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A Semi-explicit Algorithm for Parameters Estimation in a Time-Fractional Dual-Phase-Lag Heat Conduction Model
Version 1
: Received: 30 May 2024 / Approved: 30 May 2024 / Online: 30 May 2024 (14:24:39 CEST)
A peer-reviewed article of this Preprint also exists.
Lukashchuk, S.Y. A Semi-Explicit Algorithm for Parameters Estimation in a Time-Fractional Dual-Phase-Lag Heat Conduction Model. Modelling 2024, 5, 776-796. Lukashchuk, S.Y. A Semi-Explicit Algorithm for Parameters Estimation in a Time-Fractional Dual-Phase-Lag Heat Conduction Model. Modelling 2024, 5, 776-796.
Abstract
This paper presents a new semi-explicit algorithm for parameters estimation in a time-fractional generalization of dual-phase-lag heat conduction model with the Caputo fractional derivatives. It is shown that this model can be derived from a general linear constitutive relation for the heat transfer by conduction when the heat conduction relaxation kernel contains the Mittag-Leffler function. The model can be used to describe heat conduction phenomena in a material with power-law memory. The proposed algorithm of parameters estimation is based on the time integral characteristics method. The explicit representations of the thermal diffusivity and the fractional analogues of the thermal relaxation time and the thermal retardation are obtained via a Laplace transform of the temperature field and utilized in the algorithm. An implicit relation is derived for the order of fractional differentiation. In the algorithm, this relation is resolved numerically. An example illustrates the proposed technique.
Keywords
non-Fourier heat conduction model; Caputo fractional derivative; inverse problem; parameters estimation; time integral characteristic
Subject
Physical Sciences, Thermodynamics
Copyright: 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.
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