Entropy flux in non-equilibrium thermodynamics

Jou, David; Lebon, Georgy; Mongiovı̀, Maria Stella; Peruzza, R.A.

doi:10.1016/j.physa.2004.02.011

Cited by 23 publications

(19 citation statements)

References 11 publications

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“…The occurrence of ∇ and ∇ · is consistent with the results for non-simple heat conductors [16,21,22]. Moreover, we disregard a possible dependence on ∇ and let the free energy take the form…”

Section: An Examplesupporting

confidence: 80%

Evolution Equations for Non-Simple Viscoelastic Solids

Morro

2010

J Elast

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Objectivity and compatibility with thermodynamics of evolution equations are examined in connection with the modelling of viscoelastic solids. The purpose of the paper is to show that the evolution equation for the stress is eventually obtained by means of a tensorial internal variable within the framework of the reference configuration. The non-simple character is realized by gradients of the internal variable. The thermodynamic analysis is developed by investigating the entropy inequality in the reference configuration and allowing for a non-zero extra-entropy flux. It follows that the evolution for the Cauchy stress tensor involves the Oldroyd derivative, irrespective of the form of the non-local terms.

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Section: An Examplesupporting

confidence: 80%

Evolution Equations for Non-Simple Viscoelastic Solids

Morro

2010

J Elast

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“…(1), namely, P ðnlÞ x; y; t ð Þ(see Fig. 1 where the integral at the right-hand side is the non-local heat transfer contribute due to the interaction between the particle located at position x and all the other particles of the body [45].…”

Section: The Fractional-order Theory Of Classical Irreversible Thermomentioning

confidence: 99%

“…(35) with the corresponding expression in terms of temperature gradients as reported in Eq. (8) we get the 3D counterpart of the temperature equation yet obtained for the 1D case [45], in the form: …”

Section: A Non-equilibrium Model Of Fractional-order Thermal Energy Tmentioning

confidence: 99%

Fractional-order theory of heat transport in rigid bodies

Zingales¹

2014

Communications in Nonlinear Science and Numerical Simulation

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a b s t r a c tThe non-local model of heat transfer, used to describe the deviations of the temperature field from the well-known prediction of Fourier/Cattaneo models experienced in complex media, is framed in the context of fractional-order calculus. It has been assumed (Borino et al., 2011 [53], Mongioví and Zingales, 2013 [54]) that thermal energy transport is due to two phenomena: (i) A short-range heat flux ruled by a local transport equation; (ii) A long-range thermal energy transfer proportional to a distance-decaying function, to the relative temperature and to the product of the interacting masses. The distance-decaying function is assumed in the functional class of the power-law decay of the distance yielding a novel temperature equation in terms of a-order Marchaud fractional-order derivative ð0 6 a 6 1Þ. Thermodynamical consistency of the model is provided in the context of Clausius-Plank inequality. The effects induced by the boundary conditions on the temperature field are investigated for diffusive as well as ballistic local heat flux. Deviations of the temperature field from the linear distributions in the neighborhood of the thermostated zones of small-scale conductors are qualitatively predicted by the used fractional-order heat transport model, as shown by means of molecular dynamics simulations.

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“…(6) is a particular hypothesis concerning the form of the entropy flux, which turns out to be far more general than the classical expression J s =q/T . Analyses of generalized expressions of entropy flux may be found in [21,22,[35][36][37][38][39][40][41][42]. Substitution of Eq.…”

Section: Entropy Entropy Flux and Second Lawmentioning

confidence: 99%

Thermodynamic framework for a generalized heat transport equation

Guo

Wang

2016

Communications in Applied and Industrial Mathematics

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In this paper, a generalized heat transport equation including relaxational, nonlocal and nonlinear effects is provided, which contains diverse previous phenomenological models as particular cases. The aim of the present work is to establish an extended irreversible thermodynamic framework, with generalized expressions of entropy and entropy flux. Nonlinear thermodynamic force-flux relation is proposed as an extension of the usual linear one, giving rise to the nonlinear terms in the heat transport equation and ensuring compatibility with the second law. Several previous results are recovered in the linear case, and some additional results related to nonlinear terms are also obtained.

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Entropy flux in non-equilibrium thermodynamics

Cited by 23 publications

References 11 publications

Evolution Equations for Non-Simple Viscoelastic Solids

Evolution Equations for Non-Simple Viscoelastic Solids

Fractional-order theory of heat transport in rigid bodies

Thermodynamic framework for a generalized heat transport equation

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