THERMAL SCIENCE

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Rafał Brociek

,

Damian Słota

RECONSTRUCTION OF THE THERMAL CONDUCTIVITY COEFFICIENT IN THE SPACE FRACTIONAL HEAT CONDUCTION EQUATION

ABSTRACT
In this paper an inverse problem for the space fractional heat conduction equation is investigated. Firstly, we describe the approximate solution of the direct problem. Secondly, for the inverse problem part, we define the functional illustrating the error of approximate solution. To recover the thermal conductivity coefficient we need to minimize this functional. In order to minimize this functional the Real Ant Colony Optimization (RealACO) algorithm is used. In the model we apply the Riemann-Liouville fractional derivative. The paper presents also some examples to illustrate the accuracy and stability of the presented algorithm.
KEYWORDS
inverse problem, thermal conductivity coefficient, fractional derivative, identification, space fractional heat conduction equation
PAPER SUBMITTED: 2016-04-15
PAPER REVISED: 2016-05-25
PAPER ACCEPTED: 2016-06-25
PUBLISHED ONLINE: 2016-10-01
DOI REFERENCE: https://doi.org/10.2298/TSCI160415240B
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Issue 1, PAGES [81 - 88]
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Reconstruction of the thermal conductivity coefficient in the space fractional heat conduction equation

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence