Fractional Green–Naghdi theory for thermoelectric MHD

Aldawody, Dalia A.; Hendy, Mohamed H.; Ezzat, Magdy A.

doi:10.1080/17455030.2018.1459061

Cited by 14 publications

(9 citation statements)

References 48 publications

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“…Usually, the mathematical conditions are solved to get the dynamic critical value condition for forming the dissipative structure: the negative entropy B of the system is more significant than 1 + A2. This article escapes the model based on the characteristics of the information teaching ecology [9]. We set the positive entropy of the information teaching ecology to be equal to A and the negative entropy to be equal to B.…”

Section: Establishment Of Positive and Negative Entropy Index Systemmentioning

confidence: 99%

Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching

Wang

Alassafi

Keir

2021

Applied Mathematics and Nonlinear Sciences

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The advancement of Chinese education informatisation construction has injected new vitality into the development of Chinese educational technology in the new era and brought new challenges to the development of Chinese educational technology. Nonlinear dissipative structure theory has been a necessary enlightenment for the development of education informatisation. Based on the theory of nonlinear dissipative structure, the paper explores the relationship between the theory and education and teaching. It constructs a diversified regression calculation model of the information-based teaching ecology. Finally, it points out the strategies and ways to apply the dissipative structure theory to improve information-based teaching.

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Section: Establishment Of Positive and Negative Entropy Index Systemmentioning

confidence: 99%

Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching

Wang

Alassafi

Keir

2021

Applied Mathematics and Nonlinear Sciences

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“…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%

“…Under the framework of the fractional DPL heat conduction theory, Qiao et al (2021), Wang et al (2020), Kumar et al (2020) analyzed the thermal behavior in living biological tissues during thermal therapy. Additionally, Aldawody et al (2019), Ezzat and El-Bary (2018) proposed a unified GN model to study the fractional heat conduction problem of electro-thermo-elasticity.…”

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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“…The authors illustrated that the presented solution is proper for such problems using GN model with nonlocality. A novel mathematical model of thermoelasticity with considering the new shape of GN theory type (II), heat conduction law without consideration of energy dissipation based upon fractional time derivatives model, was presented by Aldawody et al [23]. The authors used a model to Stocks' stream of unsteady incompressible fluid because of a moving flat sheet considering the transverse magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Modified G-L thermoelasticity theory for nonlinear longitudinal wave in a porous thermoelastic medium

Shakeriaski¹,

Salehi²,

Ghodrat³

2021

Phys. Scr.

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This paper presents a nonlinear analysis of the transient response of a porous medium affected by external traction. The formulation is presented based on a new modified G-L theory of thermoelasticity while temperature and strain rate parameters are included in the governing equations. Based on the finite strain theory (FST), the Lagrangian strain-displacement equation and Second Piola-Kirchhoff stress are applied to express the generalized form of thermoelasticity equations including large deformation. Both mechanical and thermal shocks are applied and finally, the effects of loading rate on transient response are discussed. An updated finite element method and Newmark's numerical time integration method are employed to solve the nonlinear and timedependent equations. It is determined that the modified G-L model is more powerful in predicting the wave propagation phenomenon. Furthermore, the findings indicate that the external surface shock induces compressive stresses, temperature raise, and volume fraction field increase in a porous medium. It is found compared to the classic model, the modified G-L model is superior in capturing the perceived wave propagation phenomenon.

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Fractional Green–Naghdi theory for thermoelectric MHD

Cited by 14 publications

References 48 publications

Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching

Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching

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

Modified G-L thermoelasticity theory for nonlinear longitudinal wave in a porous thermoelastic medium

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