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An Adaptive Matrix Method for the Solution of a Nonlinear Inverse Heat Transfer Problem and Its Experimental Verification

Author

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  • Piotr Duda

    (Institute of Thermal and Process Engineering, Cracow University of Technology, Al. Jana Pawła II 37, 31-864 Krakow, Poland)

  • Mariusz Konieczny

    (Institute of Thermal and Process Engineering, Cracow University of Technology, Al. Jana Pawła II 37, 31-864 Krakow, Poland)

Abstract

An adaptive matrix inverse (AMI) method is presented to identify the temperature and unknown boundary heat flux in a domain of a regular or irregular shape with temperature-dependent properties. The nonlinear problem is broken down into a number of linear submodels, and for each submodel, the temperature is obtained in measuring points. Next, based on the matching degree between the temperatures measured and calculated by each prediction submodel, the submodels are weighted and combined to create the full model for the solution of an inverse nonlinear heat transfer problem. Comparisons are also made with the existing multiple model adaptive inverse (MMAI) algorithm and method based on the Levenberg–Marquardt algorithm (LMA). The results of the presented numerical tests for undisturbed and disturbed “measuring” data indicate that the heat fluxes identified by the AMI method are close to the exact values. The application of the presented method for bodies with an irregular shape is also demonstrated. The AMI method has been experimentally verified during the thick-walled cylinder cooling process. The proposed method can be applied in online diagnostic systems for thermal state monitoring.

Suggested Citation

  • Piotr Duda & Mariusz Konieczny, 2023. "An Adaptive Matrix Method for the Solution of a Nonlinear Inverse Heat Transfer Problem and Its Experimental Verification," Energies, MDPI, vol. 16(6), pages 1-22, March.
    • Handle: RePEc:gam:jeners:v:16:y:2023:i:6:p:2649-:d:1094363
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    References listed on IDEAS

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    1. Chertkov, Michael & Novitsky, Nikolai N., 2019. "Thermal Transients in District Heating Systems," Energy, Elsevier, vol. 184(C), pages 22-33.
    2. Piotr Duda & Mariusz Konieczny, 2022. "An Iterative Algorithm for the Estimation of Thermal Boundary Conditions Varying in Both Time and Space," Energies, MDPI, vol. 15(7), pages 1-13, April.
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