Estimation of Functional Form of Time-Dependent Heat Transfer Coefficient Using an Accurate and Robust Parameter Estimation Approach: An Inverse Analysis
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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| Format: | Article |
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MDPI AG
2021-08-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/14/16/5073 |
| _version_ | 1797523945540288512 |
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| author | Farzad Mohebbi Mathieu Sellier |
| author_facet | Farzad Mohebbi Mathieu Sellier |
| author_sort | Farzad Mohebbi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T08:50:19Z |
| format | Article |
| id | doaj.art-0cd7269ddf8b4a7e99c9bd6237460696 |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-10T08:50:19Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-0cd7269ddf8b4a7e99c9bd62374606962023-11-22T07:31:35ZengMDPI AGEnergies1996-10732021-08-011416507310.3390/en14165073Estimation of Functional Form of Time-Dependent Heat Transfer Coefficient Using an Accurate and Robust Parameter Estimation Approach: An Inverse AnalysisFarzad Mohebbi0Mathieu Sellier1Zienkiewicz Centre for Computational Engineering, Faculty of Science and Engineering, Swansea University, Swansea SA1 8EN, UKDepartment of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New ZealandThis 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.https://www.mdpi.com/1996-1073/14/16/5073inverse heat transfersteepest-descent methodsensitivity analysisfunction estimationparameter estimationbody-fitted grid generation |
| spellingShingle | Farzad Mohebbi Mathieu Sellier Estimation of Functional Form of Time-Dependent Heat Transfer Coefficient Using an Accurate and Robust Parameter Estimation Approach: An Inverse Analysis Energies inverse heat transfer steepest-descent method sensitivity analysis function estimation parameter estimation body-fitted grid generation |
| title | Estimation of Functional Form of Time-Dependent Heat Transfer Coefficient Using an Accurate and Robust Parameter Estimation Approach: An Inverse Analysis |
| title_full | Estimation of Functional Form of Time-Dependent Heat Transfer Coefficient Using an Accurate and Robust Parameter Estimation Approach: An Inverse Analysis |
| title_fullStr | Estimation of Functional Form of Time-Dependent Heat Transfer Coefficient Using an Accurate and Robust Parameter Estimation Approach: An Inverse Analysis |
| title_full_unstemmed | Estimation of Functional Form of Time-Dependent Heat Transfer Coefficient Using an Accurate and Robust Parameter Estimation Approach: An Inverse Analysis |
| title_short | Estimation of Functional Form of Time-Dependent Heat Transfer Coefficient Using an Accurate and Robust Parameter Estimation Approach: An Inverse Analysis |
| title_sort | estimation of functional form of time dependent heat transfer coefficient using an accurate and robust parameter estimation approach an inverse analysis |
| topic | inverse heat transfer steepest-descent method sensitivity analysis function estimation parameter estimation body-fitted grid generation |
| url | https://www.mdpi.com/1996-1073/14/16/5073 |
| work_keys_str_mv | AT farzadmohebbi estimationoffunctionalformoftimedependentheattransfercoefficientusinganaccurateandrobustparameterestimationapproachaninverseanalysis AT mathieusellier estimationoffunctionalformoftimedependentheattransfercoefficientusinganaccurateandrobustparameterestimationapproachaninverseanalysis |