Journal ArticleDOI
On A Thermoelastic Three-Phase-Lag Model
TLDR
In this paper, a three-phase-lag model of the linearized theory of coupled thermoelasticity is formulated by considering the heat condition law that includes temperature gradient and the thermal displacement gradient among the constitutive variables.Abstract:
A three-phase-lag model of the linearized theory of coupled thermoelasticity is formulated by considering the heat condition law that includes temperature gradient and the thermal displacement gradient among the constitutive variables. The Fourier law is replaced by an approximation to a modification of the Fourier law with three different translations for the heat flux vector, the temperature gradient and also for the thermal displacement gradient. The model formulated is an extension of the thermoelastic models proposed by Lord–Shulman, Green–Naghdi and Tzou.read more
Citations
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Journal ArticleDOI
A note on stability in three-phase-lag heat conduction
Ramón Quintanilla,Reinhard Racke +1 more
TL;DR: In this article, the authors considered two cases in the theory of the heat conduction models with three-phase-lag and proposed a suitable Lyapunov function for each one.
Journal ArticleDOI
Moore–Gibson–Thompson thermoelasticity:
TL;DR: In this article, a relaxation of the Moore-Gibson-Thompson equation has been proposed for a thermo-elastic model where the heat conduction is described by a relaxation.
Journal ArticleDOI
Ill-posed problems in thermomechanics
TL;DR: The ill-posedness is proved, showing the lack of continuous dependence on the data, and thus showing that these models (delay or higher-order expansion ones) are highly explosive.
Journal ArticleDOI
The effect of a dipolar structure on the Hölder stability in Green–Naghdi thermoelasticity
Marin Marin,Andreas Öchsner +1 more
TL;DR: In this paper, the mixed initial boundary value problem for a dipolar body in the context of the thermoelastic theory proposed by Green and Naghdi was studied and a result of Holder's-type stability on the supply terms was proved.
Journal ArticleDOI
A Well-Posed Problem for the Three-Dual-Phase-Lag Heat Conduction
TL;DR: The three-dual-phase-lag theory based on the constitutive law was proposed by Roy Choudhuri as an extension of the theory by Tzou where the recent theories of Greeen and Naghdi could be recover.
References
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Journal ArticleDOI
A generalized dynamical theory of thermoelasticity
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.
Journal ArticleDOI
Thermoelasticity and Irreversible Thermodynamics
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.
Journal ArticleDOI
Thermoelasticity without energy dissipation
Albert Edward Green,P. M. Naghdi +1 more
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.
Journal ArticleDOI
A Unified Field Approach for Heat Conduction From Macro- to Micro-Scales
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.
Journal ArticleDOI
On undamped heat waves in an elastic solid
Albert Edward Green,P. M. Naghdi +1 more
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.