scholarly journals A case study of non-Fourier heat conduction using internal variables and GENERIC

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mátyás Szücs ◽  
Michal Pavelka ◽  
Róbert Kovács ◽  
Tamás Fülöp ◽  
Péter Ván ◽  
...  
Keyword(s):  
Heat Conduction ◽  
General Equation ◽  
Internal Variables ◽  
State Variables ◽  
Equilibrium Thermodynamics ◽  
Ginzburg Landau ◽  
Entropy Current ◽  
Fourier Heat Conduction ◽  
Non Equilibrium

Abstract Applying simultaneously the methodology of non-equilibrium thermodynamics with internal variables (NET-IV) and the framework of General Equation for the Non-Equilibrium Reversible–Irreversible Coupling (GENERIC), we demonstrate that, in heat conduction theories, entropy current multipliers can be interpreted as relaxed state variables. Fourier’s law and its various extensions—the Maxwell–Cattaneo–Vernotte, Guyer–Krumhansl, Jeffreys type, Ginzburg–Landau (Allen–Cahn) type and ballistic–diffusive heat conduction equations—are derived in both formulations. Along these lines, a comparison of NET-IV and GENERIC is also performed. Our results may pave the way for microscopic/multiscale understanding of beyond-Fourier heat conduction and open new ways for numerical simulations of heat conduction problems.

scholarly journals Theories and heat pulse experiments of non-Fourier heat conduction

2016 ◽  
Vol 7 (2) ◽  
pp. 150-166 ◽  
Author(s):  
Péter Ván
Keyword(s):  
Heat Conduction ◽  
Heat Pulse ◽  
Theoretical Background ◽  
Point Of View ◽  
Experimental Basis ◽  
Equilibrium Thermodynamics ◽  
Fourier Heat Conduction ◽  
Non Equilibrium

Abstract The experimental basis and theoretical background of non-Fourier heat conduction is shortly reviewed from the point of view of non-equilibrium thermodynamics. The performance of different theories is compared in case of heat pulse experiments.

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.

scholarly journals Kluitenberg–Verhás Rheology of Solids in the GENERIC Framework

2019 ◽  
Vol 44 (3) ◽  
pp. 247-259 ◽  
Author(s):  
Mátyás Szücs ◽  
Tamás Fülöp
Keyword(s):  
General Equation ◽  
Rheological Model ◽  
Soft Rock ◽  
Internal Variable ◽  
Equilibrium Thermodynamics ◽  
Practical Applications ◽  
Generic Framework ◽  
Ground Conditions ◽  
Model Family ◽  
Non Equilibrium

Abstract The internal variable methodology of non-equilibrium thermodynamics, with a symmetric tensorial internal variable, provides an important rheological model family for solids, the so-called Kluitenberg–Verhás model family [Cs. Asszonyi et al., Contin. Mech. Thermodyn. 27, 2015]. This model family is distinguished not only by theoretical aspects but also on experimental grounds (see [Cs. Asszonyi et al., Period. Polytech., Civ. Eng. 60, 2016] for plastics and [W. Lin et al., Rock Engineering in Difficult Ground Conditions (Soft Rock and Karst), Proceedings of Eurock’09, 2009; K. Matsuki, K. Takeuchi, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 30, 1993; K. Matsuki, Int. J. Rock Mech. Min. Sci. 45, 2008] for rocks). In this article, we present and discuss how the internal variable formulation of the Kluitenberg–Verhás model family can be presented in the non-equilibrium thermodynamical framework GENERIC (General Equation for the Non-Equilibrium Reversible–Irreversible Coupling) [H. C. Öttinger, Beyond Equilibrium Thermodynamics, 2005; M. Grmela, J. Non-Newton. Fluid Mech. 165, 2010; M. Grmela, H. C. Öttinger, Phys. Rev. E 56, 1997; H. C. Öttinger, M. Grmela, Phys. Rev. E 56, 1997], for the benefit of both thermodynamical methodologies and promising practical applications.

Non-Equilibrium Dislocation Dynamics in Semiconductor Crystals and Superlattices

2018 ◽  
Vol 43 (2) ◽  
pp. 163-170 ◽  
Author(s):  
David Jou ◽  
Liliana Restuccia
Keyword(s):  
Mechanical Properties ◽  
Heat Flux ◽  
Relative Orientation ◽  
Dislocation Dynamics ◽  
Rate Equations ◽  
Internal Variables ◽  
Equilibrium Thermodynamics ◽  
Semiconductor Crystals ◽  
Standard Procedures ◽  
Non Equilibrium

AbstractA model for semiconductor crystals and superlattices with dislocations proposed in a previous paper is used here to study the thermal, electrical and mechanical properties of these defective materials. The standard procedures of non-equilibrium thermodynamics with internal variables are applied to derive in the linear approximation constitutive equations as well as rate equations for the dislocation, charges and heat flux fields, containing coupled effects among the different fields. A new dislocation tensor is used to describe the geometry of the dislocation lines, because their relative orientation with respect to the superlattice interfaces is very relevant.

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.

A Study of Non-Equilibrium Heat Transfer in Microporous Media

2003 ◽  
Author(s):  
A. G. Agwu Nnanna
Keyword(s):  
Heat Conduction ◽  
Thermal Diffusivity ◽  
Early Stage ◽  
Near Field ◽  
Heating Process ◽  
Conduction Model ◽  
Heat Conduction Model ◽  
Fourier Heat Conduction ◽  
Microporous Media ◽  
Non Equilibrium

A numerical study of the non-Fourier heat conduction in microporous media is presented. The governing energy equation is formulated based on the two-equation model and the non-Fourier heat conduction model. This formulation leads to the emergence of three thermal lag-times. These parameters account for the thermal interaction between the fluid and neighboring solid matrix as well as the delay time needed for both phases to approach thermal equilibrium. Numerical experiments were conducted for various microporous media to study the thermal non-equilibrium behavior. Results show that the thermal non-equilibrium phenomena have significant effect on the transient response of the porous media only during the early stage of the heating process and in the near-field region where the heat source is located. The thermal responses of the various microporous media were compared to gain understanding of the effect of thermal diffusivity on thermodynamic non-equilibrium phenomena. It was found that the influence of thermal diffusivity is small especially in the near-field (96–200μm). Also, results obtained using the non-Fourier heat conduction model deviates from the predictions based on the classical Fourier model only during the early stage of the heating process. At large time, results obtained from both models are in good agreement.

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