scholarly journals Open Mathematical Aspects of Continuum Thermodynamics: Hyperbolicity, Boundaries and Nonlinearities

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1469
Author(s):  
Mátyás Szücs ◽  
Róbert Kovács ◽  
Srboljub Simić
Keyword(s):  
Irreversible Thermodynamics ◽  
Internal Variables ◽  
Engineering Practice ◽  
Continuum Thermodynamics ◽  
Mathematical Properties ◽  
Points Of View ◽  
Continuum Thermodynamic ◽  
Classical Knowledge ◽  
Rational Extended Thermodynamics ◽  
Non Equilibrium

Thermodynamics is continuously spreading in the engineering practice, which is especially true for non-equilibrium models in continuum problems. Although there are concepts and approaches beyond the classical knowledge, which are known for decades, their mathematical properties, and consequences of the generalizations are less-known and are still of high interest in current researches. Therefore, we found it essential to collect the most important and still open mathematical questions that are related to different continuum thermodynamic approaches. First, we start with the example of Classical Irreversible Thermodynamics (CIT) in order to provide the basis for the more general and complex frameworks, such as the Non-Equilibrium Thermodynamics with Internal Variables (NET-IV) and Rational Extended Thermodynamics (RET). Here, we aim to present that each approach has its specific problems, such as how the initial and boundary conditions can be formulated, how the coefficients in the partial differential equations are connected to each other, and how it affects the appearance of nonlinearities. We present these properties and comparing the approach of NET-IV and RET to each other from these points of view. In the present work, we restrict ourselves on non-relativistic models.

scholarly journals Relationships between rational extended thermodynamics and extended irreversible thermodynamics

2020 ◽  
Vol 378 (2170) ◽  
pp. 20190172 ◽  
Author(s):  
David Jou
Keyword(s):  
Nonequilibrium Thermodynamics ◽  
Irreversible Thermodynamics ◽  
Extended Thermodynamics ◽  
Internal Variables ◽  
Second Law ◽  
Hamiltonian Approach ◽  
Theme Issue ◽  
Extended Irreversible Thermodynamics ◽  
Independent Variables ◽  
Rational Extended Thermodynamics

We consider a few conceptual questions on extended thermodynamics, with the aim to contribute to a higher contact between rational extended thermodynamics and extended irreversible thermodynamics. Both theories take a number of fluxes as independent variables, but they differ in the formalism being used to deal with the exploitation of the second principle (rational thermodynamics in the first one and classical irreversible thermodynamics in the second one). Rational extended thermodynamics is more restricted in the range of systems to be analysed, but it is able to obtain a wider number of restrictions and deeper specifications from the second law. By contrast, extended irreversible thermodynamics is more phenomenological, its mathematical formalism is more elementary, but it may deal with a wider diversity of systems although with less detail. Further comparison and dialogue between both branches of extended thermodynamics would be useful for a fuller deployment and deepening of extended thermodynamics. Besides these two approaches, one should also consider the Hamiltonian approach, formalisms with internal variables, and more microscopic approaches, based on kinetic theory or on non-equilibrium ensemble formalisms. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

Non-Equilibrium Thermodynamics

1994 ◽  
Author(s):  
Antony N. Beris ◽  
Brian J. Edwards
Keyword(s):  
Time Scales ◽  
Irreversible Thermodynamics ◽  
Transport Processes ◽  
Irreversible Processes ◽  
Internal Variables ◽  
Equilibrium Thermodynamics ◽  
System P ◽  
The Subject ◽  
Thermodynamic Variables ◽  
Non Equilibrium

