An Extended Thermodynamic Approach to Transport Phenomena in Porous Media

1990 ◽  
Vol 195 ◽  
Author(s):  
J. A. del Rio ◽  
M. López de Haro
Keyword(s):  
Porous Media ◽  
Constitutive Equations ◽  
Evolution Equations ◽  
Transport Phenomena ◽  
Irreversible Thermodynamics ◽  
Extended Irreversible Thermodynamics ◽  
Independent Variables ◽  
Extended Thermodynamic ◽  
Momentum Fluxes ◽  
Linear Irreversible Thermodynamics

ABSTRACTA formalism of extended irreversible thermodynamics (EIT) is used to study the physical aspects of heat, momentum and mass transport through porous media.The thermodynamic space is enlarged with respect to that of classical linear irreversible thermodynamics (LIT) to include the mass, heat and momentum fluxes as independent variables. The time evolution equations for such variables are derived self-consistently and reduce to the usual constitutive equations of LIT when the appropriate limits are taken. Equations that involve effects characterized by terms of second order in the gradients of conserved variables (such as the Darcy-Brinkman law) may also be derived within the same formalism. Finally, EIT provides the natural framework beyond LIT to introduce non-isothermal effects in the study of transport phenomena in porous media.

scholarly journals A Unified Extended Thermodynamic Description of Diffusion, Thermo-Diffusion, Suspensions, and Porous Media

2005 ◽  
Vol 73 (1) ◽  
pp. 16-20 ◽  
Author(s):  
Georgy Lebon ◽  
Thomas Desaive ◽  
Pierre Dauby
Keyword(s):  
Porous Media ◽  
Evolution Equations ◽  
Diffusion Flux ◽  
Thermodynamic Description ◽  
Fluid Flows ◽  
Irreversible Thermodynamics ◽  
Heat Fluxes ◽  
Flows In Porous Media ◽  
Extended Thermodynamic ◽  
Higher Order Terms

It is shown that extended irreversible thermodynamics (EIT) provides a unified description of a great variety of processes, including matter diffusion, thermo-diffusion, suspensions, and fluid flows in porous media. This is achieved by enlarging the set of classical variables, as mass, momentum and temperature by the corresponding fluxes of mass, momentum and heat. For simplicity, we consider only Newtonian fluids and restrict ourselves to a linear analysis: quadratic and higher order terms in the fluxes are neglected. In the case of diffusion in a binary mixture, the extra flux variable is the diffusion flux of one the constituents, say the solute. In thermo-diffusion, one adds the heat flux to the set of variables. The main result of the present approach is that the traditional equations of Fick, Fourier, Soret, and Dufour are replaced by time-evolution equations for the matter and heat fluxes, such generalizations are useful in high-frequency processes. It is also shown that the analysis can be easily extended to the study of particle suspensions in fluids and to flows in porous media, when such systems can be viewed as binary mixtures with a solid and a fluid component.

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’.

scholarly journals Differential consequences of balance laws in extended irreversible thermodynamics of rigid heat conductors

2019 ◽  
Vol 475 (2227) ◽  
pp. 20180482 ◽  
Author(s):  
P. Rogolino ◽  
V. A. Cimmelli
Keyword(s):  
Cauchy Problem ◽  
Evolution Equations ◽  
Transport Model ◽  
Initial Conditions ◽  
Original System ◽  
Irreversible Thermodynamics ◽  
Order System ◽  
Balance Laws ◽  
Extended Irreversible Thermodynamics ◽  
The Cauchy Problem

We consider a system of balance laws arising in extended irreversible thermodynamics of rigid heat conductors, together with its differential conse- quences, namely the higher-order system obtained by taking into account the time and space derivatives of the original system. We point out some mathematical properties of the differential consequences, with particular attention to the problem of the propagation of thermal perturbations with finite speed. We prove that, under an opportune choice of the initial conditions, a solution of the Cauchy problem for the system of differential consequences is also a solution of the Cauchy problem for the original system. We investigate the thermodynamic compatibility of the system at hand by applying a generalized Coleman–Noll procedure. On the example of a generalized Guyer–Krumhansl heat-transport model, we show that it is possible to get a hyperbolic system of evolution equations even when the state space is non-local.

scholarly journals Constitutive equations for heat conduction in nanosystems and nonequilibrium processes: an overview

2016 ◽  
Vol 7 (2) ◽  
pp. 196-222 ◽  
Author(s):  
David Jou ◽  
Vito Antonio Cimmelli
Keyword(s):  
Heat Conduction ◽  
Heat Transport ◽  
Constitutive Equations ◽  
Irreversible Thermodynamics ◽  
Nonequilibrium Processes ◽  
Extended Irreversible Thermodynamics ◽  
Equilibrium Processes ◽  
Far From Equilibrium ◽  
Conceptual Discussion

AbstractWe provide an overview on the problem of modeling heat transport at nanoscale and in far-from-equilibrium processes. A survey of recent results is summarized, and a conceptual discussion of them in the framework of Extended Irreversible Thermodynamics is developed.

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