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Estimation of Functional Form of Time-Dependent Heat Transfer Coefficient Using an Accurate and Robust Parameter Estimation Approach: An Inverse Analysis

Farzad Mohebbi, Mathieu Sellier

Energies, Volume: 14, Issue: 16, Start page: 5073

Swansea University Author: Farzad Mohebbi

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DOI (Published version): 10.3390/en14165073

Abstract

This paper presents a numerical method to address function estimation problems in inverse heat transfer problems using parameter estimation approach without prior information on the functional form of the variable to be estimated. Using an inverse analysis, the functional form of a time-dependent he...

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Published in: Energies
ISSN: 1996-1073
Published: MDPI AG 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa57741
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Abstract: This paper presents a numerical method to address function estimation problems in inverse heat transfer problems using parameter estimation approach without prior information on the functional form of the variable to be estimated. Using an inverse analysis, the functional form of a time-dependent heat transfer coefficient is estimated efficiently and accurately. The functional form of the heat transfer coefficient is assumed unknown and the inverse heat transfer problem should be treated using a function estimation approach by solving sensitivity and adjoint problems during the minimization process. Based on proposing a new sensitivity matrix, however, the functional form can be estimated in an accurate and very efficient manner using a parameter estimation approach without the need for solving the sensitivity and adjoint problems and imposing extra computational cost, mathematical complexity, and implementation efforts. In the proposed sensitivity analysis scheme, all sensitivity coefficients can be computed in only one direct problem solution at each iteration. In this inverse heat transfer problem, the body shape is irregular and meshed using a body-fitted grid generation method. The direct heat conduction problem is solved using the finite-difference method. The steepest-descent method is used as a minimization algorithm to minimize the defined objective function and the termination of the minimization process is carried out based on the discrepancy principle. A test case with three different functional forms and two different measurement errors is considered to show the accuracy and efficiency of the used inverse analysis.
Keywords: inverse heat transfer; steepest-descent method; sensitivity analysis; function estimation; parameter estimation; body-fitted grid generation; time-dependent heat transfer coefficient
College: Faculty of Science and Engineering
Funders: This research was supported by funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 663830.
Issue: 16
Start Page: 5073