After having devoted five chapters of this book to the discussion of equilibrium thermodynamics and conservative dynamic phenomena, it is now high time that we entered into the realm of irreversible transport processes. As mentioned in chapter 1, most of the physical systems which engineers wish to model exhibit dissipative phenomena. Therefore, although the techniques touched upon in the previous chapters are mathematically profound and well-suited for diverse analyses for conservative systems, it is in this chapter and the next that the major engineering applications will find their foundation. Granted, in describing irreversible phenomena on the continuum level a certain amount of phenomenology is necessarily introduced; yet we hope to illustrate here how the application of thermodynamic knowledge to the irreversible system can reduce this phenomenology to the bare minimum. The objective of this chapter is similar to that of chapter 4; we wish to present a brief, yet sufficiently thorough, discussion concerning the theory of non-equilibrium thermodynamics applied to irreversible processes. There already exist several outstanding references on the subject [De Groot and Mazur, 1962; Yourgrau et al., 1966; Prigogine, 1967; Gyarmati, 1970; Woods, 1975; Lavenda, 1978; Truesdell, 1984]. Thus, the objective of our discussion here is mainly to introduce the principles that are subsequently used to formulate the dissipative bracket, as outlined in the next chapter. Moreover, the presentation of the subject is biased towards the presentation of the concepts that we consider as most helpful to continuum modeling. For example, the notion of internal variables is introduced early on, in §6.2. As we shall see, the inclusion of internal variables in the non-equilibrium description of the system has profound implications concerning the roles of the various thermodynamic variables and the definitions of the various state functions, in particular, the entropy. Indeed, the definitions of these functions hinge upon the notion of time scales which become of chief importance in the discussion of irreversible thermodynamics. In the philosophy of equilibrium thermodynamics, it is assumed that the time scale for changes in the system is sufficiently large as compared to the intrinsic time scales of any internal variables within the system.

Analysis of Compression Ignition Engine Cycle Based on Irreversible Thermodynamics

2013 ◽  
Vol 837 ◽  
pp. 446-451
Author(s):  
Ion Omocea
Keyword(s):  
Pressure Drop ◽  
Irreversible Thermodynamics ◽  
Pressure Variation ◽  
Compression Ignition ◽  
Compression Ignition Engine ◽  
Fuel Flow ◽  
Marine Propulsion ◽  
Complex Optimization ◽  
Points Of View ◽  
Engine Cycle

We use a model that is based on the cycle behavior inlet pressure variation. This analysis revealed the two main regimes of operation marine propulsion engines. Pressure drop in the suction process can be seen from two points of view: this pressure drop is an active dissipation and at the same time is a passive dissipation, contributing to the deterioration of cycle infrastructure. Interference of the two effects is reflected by the appearance of a ψaopt=0,3...0,35, for which indicated power Pi becomes maximum in terms of given geometric and gazodynamic configurations. Respectively for a weighting of conductance gazodynamic imposed. When fuel flow is imposed, the analysis revealed that the share of shall be amended to variation of ψa, which involves the geometric and gazodynamic configuration variable. In this numerical analysis showed the existence of ψaopt=0,1...0,15, for which indicated efficiency ηi is maximum. These findings are the basis for the complex optimization cycle program for four-stroke compression ignition engine.

scholarly journals Closure conditions for a one temperature non-equilibrium multi-component model of baer-nunziato type

2019 ◽  
Vol 66 ◽  
pp. 42-60 ◽  
Author(s):  
M. Hantke ◽  
S. Müller
Keyword(s):  
Water Vapor ◽  
Physical Properties ◽  
Sufficient Conditions ◽  
Component Model ◽  
Interfacial Velocity ◽  
Mathematical Properties ◽  
Chemical Potentials ◽  
Closure Conditions ◽  
Velocity Pressure ◽  
Non Equilibrium

A class of non-equilibrium models for compressible multi-component uids is investigated. These models are subject to the choice of interfacial pressures and interfacial velocity as well as relaxation terms for velocity, pressure and chemical potentials. Sufficient conditions are derived for these quantities that ensure meaningful physical properties such as a non-negative entropy production and thermodynamical stability as well as mathematical properties such as hyperbolicity. For the relaxation of chemical potentials a three-component model gas-water-vapor is considered.

A Thermodynamical Theory with Internal Variables Describing Thermal Effects in Viscous Fluids

2018 ◽  
Vol 43 (2) ◽  
pp. 171-184
Author(s):  
Vincenzo Ciancio ◽  
Annunziata Palumbo
Keyword(s):  
Heat Conduction ◽  
Current Density ◽  
Thermal Effects ◽  
Local Equilibrium ◽  
Irreversible Thermodynamics ◽  
Viscous Fluids ◽  
Internal Variables ◽  
Generalized Entropy ◽  
Entropy Current ◽  
Newton’S Laws

AbstractIn this paper the heat conduction in viscous fluids is described by using the theory of classical irreversible thermodynamics with internal variables. In this theory, the deviation from the local equilibrium is characterized by vectorial internal variables and a generalized entropy current density expressed in terms of so-called current multipliers. Cross effects between heat conduction and viscosity are also considered and some phenomenological generalizations of Fourier’s and Newton’s laws are obtained.

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