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Generalized thermoelastic heat conduction model involving three different fractional operators

Saidi Anouar, Yahya Ahmed M. H, Abouelregal Ahmed E., Dargail Husam E., Ahmed Ibrahim-Elkhalil, Ali Elsiddeg, Mohammed F. A.

Advances in Materials Science

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2023

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Vol. 23, nr 2(76)

25--44

EN

The purpose of this paper is to introduce a new time-fractional heat conduction model with three-phase-lags and three distinct fractional-order derivatives. We investigate the introduced model in the situation of an isotropic and homogeneous solid sphere. The exterior of the sphere is exposed to a thermal shock and a decaying heat generation rate. We recuperate some earlier thermoelasticity models as particular cases from the proposed model. Moreover, the effects of different fractional thermoelastic models and the effect of instant time on the physical variables of the medium are studied. We obtain the numerical solutions for the various physical fields using a numerical Laplace inversion technique. We represent the obtained results graphically and discuss them. Physical views presented in this article may be useful for the design of new materials, bio-heat transfer mechanisms between tissues and other scientific domains.

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Two-temperature theory for a heated semi-infinite solid by a pulsed laser radiation

Zenkour Ashraf M., Abouelregal Ahmed E.

Archives of Thermodynamics

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2020

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Vol. 41, no 2

85--101

EN

In this paper, the two-temperature thermoelasticity model is proposed to a specific problem of a thermoelastic semi-infinite solid. The bounding plane surface of the semi-infinite solid is considered to be under a non-Gaussian laser pulse. Generalized thermoelasticity analysis with dual-phase-lags is taken into account to solve the present problem. Laplace transform and its inversion techniques are applied and an analytical solution as well as its numerical outputs of the field variables are obtained. The coupled theory and other generalized theory with one relaxation time may be derived as special cases. Comparison examples have been made to show the effect of dual-phase-lags, temperature discrepancy, laser-pulse and laser intensity parameters on all felids. An additional comparison is also made with the theory of thermoelasticity at a single temperature.

3

A generalized thermoelastic medium subjected to pulsed laser heating via a two-temperature model

Abouelregal Ahmed E., Zenkour Ashraf M.

Journal of Theoretical and Applied Mechanics

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2019

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Vol. 57 nr 3

631--639

EN

This article investigates stress and induced temperature in an isotropic, homogeneous, thermoelastic half-space using a two-temperature generalized thermoelasticity model. The bounding plane surface of the present half-space continuum is subjected to a non-Gaussian laser pulse. Laplace’s transform space is considered to deduce a closed-form solution to the problem. In addition, the inversions of Laplace’s transformations have been carried numerically to obtain field quantities in the transient state. The effects of parameters of two-temperature, laser-pulse and laser intensity are investigated. A concluding remark for the graphical forms of the derived expressions is presented.