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Fractal Fract 2017, 1(1), 17; https://doi.org/10.3390/fractalfract1010017

Modeling of Heat Distribution in Porous Aluminum Using Fractional Differential Equation

1
Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
2
Institute of Engineering Materials and Biomaterials, Silesian University of Technology, Konarskiego 18A, 44-100 Gliwice, Poland
*
Author to whom correspondence should be addressed.
Received: 20 November 2017 / Revised: 8 December 2017 / Accepted: 9 December 2017 / Published: 12 December 2017
(This article belongs to the Special Issue The Craft of Fractional Modelling in Science and Engineering)
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Abstract

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. View Full-Text
Keywords: fractional derivative; inverse problem; heat conduction in porous media; thermal conductivity; heat transfer coefficient fractional derivative; inverse problem; heat conduction in porous media; thermal conductivity; heat transfer coefficient
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Brociek, R.; Słota, D.; Król, M.; Matula, G.; Kwaśny, W. Modeling of Heat Distribution in Porous Aluminum Using Fractional Differential Equation. Fractal Fract 2017, 1, 17.

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