Thermodynamical consistency of the dual-phase-lag heat conduction equation

Kovács, Róbert; Ván, P.

doi:10.1007/s00161-017-0610-x

Cited by 35 publications

(19 citation statements)

References 56 publications

(96 reference statements)

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“…The inequality sign in (20) is a direct consequence of the four properties of dissipation potentials listed in Section 3.2. Since bothĖ = 0 andṠ (M) > 0 hold then also the inequalityΦ (M) < 0 holds.…”

Section: Properties Of Solutions To Eq(17)mentioning

confidence: 99%

Entropy and Entropy Production in Multiscale Dynamics

Grmela

Pavelka

Klika

et al. 2019

Journal of Non-Equilibrium Thermodynamics

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Heat conduction is investigated on three levels: equilibrium, Fourier, and Cattaneo. The Fourier level is either the point of departure for investigating the approach to equilibrium or the final stage in the investigation of the approach from the Cattaneo level. Both investigations bring to the Fourier level an entropy and a thermodynamics. In the absence of external and internal influences preventing the approach to equilibrium the entropy that arises in the latter investigation is the production of the classical entropy that arises in the former investigation. If the approach to equilibrium is prevented, then the entropy that arises in the investigation of the approach from the Cattaneo level to the Fourier level still brings to the Fourier level the entropy and the thermodynamics even if the classical entropy and the classical thermodynamics is absent. We also note that vanishing total entropy production as a characterization of equilibrium state is insufficient.

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Section: Properties Of Solutions To Eq(17)mentioning

confidence: 99%

Entropy and Entropy Production in Multiscale Dynamics

Grmela

Pavelka

Klika

et al. 2019

Journal of Non-Equilibrium Thermodynamics

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“…In this regard, we are convinced that the dual-phase lag (DPL) model, together with its time-differential formulation, turned out to be particularly suited to respond to this kind of needs, having its features in fact already deepened in a very wide number of works, of which [3][4][5][6][7][8][9][10][11][12][13][14] and the references therein just represent a selection also accounting for high expansion orders in thermoelasticity. The DPL constitutive equation puts in relation the temperature variation gradient , at a certain time + with the heat flux vector at a different time + .…”

Section: Introductionmentioning

confidence: 99%

On the Increase in Signal Depth due to High‐Order Effects in Micro‐ and Nanosized Deformable Conductors

Zampoli

2019

Mathematical Problems in Engineering

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With regard to the transmission of a thermomechanical signal on extremely short temporal and spatial scales, which represents an issue particularly important dealing with micro- and nanosized electromechanical systems, it is well known that the so-called non-Fourier effects become not negligible. In addition, it has to be considered that the interaction among multiple energy carriers has, as a direct consequence, the involvement of high-order terms in the time-differential formulation of the dual-phase lag heat conduction constitutive equation linking the heat flux vector with the temperature variation gradient. Accepting that the deformations caused by the temperature variations are small enough to be modeled under the assumptions typical of the linear thermoelasticity, in the present article we take into account the highest Taylor expansion orders able to guarantee (under appropriate assumptions) stability conditions, thermodynamic consistency, and at the same time the existence of an influence domain of the external data linked to the energy transmission as thermal waves. To this aim, a cylindrical domain filled by an anisotropic and inhomogeneous thermoelastic material is investigated, although the results obtained will be independent from the considered geometry: for such a reason, we will be able to consider as illustrative examples some simulations referred to single-layer graphene and to show how the expansion orders selected strongly influence the domain of influence depth.

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“…Though different time nonlocal generalizations of the Fourier law have a long history, they still attract the attention of researchers (see, for example, Reference [9], and the extensive discussion in [10]).…”

Section: Introductionmentioning

confidence: 99%

Time-Fractional Heat Conduction in Two Joint Half-Planes

Povstenko

Klekot

2019

Symmetry

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The heat conduction equations with Caputo fractional derivative are considered in two joint half-planes under the conditions of perfect thermal contact. The fundamental solution to the Cauchy problem as well as the fundamental solution to the source problem are examined. The Fourier and Laplace transforms are employed. The Fourier transforms are inverted analytically, whereas the Laplace transform is inverted numerically using the Gaver–Stehfest method. We give a graphical representation of the numerical results.

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Thermodynamical consistency of the dual-phase-lag heat conduction equation

Abstract: Abstract. Dual phase lag equation for heat conduction is analyzed from the point of view of non-equilibrium thermodynamics. Its first order Taylor series expansion is consistent with the second law as long as the two relaxation times are not negative.

Cited by 35 publications

References 56 publications

Entropy and Entropy Production in Multiscale Dynamics

Entropy and Entropy Production in Multiscale Dynamics

On the Increase in Signal Depth due to High‐Order Effects in Micro‐ and Nanosized Deformable Conductors

Time-Fractional Heat Conduction in Two Joint Half-Planes

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