On the evolution of higher order fluxes in non-equilibrium thermodynamics

Ciancio, Vincenzo; Cimmelli, Vito Antonio; Ván, P.

doi:10.1016/j.mcm.2006.04.009

Cited by 14 publications

(13 citation statements)

References 33 publications

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“…be found for instance in [18]. An alternative way, leading to a gradient dependent free energy density, can be found in [46][47][48], where in the exploitation of the dissipation inequality not only the evolution equations are taken into account, but also the gradients of evolution equations.…”

Section: Discussionmentioning

confidence: 99%

Thermodynamical Frameworks for Higher Grade Material Theories with Internal Variables or Additional Degrees of Freedom

Papenfuß¹,

Forest²

2006

Journal of Non-Equilibrium Thermodynamics

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The objective of the present work is to compare several thermomechanical frameworks, taking into account the influence of strain gradient, internal variables, gradient of internal variables, and temperature gradient on the constitutive behavior of materials. In particular, the restrictions by the second law of thermodynamics are derived. The method of exploitation consists of two steps: an application of the well-known method by Liu and a new method of exploiting the residual inequality. The first example introduces an enlarged set of variables for the constitutive functions including in particular the strain gradient, an internal variable, its gradient, and the temperature gradient. In the second example, the power of internal forces is enriched to incorporate generalized stress measures. In the third example, the classical thermomechanical setting is complemented by a balance-type di¤erential equation for an additional variable. Finally, material theories of grade n are envisaged. It is shown that the free energy density may depend on gradients only in the case that an additional balance equation is introduced. We also demonstrate that for isotropic materials the second law of thermodynamics implies for a large class of state spaces that the entropy flux equals the heat flux divided by temperature.

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Section: Discussionmentioning

confidence: 99%

Thermodynamical Frameworks for Higher Grade Material Theories with Internal Variables or Additional Degrees of Freedom

Papenfuß¹,

Forest²

2006

Journal of Non-Equilibrium Thermodynamics

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“…The flux of the heat flux is a second-order tensor usually considered in non-local models of heat transport [24,[50][51][52][53]. We aim to obtain evolution equations for q and Q compatible with the second law of thermodynamics, which requires a positive definite character of the entropy production.…”

Section: Approximate Constitutive Equation For Heat Flux In Gradmentioning

confidence: 99%

A thermodynamic model for heat transport and thermal wave propagation in graded systems

Jou

Carlomagno

Cimmelli

2015

Physica E: Low-dimensional Systems and Nanostructures

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“…So, the definition of the macroscopic material velocity of the component A, v A (x, t), i.e., the mean velocity of the component A of the mixture, is 17) and equation (5.7) leads to the macroscopic mass balance of component A (4.4) if we take…”

Section: Mesoscopic Balance Equations For the Components Of The Mixturementioning

confidence: 99%

“…This differential equation is derived either from an Irreversible Thermodynamics treatment [6,7] of the dissipation inequality (for other applications see [8,9,10,11,12,13]), or a balance type equation for the non-convective fluxes, here the diffusion flux, is postulated in Rational Extended Thermodynamics [14,5,15]. For a purely macroscopic derivation of balance type differential equations for higher order fluxes see [16,17]. Within Rational Extended Thermodynamics it has been shown that the resulting system of field equations is symmetric hyperbolic with a convex extension [18,5,19], thereby allowing for finite speeds of disturbances only [20,21,18].…”

Section: Introductionmentioning

confidence: 99%

A mesoscopic approach to diffusion phenomena in mixtures

Palumbo

Papenfuß

Rogolino

2005

Journal of Non-Equilibrium Thermodynamics

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The mesosocpic concept is applied to the theory of mixtures. The aim is to investigate the diffusion phenomenon from a mesoscopic point of view. The domain of the field quantities is extended by the set of mesoscopic variables, here the velocities of the components. Balance equations on this enlarged space are the equations of motion for the mesoscopic fields. Moreover, local distribution functions of the velocities are introduced as a statistical element, and an equation of motion for this distribution function is derived. From this equation of motion differential equations for the diffusion fluxes, and also for higher order fluxes are obtained. These equations are of balance type, as it is postulated in Extended Thermodynamics. The resulting evolution equation for the diffusion flux generalizes the Fick's law.

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On the evolution of higher order fluxes in non-equilibrium thermodynamics

Cited by 14 publications

References 33 publications

Thermodynamical Frameworks for Higher Grade Material Theories with Internal Variables or Additional Degrees of Freedom

Thermodynamical Frameworks for Higher Grade Material Theories with Internal Variables or Additional Degrees of Freedom

A thermodynamic model for heat transport and thermal wave propagation in graded systems

A mesoscopic approach to diffusion phenomena in mixtures

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