Some solutions for a family of exact phase-lag heat conduction problems

Quintanilla, R.

doi:10.1016/j.mechrescom.2011.04.008

Cited by 36 publications

(25 citation statements)

References 30 publications

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“…Gupta and Mukhopadhyay 36 introduced the generalized nonlocal thermoelasticity model depending on the nonlocal heat transfer law including dual‐phase lag. Quintanilla 37 extracted the three‐phase‐lag model differently and investigated the spatial behavior and stability of the new proposed model. Recently, Cao and Guo 38,39 and Guo and Huo 40 established the heat conduction equation depending on the idea of thermomass theory.…”

Section: Introductionmentioning

confidence: 99%

A novel model of nonlocal thermoelasticity with time derivatives of higher order

Abouelregal

2020

Math Methods in App Sciences

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The objective of this work is to introduce a new system of differential equations describing the nonlocal thermoelasticity theory with higher time derivatives and two-phase lags. In order to obtain this model, we used the nonlocal continuum theory proposed by Eringen and the methodology of the Taylor series expansion of higher-order time derivatives. Some generalized thermoelasticity theories follow as limited cases. This model is used to study the thermoelastic interaction in a nonlocal medium. The medium is exposed to an applied magnetic field and a periodic time heat source with a constant strength. Some comparisons have been displayed in figures to estimate the influences of the nonlocal parameter and magnetic field as well as the parameters of higher-order on all the field quantities.

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Section: Introductionmentioning

confidence: 99%

A novel model of nonlocal thermoelasticity with time derivatives of higher order

Abouelregal

2020

Math Methods in App Sciences

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“…TPL [122,123]. TDPL [124,125]. Thermomechanical models [131] Separation of variables [67,69,[132][133][134] Cartesian, Spherical 1-D, 2.5-D, 3-D CV, DPL Spherical coordinates [69].…”

Section: Uniquenessmentioning

confidence: 99%

“…Also, the stability analysis is performed for the TPL model by [122,123] and for the three-dual-phase-lag model (TDPL) by [124,125]. In addition, a complete investigation of the wellposedness of the problem of heat transport by means of the phase-lagging models is presented in [126][127][128][129][130][131].…”

Section: Stabilitymentioning

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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“…In recent papers Quintanilla [14–16] has proposed several modifications of the theories of Tzou and Choudhuri to obtain heat conduction equations with delay. In the last reference considering the limit case when τ q = τ θ and τ = τ ν − τ q was proposed.…”

Section: Introductionmentioning

confidence: 99%

On uniqueness and stability for a thermoelastic theory

Quintanilla¹

2016

Mathematics and Mechanics of Solids

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In this paper we investigate a thermoelastic theory obtained from the Taylor approximation for the heat flux vector proposed by Choudhuri. This new thermoelastic theory gives rise to interesting mathematical questions. We here prove a uniqueness theorem and instability of solutions under the relaxed assumption that the elasticity tensor can be negative. Later we consider the one-dimensional and homogeneous case and we prove the existence of solutions. We finish the paper by proving the slow decay of the solutions. That means that the solutions do not decay in a uniform exponential way. This last result is relevant if it is compared with other thermoelastic theories where the decay of solutions for the one-dimensional case is of exponential way.Peer ReviewedPostprint (author's final draft

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Some solutions for a family of exact phase-lag heat conduction problems

Cited by 36 publications

References 30 publications

A novel model of nonlocal thermoelasticity with time derivatives of higher order

A novel model of nonlocal thermoelasticity with time derivatives of higher order

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

On uniqueness and stability for a thermoelastic theory

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