Extended Irreversible Thermodynamics and Generalization of the Dual-Phase-Lag Model in Heat Transfer

Serdyukov, S. I.; Voskresenskii, N. M.; Bel'nov, V. K.; Karpov, I. I.

doi:10.1515/jnetdy.2003.013

Cited by 13 publications

(9 citation statements)

References 11 publications

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“…According to the local uniformity hypothesis [ 26 ], a system that is non-equilibrium as a whole is considered as uniform in each point, and that is why we may increase the number of state variables. For diffusion and chemical reactions without convection, instead of Equation (3) we have [ 21 , 22 ]:

where

is the first-order derivative,

is the second-order derivative, …,

is the

-th-order derivative, and

.…”

Section: Higher-order Time Derivatives Of Usual Variablesmentioning

confidence: 99%

“…Another type of EIT involves the time derivatives of common thermodynamic variables as extra variables [ 21 , 22 , 23 , 24 , 25 ]. In this case, the local-equilibrium hypothesis is not applicable, and we must proceed from a less strict postulate.…”

Section: Introductionmentioning

confidence: 99%

“…Based on this postulate, one can construct the thermodynamic formalism which is similar to classical, where the main laws and consequences of non-equilibrium thermodynamics are preserved [ 27 ]. In this paper, we have used for the first time the approach based on the works [ 21 , 22 , 23 , 24 , 25 , 26 , 27 ] for describing the properties of nanosystems.…”

Section: Introductionmentioning

confidence: 99%

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Macroscopic Entropy of Non-Equilibrium Systems and Postulates of Extended Thermodynamics: Application to Transport Phenomena and Chemical Reactions in Nanoparticles

Serdyukov

2018

Entropy

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In this work, we consider extended irreversible thermodynamics in assuming that the entropy density is a function of both common thermodynamic variables and their higher-order time derivatives. An expression for entropy production, and the linear phenomenological equations describing diffusion and chemical reactions, are found in the context of this approach. Solutions of the sets of linear equations with respect to fluxes and their higher-order time derivatives allow the coefficients of diffusion and reaction rate constants to be established as functions of size of the nanosystems in which these reactions occur. The Maxwell-Cattaneo and Jeffreys constitutive equations, as well as the higher-order constitutive equations, which describe the processes in reaction-diffusion systems, are obtained. by the parameters of atoms and molecules (e.g., for gases they are mean free path and mean time between two collisions of molecules, respectively). Macroscales is the characteristic macroscale of the system and characteristic time of changing of macroscopic parameters. In our case, spatial macroscale is a linear dimension of a system whether it is a particle size or a nanolayer thickness. When a spatial macroscale is much larger than the relevant microscale (at constant time scales), then local-equilibrium hypothesis remains valid that enables us to use classical irreversible thermodynamics. In turn, if a spatial macroscale is comparable or smaller than the microscale, there is no local equilibrium and the non-equilibrium system has to be described in the contents of more general theory.The latest development in irreversible thermodynamics led to elaboration of extended irreversible thermodynamics (EIT) which allowed study of fast and steep phenomena [11][12][13][14][15]. Extended irreversible thermodynamics involves investigations of irreversible processes with high frequencies and small length scales, which take place in nanosystems [16]. Heat conduction in thin layers [1,2], diffusion and chemical reactions in nanoparticles [17], as well as nanocatalysis [18,19] are of great interest in the context of EIT, where memory and non-local effects are taken into consideration [20].Extended irreversible thermodynamics is based on the generalization of classical local-equilibrium theory by using additional thermodynamic variables (or extra variables). Their choice is an important problem which can be solved by different ways. The most common route to extend a classical theory is the introduction of dissipative fluxes as extra variables [11][12][13][14]. For this kind of EIT, variables are both well-known fluxes, which arise in balance equations, and higher-order fluxes (fluxes of the fluxes) that allows the unlimited number of extra variables.Another type of EIT involves the time derivatives of common thermodynamic variables as extra variables [21][22][23][24][25]. In this case, the local-equilibrium hypothesis is not applicable, and we must proceed from a less strict postulate. Such a hypothesis is the local uniformity hypothesi...

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where

is the first-order derivative,

is the second-order derivative, …,

is the

-th-order derivative, and

.…”

Section: Higher-order Time Derivatives Of Usual Variablesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Macroscopic Entropy of Non-Equilibrium Systems and Postulates of Extended Thermodynamics: Application to Transport Phenomena and Chemical Reactions in Nanoparticles

Serdyukov

2018

Entropy

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“…A postulate of extended irreversible thermodynamics is suggested, according to which the entropy is a function of the internal energy and its time derivatives up to the third-order derivative in the DPL model [98]. The extended thermodynamics of irreversible processes is developed, based on the two postulates by which the additional variables of the entropy density are dissipative fluxes and material time derivatives of the ordinary thermodynamic variables.…”

Section: Boundary Conditionsmentioning

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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“…We note that we can obtain an equation which bears some resemblance with (1.13) by considering the following generalization of the Maxwell-Cattaneo law [31,32]:…”

Section: Introductionmentioning

confidence: 99%