Hybrid Model of Cooling Tower Based on First Principles and Neural Networks

  • Nenad Milosavljevic
  • Henrik Saxén
Conference paper


Mathematical modelling in paper industry is to a large extent based on physical models that usually contain empirical correlations and assumptions. Milosavljevic and Heikkilå [1] derived a mathematical model for a counter-flow wet cooling tower based on one-dimensional heat and mass balance equations using an expression for the volumetriv heat transfer coefficient. In the present study, volumetric heat transfer coefficient values determined by the above-mentioned model on the basis of measurements from a pilot cooling tower were approximated with feed-forward neural networks. It was found that a considerably more accurate approximation of the coefficient was obtained with the neural network than by conventional non-linear regression. The implementation of the expression in the first-principles model can lead to more accurate dimensioning of cooling towers, which results in lower equipment costs and better energy utilization.


Heat Transfer Coefficient Mass Flow Rate Mass Balance Equation Water Film Cool Tower 
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  1. [1]
    Milosavljevic, N. and Heikkilä, P.: A Comprehensive Approach to Cooling Tower Design. To appear in Applied Thermal Engineering, (2001).Google Scholar
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    Fredman, T. and Saxen H.: Modelling and Simulation of a Cooling Tower. Proceedings of European Simulation Multiconference, 66–70, (1995).Google Scholar
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    Levenberg, K.: A Method for Solution of Certain Nonlinear Problems in Least-Squares. Quart. Appl. Math. 2, 164–168, (1944).MathSciNetMATHGoogle Scholar
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    Marquardt, D.W.: An algorithm for least-squares estimation of nonlinear parameters, J. SIAM. 11, 431–441, (1963).MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • Nenad Milosavljevic
    • 1
  • Henrik Saxén
    • 2
  1. 1.Valmet Corporation, Air SystemsPansio, TurkuFinland
  2. 2.Heat Eng. Lab.Åbo Akademi UniversityTurkuFinland

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