Fractional heat conduction in a thin hollow circular disk and associated thermal deflection

Warbhe, S. D.; Tripathi, J. J.; Deshmukh, K. C.; Verma, J.

doi:10.1080/01495739.2017.1393645

Cited by 14 publications

(7 citation statements)

References 45 publications

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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%

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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“…In the past decade, many models in viscoelasticity, bioengineering, and heat conduction [32][33][34] have been effectively revised using fractional order calculus. As a result, fractional order should be incorporated into generalized thermoelastic diffusion theory [35].…”

Section: Introductionmentioning

confidence: 99%

Dual‐phase‐lag thermoelastic diffusion analysis of a size‐dependent microplate based on modified fractional‐order heat conduction model

Tian

Peng

2022

Z Angew Math Mech

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With the rapid evolution of small-scale devices, the effect of size dependence on elastic deformation becomes more and more obvious. Furthermore, the physical processes usually involve memory and inheritance for some anomalous diffusion that the constitutive relation does not obey the standard gradient rate. Owing to capturing the memory-dependent effect and the size-dependent effect, the existing thermoelastic diffusion theories cannot be applicable. To further refine the thermoelastic diffusion model for micro/nano structures, a refined nonlocal thermoelastic diffusion model is developed by combining the fractional-order dual-phase-lag (DPL) heat conduction model and fractional-order diffusion model in this paper. In addition, the Tempered-Caputo (TC) definition is an extension of the Caputo definition without the fractional derivative of the singular kernel, which is adopted for the first time to reflect the memory-dependent effects of heat conduction and stress-strain relationship. Then, this new model is applied to investigating the transient response of an elastic microplate subjected to a sinusoidal thermal loading. The corresponding governing equations are formulated and solved by the Laplace transform method and its numerical inversion. In calculation, the influences of the fractional-order parameter, the tempered parameter and the nonlocal parameter on the variations of the considered quantities are presented and discussed in detail. It is expected to provide new insights into thermoelastic diffusion behaviors of structures at the micro/nanoscale.

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“…Along with the development of the generalized thermoelasticity with integer order derivative, due to the successful applications of fractional order derivative in characterizing the anomalous heat conduction [50][51][52] and in modifying many existing models in viscoelasticity, bioengineering and heat conduction etc. [53][54][55], the generalized thermoelasticity with fractional order derivative has also been developed. For instance, Sherief et al [56] came up with a fractional order thermoelasticity by introducing the Caputo-type fractional order derivative into the non-Fourier's heat conduction law.…”

Section: Introductionmentioning

confidence: 99%

Transient thermoelastic response of a size‐dependent nanobeam under the fractional order thermoelasticity

Peng

2021

Z Angew Math Mech

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With the miniaturization of structures, such as MEMS/NEMS, the sizedependent effect has become an issue and attracted much attention. The wellknown theories describing the size-dependent effect mainly include the nonlocal elasticity theory, the strain gradient theory and the modified coupled stress theory. Based on these theories, a number of works have been conducted to explore the size-dependent behaviors of structures or devices in micro/nanoscale, among them, majorities are on elastic performances, while, minorities are on thermoelastic performances. It is inevitable for structures suffering changeable temperature, as a consequence, thermal-induced stress and deformation occur in structures and they are worth being fully concerned. For thermoelastic behaviors limited to small scale problems, the classical Fourier's heat conduction law may fail, meanwhile, new models, for example, fractional order heat conduction model, have been developed to modify Fourier's law. In present paper, the transient thermoelastic response of a nanobeam subjected to a ramp heating is investigated by combining the nonlocal elasticity theory and the fractional order heat conduction model. The governing equations are formulated and then solved by Laplace transform and its numerical inversion. The non-dimensional temperature, displacement, stress, and deflection in the nanobeam are obtained and illustrated graphically. In calculation, the effects of the ramp-heating time parameter, the nonlocal parameter and the fractional order parameter on the considered physical quantities are examined and discussed in detail.

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Fractional heat conduction in a thin hollow circular disk and associated thermal deflection

Cited by 14 publications

References 45 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

Dual‐phase‐lag thermoelastic diffusion analysis of a size‐dependent microplate based on modified fractional‐order heat conduction model

Transient thermoelastic response of a size‐dependent nanobeam under the fractional order thermoelasticity

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