Estimating Relaxation Time and Fractionality Order Parameters in Fractional Non-Fourier Heat Conduction Using Conjugate Gradient Inverse Approach in Single and Three-Layer Skin Tissues

Goudarzi, Piran; Abidi, Awatef; Mehryan, S.A.M.; Ghalambaz, Mohammad; Sheremet, Mikhail А.

doi:10.3390/pr9111877

Cited by 3 publications

(1 citation statement)

References 26 publications

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“…In addition, the Laplace transform, by, combining with other techniques, is very practical for solving the time-fractional heat transfer (Ghanmi and Abbas, 2019). Recently, some efficient optimization algorithms, such as the conjugate gradient inverse method (Goudarzi et al , 2021) and the cuckoo search algorithm (Chi et al , 2020), have been proposed to estimate the model parameters in inverse fractional heat transfer problems. Their research studies may play a very important role in promoting the development of fractional heat transfer in biological tissues.…”

Section: Introductionmentioning

confidence: 99%

A symplectic approach for the fractional heat transfer and thermal damage in 2D biological tissues

Leng

et al. 2023

HFF

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Purpose This paper aims to focus on the accurate analysis of the fractional heat transfer in a two-dimensional (2D) rectangular monolayer tissue with three different kinds of lateral boundary conditions and the quantitative evaluation of the degree of thermal damage and burn depth. Design/methodology/approach A symplectic method is used to analytically solve the fractional heat transfer dual equation in the frequency domain (s-domain). Explicit expressions of the dual vector can be constructed by superposing the symplectic eigensolutions. The solution procedure is rigorously rational without any trial functions. And the accurate predictions of temperature and heat flux in the time domain (t-domain) are derived through numerical inverse Laplace transform. Findings Comparison study shows that the maximum relative error is less than 0.16%, which verifies the accuracy and effectiveness of the proposed method. The results indicate that the model and heat source parameters have a significant effect on temperature and thermal damage. The pulse duration (Δt) of the laser heat source can effectively control the time to reach the peak temperature and the peak slope of the thermal damage curve. The burn depth is closely correlated with exposure temperature and duration. And there exists the delayed effect of fractional order on burn depth. Originality/value A symplectic approach is presented for the thermal analysis of 2D fractional heat transfer. A unified time-fractional heat transfer model is proposed to describe the anomalous thermal behavior of biological tissue. New findings might provide guidance for temperature prediction and thermal damage assessment of biological tissues during hyperthermia.

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Section: Introductionmentioning

confidence: 99%

A symplectic approach for the fractional heat transfer and thermal damage in 2D biological tissues

Leng

et al. 2023

HFF

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Assessment of stresses and strains accompanying the degradation of the surface layer composition of a coated cylindrical part under operating conditions

Knyazeva

Nazarenko

2023

J Eng Math

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A Semi-Explicit Algorithm for Parameters Estimation in a Time-Fractional Dual-Phase-Lag Heat Conduction Model

Lukashchuk

2024

Modelling

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This paper presents a new semi-explicit algorithm for parameters estimation in a time-fractional generalization of a dual-phase-lag heat conduction model with 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.

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Estimating Relaxation Time and Fractionality Order Parameters in Fractional Non-Fourier Heat Conduction Using Conjugate Gradient Inverse Approach in Single and Three-Layer Skin Tissues

Cited by 3 publications

References 26 publications

A symplectic approach for the fractional heat transfer and thermal damage in 2D biological tissues

A symplectic approach for the fractional heat transfer and thermal damage in 2D biological tissues

Assessment of stresses and strains accompanying the degradation of the surface layer composition of a coated cylindrical part under operating conditions

A Semi-Explicit Algorithm for Parameters Estimation in a Time-Fractional Dual-Phase-Lag Heat Conduction Model

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