Generalized magneto-thermoelastic half-space with diffusion under initial stress using three-phase-lag model
03 Apr 2017-Mechanics Based Design of Structures and Machines (Taylor & Francis)-Vol. 45, Iss: 2, pp 145-159
TL;DR: In this article, the effect of initial stress and the magnetic field on thermoelastic interactions in an isotropic, thermally and electrically conducting half-space whose surface is subjected to mechanical and thermal loads is investigated.
Abstract: The present paper is aimed at studying the effect of initial stress and the magnetic field on thermoelastic interactions in an isotropic, thermally and electrically conducting half-space whose surface is subjected to mechanical and thermal loads. The formulation is applied under the thermoelasticity theory with three-phase-lag, proposed by Choudhuri (2007). The normal mode analysis is used to obtain the expressions for the variables considered. Numerical and computations are performed for a specific material and the results obtained are represented graphically. Comparisons are made with the results predicted by different theories Lord–Shulman theory (L–S), the theory of thermoelasticity type III (G-N III) and the three-phase-lag model (3PHL) in the absence and presence of the initial stress and magnetic field.
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Cites background from "Generalized magneto-thermoelastic h..."
...The theory of generalized thermoelasticity has drawn attention of researchers due to its applications in various diverse fields such as engineering, nuclear reactor’s design, high energy particle accelerators, etc (Othman and Eraki 2017)....
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Cites background from "Generalized magneto-thermoelastic h..."
...In many engineering applications, non-isothermal elastic problems are of great interest and have become increasingly important (Sur and Kanoria 2015a; Biswas 2019a; Li 2017; Othman and Eraki 2017; El-Attar, Hendy, and Ezzat 2019)....
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References
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TL;DR: In this article, a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of heat flow.
Abstract: In this work a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of the heat flow. The theory takes into account the coupling effect between temperature and strain rate, but the resulting coupled equations are both hyperbolic. Thus, the paradox of an infinite velocity of propagation, inherent in the existing coupled theory of thermoelasticity, is eliminated. A solution is obtained using the generalized theory which compares favourably with a known solution obtained using the conventional coupled theory.
3,266 citations
"Generalized magneto-thermoelastic h..." refers methods in this paper
...We recall the rst two earliest andwell-known generalized theories proposed by Lord and Shulman (1967) and Green and Lindsay (1972) In the model (1967), the Fourier law of heat conduction is replaced byMaxwell–Cattaneo law that introduces one thermal relaxation time parameter in Fourier’s law,…...
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TL;DR: In this article, a unified treatment of thermoelasticity by application and further developments of the methods of irreversible thermodynamics is presented, along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement.
Abstract: A unified treatment is presented of thermoelasticity by application and further developments of the methods of irreversible thermodynamics. The concept of generalized free energy introduced in a previous publication plays the role of a ``thermoelastic potential'' and is used along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement. The general laws of thermoelasticity are formulated in a variational form along with a minimum entropy production principle. This leads to equations of the Lagrangian type, and the concept of thermal force is introduced by means of a virtual work definition. Heat conduction problems can then be formulated by the methods of matrix algebra and mechanics. This also leads to the very general property that the entropy density obeys a diffusion‐type law. General solutions of the equations of thermoelasticity are also given using the Papkovitch‐Boussinesq potentials. Examples are presented and it is shown how the generalized coordinate method may be used to calculate the thermoelastic internal damping of elastic bodies.
2,287 citations
"Generalized magneto-thermoelastic h..." refers background in this paper
...Introduction The generalized theories of thermoelasticity have been developed to overcome the in nite propagation speed of thermal signals predicted by the classical coupled dynamical theory of thermoelasticity (Biot, 1956)....
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...The generalized theories of thermoelasticity have been developed to overcome the in nite propagation speed of thermal signals predicted by the classical coupled dynamical theory of thermoelasticity (Biot, 1956)....
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TL;DR: In this article, a general uniqueness theorem for linear thermoelasticity without energy dissipation is proved and a constitutive equation for an entropy flux vector is determined by the same potential function which also determines the stress.
Abstract: This paper deals with thermoelastic material behavior without energy dissipation; it deals with both nonlinear and linear theories, although emphasis is placed on the latter. In particular, the linearized theory of thermoelasticity discussed possesses the following properties: (a) the heat flow, in contrast to that in classical thermoelasticity characterized by the Fourier law, does not involve energy dissipation; (b) a constitutive equation for an entropy flux vector is determined by the same potential function which also determines the stress; and (c) it permits the transmission of heat as thermal waves at finite speed. Also, a general uniqueness theorem is proved which is appropriate for linear thermoelasticity without energy dissipation.
1,649 citations
"Generalized magneto-thermoelastic h..." refers background in this paper
...Later on, Green and Naghdi (1991, 1992, 1993) proposed another three models, which are subsequently referred to a GN-I, II, and III models....
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TL;DR: In this article, a universal constitutive equation between the heat flux vector and the temperature gradient is proposed to cover the fundamental behaviors of diffusion, wave, phonon-electron interactions, and pure phonon scattering.
Abstract: A universal constitutive equation between the heat flux vector and the temperature gradient is proposed to cover the fundamental behaviors of diffusion (macroscopic in both space and time), wave (macroscopic in space but microscopic in time), phonon-electron interactions (microscopic in both space and time), and pure phonon scattering The model is generalized from the dual-phase-lag concept accounting for the laging behavior in the high-rate response While the phase lag of the heat flux captures the small-scale response in time, the phase lag of the temperature gradient captures the small-scale response in space The universal form of the energy equation facilitates identifications of the physical parameters governing the transition from one mechanism (such as diffusion or wave) to another (the phonon-electron interaction)
1,435 citations
"Generalized magneto-thermoelastic h..." refers background or methods in this paper
...In particular, the models of Green and Naghdi are recovered, this theory seems an extension of the one proposed by Tzou (1995)....
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...The other hyperbolic thermoelasticity theory was proposed by Tzou (1995), called dual-phase-lag model, in which Fourier’s law is replaced by an approximation to a modi cation of Fourier’s law with CONTACT Ebtesam E. M. Eraki ebtesam.eraki@yahoo.com Department of Mathematics, Faculty of Science,…...
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TL;DR: In this article, the authors focused on the thermal properties of the constitutive response functions in the context of both nonlinear and linear theories, and provided an easy comparison of the one-dimensional version of the equation for the determination of temperature in the linearized theory.
Abstract: This paper is concerned with thermoelastic material behavior whose constitutive response functions possess thermal features that are more general than in the usual classical thermoelasticity. After a general development of the constitutive equations in the context of both nonlinear and linear theories, attention is focused on the latter. In particular, the one-dimensional version of the equation for the determination of temperature in the linearized theory provides an easy comparative basis of its predictive capability: In one special case where the Fourier conductivity is dominant, the temperature equation reduces to the classical Fourier law of heat conduction, which does not permit the possibility of undamped thermal waves; however,'in another special case in which the effect of conductivity is negligible, the equation has undamped thermal wave solutions without energy dissipation.
1,143 citations
"Generalized magneto-thermoelastic h..." refers background in this paper
...Later on, Green and Naghdi (1991, 1992, 1993) proposed another three models, which are subsequently referred to a GN-I, II, and III models....
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