THERMAL SCIENCE

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Rafal Brociek

,

Damian Slota

RECONSTRUCTION OF THE BOUNDARY CONDITION FOR THE HEAT CONDUCTION EQUATION OF FRACTIONAL ORDER

ABSTRACT
This paper describes reconstruction of the heat transfer coefficient occurring in the boundary condition of the third kind for the time fractional heat conduction equation. Fractional derivative with respect to time, occurring in considered equation, is defined as the Caputo derivative. Additional information for the considered inverse problem is given by the temperature measurements at selected points of the domain. The direct problem is solved by using the implicit finite difference method. To minimize functional defining the error of approximate solution the Nelder-Mead algorithm is used. The paper presents results of computational examples to illustrate the accuracy and stability of the presented algorithm.
KEYWORDS
inverse problem, identification, heat conduction equation, time fractional heat transfer coefficient
PAPER SUBMITTED: 2014-10-10
PAPER REVISED: 2015-02-13
PAPER ACCEPTED: 2015-02-24
PUBLISHED ONLINE: 2015-08-02
DOI REFERENCE: https://doi.org/10.2298/TSCI15S1S35B
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE Supplement 1, PAGES [S35 - S42]
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Reconstruction of the boundary condition for the heat conduction equation of fractional order

© 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