Modeling of Heat Distribution in Porous Aluminum Using Fractional Differential Equation
The authors present a model of heat conduction using the Caputo fractional derivative with respect to time. The presented model was used to reconstruct the thermal conductivity coefficient, heat transfer coefficient, initial condition and order of fractional derivative in the fractional heat conduct...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-12-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/1/1/17 |
| _version_ | 1818411841026523136 |
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| author | Rafał Brociek Damian Słota Mariusz Król Grzegorz Matula Waldemar Kwaśny |
| author_facet | Rafał Brociek Damian Słota Mariusz Król Grzegorz Matula Waldemar Kwaśny |
| author_sort | Rafał Brociek |
| collection | DOAJ |
| description | The authors present a model of heat conduction using the Caputo fractional derivative with respect to time. The presented model was used to reconstruct the thermal conductivity coefficient, heat transfer coefficient, initial condition and order of fractional derivative in the fractional heat conduction inverse problem. Additional information for the inverse problem was the temperature measurements obtained from porous aluminum. In this paper, the authors used a finite difference method to solve direct problems and the Real Ant Colony Optimization algorithm to find a minimum of certain functional (solve the inverse problem). Finally, the authors present the temperature values computed from the model and compare them with the measured data from real objects. |
| first_indexed | 2024-12-14T10:37:49Z |
| format | Article |
| id | doaj.art-6a45684cf8824fa5b9dcc67fe6ac5bb6 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-12-14T10:37:49Z |
| publishDate | 2017-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-6a45684cf8824fa5b9dcc67fe6ac5bb62022-12-21T23:05:50ZengMDPI AGFractal and Fractional2504-31102017-12-01111710.3390/fractalfract1010017fractalfract1010017Modeling of Heat Distribution in Porous Aluminum Using Fractional Differential EquationRafał Brociek0Damian Słota1Mariusz Król2Grzegorz Matula3Waldemar Kwaśny4Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, PolandInstitute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, PolandInstitute of Engineering Materials and Biomaterials, Silesian University of Technology, Konarskiego 18A, 44-100 Gliwice, PolandInstitute of Engineering Materials and Biomaterials, Silesian University of Technology, Konarskiego 18A, 44-100 Gliwice, PolandInstitute of Engineering Materials and Biomaterials, Silesian University of Technology, Konarskiego 18A, 44-100 Gliwice, PolandThe authors present a model of heat conduction using the Caputo fractional derivative with respect to time. The presented model was used to reconstruct the thermal conductivity coefficient, heat transfer coefficient, initial condition and order of fractional derivative in the fractional heat conduction inverse problem. Additional information for the inverse problem was the temperature measurements obtained from porous aluminum. In this paper, the authors used a finite difference method to solve direct problems and the Real Ant Colony Optimization algorithm to find a minimum of certain functional (solve the inverse problem). Finally, the authors present the temperature values computed from the model and compare them with the measured data from real objects.https://www.mdpi.com/2504-3110/1/1/17fractional derivativeinverse problemheat conduction in porous mediathermal conductivityheat transfer coefficient |
| spellingShingle | Rafał Brociek Damian Słota Mariusz Król Grzegorz Matula Waldemar Kwaśny Modeling of Heat Distribution in Porous Aluminum Using Fractional Differential Equation Fractal and Fractional fractional derivative inverse problem heat conduction in porous media thermal conductivity heat transfer coefficient |
| title | Modeling of Heat Distribution in Porous Aluminum Using Fractional Differential Equation |
| title_full | Modeling of Heat Distribution in Porous Aluminum Using Fractional Differential Equation |
| title_fullStr | Modeling of Heat Distribution in Porous Aluminum Using Fractional Differential Equation |
| title_full_unstemmed | Modeling of Heat Distribution in Porous Aluminum Using Fractional Differential Equation |
| title_short | Modeling of Heat Distribution in Porous Aluminum Using Fractional Differential Equation |
| title_sort | modeling of heat distribution in porous aluminum using fractional differential equation |
| topic | fractional derivative inverse problem heat conduction in porous media thermal conductivity heat transfer coefficient |
| url | https://www.mdpi.com/2504-3110/1/1/17 |
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