 2
  • A. Celen
    • 1
  • A. S. Dalkilic
    • 1
    Email author
  1. 1.Heat and Thermodynamics Division, Department of Mechanical Engineering, Faculty of Mechanical EngineeringYildiz Technical UniversityIstanbulTurkey
  2. 2.Department of Mechatronics Engineering, Faculty of Mechanical EngineeringYildiz Technical UniversityIstanbulTurkey

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