Sensitivity analysis and identification of an effective heat transport model in wavy liquid films.



  • M. Karalashvili
  • A. Mhamdi
  • G. F. Dietze
  • H. M. Bücker
  • A. Vehreschild
  • R. Kneer
  • C. H. Bischof
  • W. Marquardt


Thin liquid films flowing down vertical or inclined planes are of high industrial relevance. Nevertheless, a predictive transport model describing the effects of wave-induced intensification of heat and mass transport for the design of technical systems does not yet exist. In this paper, a systematic approach for the identification of a suitable transport model (structure and parameters) for the effective heat transport coefficient in the reduced system of heat transport equations is presented. For this transport coefficient two different model structures are proposed. An investigation of parameter identifiability based on local sensitivity analysis is carried out for both model structures prior to model identification. It is shown that the number of model parameters can be significantly reduced by targeted selection of the identifiable parameter subsets. This facilitates to reduce the overall computational effort. After setting up the best identifiable parameter sets for each model structure, a nonlinear, constrained least-squares parameter estimation problem is stated and solved using standard solution methods. Automatic differentiation techniques are applied for efficient sensitivity computations as well as for the gradients calculation within the parameter estimation step. Finally, the best model candidate is determined using statistical model discrimination techniques.