Reconstructing the Heat Transfer Coefficient in the Inverse Fractional Stefan Problem
This paper presents an algorithm for solving the inverse fractional Stefan problem. The considered inverse problem consists of determining the heat transfer coefficient at one of the boundaries of the considered region. The additional information necessary for solving the inverse problem is the set...
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| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/1/43 |
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| author | Agata Chmielowska Rafał Brociek Damian Słota |
| author_facet | Agata Chmielowska Rafał Brociek Damian Słota |
| author_sort | Agata Chmielowska |
| collection | DOAJ |
| description | This paper presents an algorithm for solving the inverse fractional Stefan problem. The considered inverse problem consists of determining the heat transfer coefficient at one of the boundaries of the considered region. The additional information necessary for solving the inverse problem is the set of temperature values in selected points of the region. The fractional derivative with respect to time used in the considered Stefan problem is of the Caputo type. The direct problem was solved by using the alternating phase truncation method adapted to the model with the fractional derivative. To solve the inverse problem, the ant colony algorithm was used. This paper contains an example illustrating the accuracy and stability of the presented algorithm. |
| format | Article |
| id | doaj-art-3c279cafe03c4acd967fcc8aef431bbd |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-3c279cafe03c4acd967fcc8aef431bbd2025-01-24T13:33:28ZengMDPI AGFractal and Fractional2504-31102025-01-01914310.3390/fractalfract9010043Reconstructing the Heat Transfer Coefficient in the Inverse Fractional Stefan ProblemAgata Chmielowska0Rafał Brociek1Damian Słota2Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, PolandDepartment of Mathematics Applications and Methods for Artificial Intelligence, Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, PolandDepartment of Mathematical Methods in Technology and Computer Science, Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, PolandThis paper presents an algorithm for solving the inverse fractional Stefan problem. The considered inverse problem consists of determining the heat transfer coefficient at one of the boundaries of the considered region. The additional information necessary for solving the inverse problem is the set of temperature values in selected points of the region. The fractional derivative with respect to time used in the considered Stefan problem is of the Caputo type. The direct problem was solved by using the alternating phase truncation method adapted to the model with the fractional derivative. To solve the inverse problem, the ant colony algorithm was used. This paper contains an example illustrating the accuracy and stability of the presented algorithm.https://www.mdpi.com/2504-3110/9/1/43fractional Stefan probleminverse problemheat conductionalternating phase truncation methodant colony algorithm |
| spellingShingle | Agata Chmielowska Rafał Brociek Damian Słota Reconstructing the Heat Transfer Coefficient in the Inverse Fractional Stefan Problem Fractal and Fractional fractional Stefan problem inverse problem heat conduction alternating phase truncation method ant colony algorithm |
| title | Reconstructing the Heat Transfer Coefficient in the Inverse Fractional Stefan Problem |
| title_full | Reconstructing the Heat Transfer Coefficient in the Inverse Fractional Stefan Problem |
| title_fullStr | Reconstructing the Heat Transfer Coefficient in the Inverse Fractional Stefan Problem |
| title_full_unstemmed | Reconstructing the Heat Transfer Coefficient in the Inverse Fractional Stefan Problem |
| title_short | Reconstructing the Heat Transfer Coefficient in the Inverse Fractional Stefan Problem |
| title_sort | reconstructing the heat transfer coefficient in the inverse fractional stefan problem |
| topic | fractional Stefan problem inverse problem heat conduction alternating phase truncation method ant colony algorithm |
| url | https://www.mdpi.com/2504-3110/9/1/43 |
| work_keys_str_mv | AT agatachmielowska reconstructingtheheattransfercoefficientintheinversefractionalstefanproblem AT rafałbrociek reconstructingtheheattransfercoefficientintheinversefractionalstefanproblem AT damiansłota reconstructingtheheattransfercoefficientintheinversefractionalstefanproblem |