Time-fractional subdiffusion model for thin metal films under femtosecond laser pulses based on Caputo fractional derivative to examine anomalous diffusion process

Mozafarifard, Milad; Toghraie, Davood

doi:10.1016/j.ijheatmasstransfer.2020.119592

Cited by 48 publications

(9 citation statements)

References 27 publications

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“…In regular diffusion, 𝑟 2 ∝ 𝐷 𝑡 where 𝑟 is mean square displacement, 𝑡 is time and 𝐷 is diffusion coefficient. In contrast to regular diffusion anamolus diffusion is given by power law 𝑟 2 ∝ 𝐷(𝑡) 𝑡 𝛼 where 𝛼 is anamolus diffusion operator and 𝐷(𝑡) is time dependent diffusion coefficient 10 . Note that 𝛼 = 1 means regular diffusion, 0 < 𝛼 < 1 implies sub diffusion and 𝛼 > 1 gives superdiffusion.…”

Section: Introductionmentioning

confidence: 99%

Approximate Solution of Sub diffusion Bio heat Transfer Equation

Sonawane¹,

Sontakke²,

Takale³

2023

Baghdad Sci.J

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In this paper, author’s study sub diffusion bio heat transfer model and developed explicit finite difference scheme for time fractional sub diffusion bio heat transfer equation by using caputo fabrizio fractional derivative. Also discussed conditional stability and convergence of developed scheme. Furthermore numerical solution of time fractional sub diffusion bio heat transfer equation is obtained and it is represented graphically by Python.

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Section: Introductionmentioning

confidence: 99%

Approximate Solution of Sub diffusion Bio heat Transfer Equation

Sonawane¹,

Sontakke²,

Takale³

2023

Baghdad Sci.J

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“…The TPL thermoelasticity has also been applied to studying structural dynamic behaviors of the spherical cavity heated by a thermal shock [32] and the porous half-space subjected to a ramp-type heating [33]. Especially, for microstructures working in ultrafast heating, the applicability of integer-order heat conduction models is increasingly questionable [34,35]. To amend such defect, the concept of fractional calculus provides a feasible mathematical tool for the theoretical analysis of heat transfer progress [36].…”

Section: Introductionmentioning

confidence: 99%

Transient thermo-mechanical analysis of a spherical microshell based on the three-phase-lag thermoelasticity incorporating small-scale and memory-dependent effects

Peng

2023

Mathematics and Mechanics of Solids

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The applicability of the Green–Naghdi (GN-III) thermoelasticity is increasingly questionable because the theory predicts that heat transfers with an infinite speed. To address this deficiency, the three-phase-lag (TPL) thermoelasticity was developed by introducing the lagging times into the GN-III thermoelasticity. On another front, the small-scale effect on elastic deformation cannot be ignored with the miniaturization of structures or devices. Meanwhile, the memory-dependent feature of heat transfer process in the case of ultrafast heating cannot be described by the integer-order heat conduction models due to the inherent local limited definition. To capture the small-scale effect and the memory-dependent effect of the microstructures, as a first attempt, the present work focuses on developing a TPL thermoelastic model by considering the memory-dependent derivative (MDD) heat conduction model and Eringen’s nonlocal model. Then, the refined model is used to investigate the transient characteristics of a spherical microshell induced by thermal and mechanical loadings. The governing equations containing the modified parameters are derived and then solved by Laplace transform method. Some parametric results are demonstrated to display the effects of the time-delay factor, the kernel function, and the nonlocal parameter on the considered physical quantities.

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“…Several fractional-order models have been proposed to investigate the heat transfer problem. With the fractional Fourier model, Jiang and Xu (2010), Yu and Jiang (2019), Warbhe et al (2018), Lizama and Trujillo (2020), Fu et al (2021), Shen et al (2020), Mozafarifard and Toghraie (2020), Žecová and Terpák (2015) investigated the anomalous heat conduction in biological tissues or thin metal films with different heat source. Based on the fractional CV (or single-phase-lag) model, Xu and Wang (2018), Qi et al (2013), Li et al (2019b), Mozafarifard et al (2020, 2021), Li et al (2020) and Goudarzi and Azimi (2019) studied the heat transfer characteristics in a solid structure or tissue under the laser pulse heating.…”

Section: Introductionmentioning

confidence: 99%

“…However, by summarizing the literature above, it is found that most all studies are limited to specific Caputo fractional Fourier (Fu et al , 2021; Jiang and Xu, 2010; Lizama and Trujillo, 2020; Mozafarifard and Toghraie, 2020; Shen et al , 2020; Warbhe et al , 2018; Yu and Jiang, 2019; Žecová and Terpák, 2015), CV (Goudarzi and Azimi, 2019; Li et al , 2020; Li et al , 2019b; Mozafarifard et al , 2020; Mozafarifard et al , 2021; Qi et al , 2013; Xu and Wang, 2018), DPL (Kumar et al , 2020; Qiao et al , 2021; Li et al , 2021; Wang et al , 2020) and GN (Aldawody et al , 2019; Ezzat and El-Bary, 2018) heat transfer models, there is a lack of a unified fractional heat transfer model to generalize these models. In addition, almost all of the analytical solutions focus on the one-dimensional (1D) fraction heat transfer problem.…”

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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Time-fractional subdiffusion model for thin metal films under femtosecond laser pulses based on Caputo fractional derivative to examine anomalous diffusion process

Cited by 48 publications

References 27 publications

Approximate Solution of Sub diffusion Bio heat Transfer Equation

Approximate Solution of Sub diffusion Bio heat Transfer Equation

Transient thermo-mechanical analysis of a spherical microshell based on the three-phase-lag thermoelasticity incorporating small-scale and memory-dependent effects

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

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