A Domain of Influence Theorem for Thermoelasticity with Dual Phase-Lags

Mukhopadhyay, Santwana; Kothari, Shweta; Kumar, Roushan

doi:10.1080/01495739.2011.601257

Cited by 20 publications

(6 citation statements)

References 22 publications

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“…Therefore, for the vanishing of the phase-lag parameters the thermoelastic disturbance described by propagates with an infinite speed, which is the fact expected since the present problem then reduces to the problem under classical thermoelasticity theory. In the case when v → 0 T → 0 a 0 = 0 but q = 0, the present problem reduces to the problem in the context of one thermal relaxation parameter and it follows from (12) that v ≥ max 2 1 + 1 q , which agrees with the definition of v as reported in [21] for the case of thermoelasticity with one thermal relaxation parameter. Moreover if T → 0 and a 0 = 0 the present problem reduces to the problem in the context of two-phase-lags model that v ≥ max 2 1 + 1 q + T 2 T 2 q which agrees with the definition of v as reported in [21].…”

Section: Theoremsupporting

confidence: 67%

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A Domain of Influence Theorem for Thermoelasticity with Three-Phase-Lag Model

Kumar

2015

Journal of Thermal Stresses

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We establish the theory of domain of influence for a potential-temperature disturbance under the generalized theory of thermoelasticity with three-phase-lag model. For a finite time t > 0, it has been proved that the potential due to the displacement and the temperature fields does not produce any disturbances outside a bounded domain and the domain of influence is dependent on the support of load, the thermoelastic coupling constant and the phase-lag parameters. It has been shown that the domain of influence of the present case reduces to the domain of influence for classical thermoelasticity theory and the thermoelasticity theory with one relaxation parameter.

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Section: Theoremsupporting

confidence: 67%

“…A detailed discussion on this subject is also available in a recent book by Ignaczak and Starzewaski [20]. Recently, Mukhopadhyay et al [21] derived the domain of influence theorem in the theory of generalized thermoelasticity with dual-phase-lag model.…”

Section: Introductionmentioning

confidence: 97%

A Domain of Influence Theorem for Thermoelasticity with Three-Phase-Lag Model

Kumar

2015

Journal of Thermal Stresses

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“…In view of the generalized thermoelasticity theory, Chirita and Quintanilla [37] also investigated the spatial decay estimates in terms of Saint-Venant’s principle. Mukhopadhyay et al [38] presented the domain of influence theorem under the dual phase-lag model. In the three phase-lag model, the domain of influence theorem has been derived by Kumar and Kumar [39].…”

Section: Introductionmentioning

confidence: 99%

A domain of influence theorem under MGT thermoelasticity theory

Jangid

Mukhopadhyay

2020

Mathematics and Mechanics of Solids

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The purpose of this article is to discuss domain of influence results under the Moore–Gibson–Thompson (MGT) thermoelasticity theory. We employ a mixed initial–boundary value problem concerning a homogeneous and isotropic material in view of the MGT thermoelasticity theory and establish the domain of influence theorem for potential–temperature disturbance. This theorem implies that the coupling of potential and temperature generates a thermoelastic disturbance, which vanishes outside the bounded domain for a prescribed bounded support of thermomechanical loading and for a finite time. The resulted bounded domain is subjected to the support of the prescribed load. The finite propagation of thermoelastic disturbance is also analyzed under the MGT theory, where the propagation speed depends on the parameters of the thermoelastic material. It is further shown that the domain of influence result for the present context reduces to the domain of influence result derived in the generalized thermoelasticity theory of Lord and Shulman under some conditions.

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“…The exact dispersion relation solutions for the plane wave are calculated analytically, and asymptotic expressions of several characterizations of the wave fields are obtained for both high and low frequencies [264]. The domain of influence theorem for a potential-temperature disturbance under the generalized thermoelasticity with the DPL model is established [265].…”

Section: Dpl Model Of Chandrasekharaiah-tzoumentioning

confidence: 99%

Macro- to Nanoscale Heat and Mass Transfer: The Lagging Behavior

2015

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The classical model of the Fourier's law is known as the most common constitutive relation for thermal transport in various engineering materials. Although the Fourier's law has been widely used in a variety of engineering application areas, there are many exceptional applications in which the Fourier's law is questionable. This paper gathers together such applications. Accordingly, the paper is divided into two parts. The first part reviews the papers pertaining to the fundamental theory of the phase-lagging models and the analytical and numerical solution approaches. The second part wrap ups the various applications of the phase-lagging models including the biological materials, ultra-high-speed laser heating, the problems involving moving media, micro/nanoscale heat transfer, multi-layered materials, the theory of thermoelasticity, heat transfer in the material defects, the diffusion problems we call as the non-Fick models, and some other applications. It is predicted that the interest in the field of phase-lagging heat transport has grown incredibly in recent years because they show good agreement with the experiments across a wide range of length and time scales.

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A Domain of Influence Theorem for Thermoelasticity with Dual Phase-Lags

Cited by 20 publications

References 22 publications

A Domain of Influence Theorem for Thermoelasticity with Three-Phase-Lag Model

A Domain of Influence Theorem for Thermoelasticity with Three-Phase-Lag Model

A domain of influence theorem under MGT thermoelasticity theory

Macro- to Nanoscale Heat and Mass Transfer: The Lagging Behavior

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