Next Article in Journal
Fractional Diffusion Models for the Atmosphere of Mars
Next Article in Special Issue
European Vanilla Option Pricing Model of Fractional Order without Singular Kernel
Previous Article in Journal / Special Issue
Series Solution of the Pantograph Equation and Its Properties

Metrics 0

## Export Article

Open AccessArticle
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)
|   Download PDF [929 KB, uploaded 12 December 2017]   |

# 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:
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

MDPI and ACS Style

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.

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

1