scholarly journals Minimization of a free-energy-like potential for non-equilibrium flow systems at steady state

2010 ◽  
Vol 365 (1545) ◽  
pp. 1323-1331 ◽  
Author(s):  
Robert K. Niven
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Entropy Production ◽  
Equilibrium Thermodynamics ◽  
Turbulent Fluid Flow ◽  
System A ◽  
Flow Heat ◽  
Observed Behaviour ◽  
New Formulation ◽  
Non Equilibrium

This study examines a new formulation of non-equilibrium thermodynamics, which gives a conditional derivation of the ‘maximum entropy production’ (MEP) principle for flow and/or chemical reaction systems at steady state. The analysis uses a dimensionless potential function ϕ st for non-equilibrium systems, analogous to the free energy concept of equilibrium thermodynamics. Spontaneous reductions in ϕ st arise from increases in the ‘flux entropy’ of the system—a measure of the variability of the fluxes—or in the local entropy production; conditionally, depending on the behaviour of the flux entropy, the formulation reduces to the MEP principle. The inferred steady state is also shown to exhibit high variability in its instantaneous fluxes and rates, consistent with the observed behaviour of turbulent fluid flow, heat convection and biological systems; one consequence is the coexistence of energy producers and consumers in ecological systems. The different paths for attaining steady state are also classified.

scholarly journals Dissipated work, stability and the internal flow structure of granular snow avalanches

2005 ◽  
Vol 51 (172) ◽  
pp. 125-138 ◽  
Author(s):  
Perry Bartelt ◽  
Othmar Buser ◽  
Martin Kern
Keyword(s):  
Steady State ◽  
Entropy Production ◽  
Dissipative Systems ◽  
Momentum Balance ◽  
Granular System ◽  
Snow Avalanches ◽  
Equilibrium Thermodynamics ◽  
Layer System ◽  
Constitutive Parameters ◽  
Non Equilibrium

AbstractWe derive work dissipation functionals for granular snow avalanches flowing in simple shear. Our intent is to apply constructive theorems of non-equilibrium thermodynamics to the snow avalanche problem. Snow chute experiments show that a bi-layer system consisting of a non-yielded flow plug overriding a sheared fluidized layer can be used to model avalanche flow. We show that for this type of constitutive behaviour the dissipation functionals are minimum at steady state with respect to variations in internal velocity; however, the functionals must be constrained by subsidiary mass- continuity integrals before the equivalence of momentum balance and minimal work dissipation can be established. Constitutive models that do not satisfy this equivalence are henceforth excluded from our consideration. Fluctuations in plug and slip velocity depend on the roughness of the flow surface and viscosity of the granular system. We speculate that this property explains the transition from flowing avalanches to powder avalanches. Because the temperature can safely be assumed constant, we demonstrate within the context of non-equilibrium thermodynamics that granular snow avalanches are irreversible, dissipative systems, minimizing – in space – entropy production. Furthermore, entropy production is linear both near and far from steady-state non-equilibrium because of the mass-continuity constraint. Finally, we derive thermodynamic forces and conjugate fluxes as well as expressing the corresponding phenomenological Onsager coefficients in terms of the constitutive parameters.

scholarly journals Pitfalls of Exergy Analysis

2017 ◽  
Vol 42 (2) ◽  
Author(s):  
Petr Vágner ◽  
Michal Pavelka ◽  
František Maršík
Keyword(s):  
Fuel Cells ◽  
Steady State ◽  
Entropy Production ◽  
Exergy Analysis ◽  
Thermodynamic Optimization ◽  
Exergy Destruction ◽  
Equilibrium Thermodynamics ◽  
Useful Power ◽  
Non Equilibrium

AbstractThe well-known Gouy–Stodola theorem states that a device produces maximum useful power when working reversibly, that is with no entropy production inside the device. This statement then leads to a method of thermodynamic optimization based on entropy production minimization. Exergy destruction (difference between exergy of fuel and exhausts) is also given by entropy production inside the device. Therefore, assessing efficiency of a device by exergy analysis is also based on the Gouy–Stodola theorem. However, assumptions that had led to the Gouy–Stodola theorem are not satisfied in several optimization scenarios, e.g. non-isothermal steady-state fuel cells, where both entropy production minimization and exergy analysis should be used with caution. We demonstrate, using non-equilibrium thermodynamics, a few cases where entropy production minimization and exergy analysis should not be applied.

Local Entropy Production Rates in a Polymer Electrolyte Membrane Fuel Cell

2017 ◽  
Vol 42 (1) ◽  
pp. 1-30 ◽  
Author(s):  
Marc Siemer ◽  
Tobias Marquardt ◽  
Gerardo Valadez Huerta ◽  
Stephan Kabelac
Keyword(s):  
Fuel Cell ◽  
Entropy Production ◽  
Polymer Electrolyte ◽  
Polymer Electrolyte Membrane ◽  
Gas Diffusion ◽  
Transport Processes ◽  
Local Entropy ◽  
Equilibrium Thermodynamics ◽  
Electrolyte Membrane ◽  
Non Equilibrium

AbstractA modeling study on a polymer electrolyte membrane fuel cell by means of non-equilibrium thermodynamics is presented. The developed model considers a one-dimensional cell in steady-state operation. The temperature, concentration and electric potential profiles are calculated for every domain of the cell. While the gas diffusion and the catalyst layers are calculated with established classical modeling approaches, the transport processes in the membrane are calculated with the phenomenological equations as dictated by the non-equilibrium thermodynamics. This approach is especially instructive for the membrane as the coupled transport mechanisms are dominant. The needed phenomenological coefficients are approximated on the base of conventional transport coefficients. Knowing the fluxes and their intrinsic corresponding forces, the local entropy production rate is calculated. Accordingly, the different loss mechanisms can be detected and quantified, which is important for cell and stack optimization.

Modelling Dynamic Recovery and Recrystallization of Metals by a New Non-Equilibrium Thermodynamics Approach

2007 ◽  
Vol 558-559 ◽  
pp. 517-522
Author(s):  
Ming Xin Huang ◽  
Pedro E.J. Rivera-Díaz-del-Castillo ◽  
Sybrand van der Zwaag
Keyword(s):  
Steady State ◽  
High Temperature ◽  
Flow Stress ◽  
Dislocation Density ◽  
Dynamic Recovery ◽  
High Temperature Deformation ◽  
Temperature Deformation ◽  
Equilibrium Thermodynamics ◽  
Burgers Vector ◽  
Non Equilibrium

A non-equilibrium thermodynamics-based approach is proposed to predict the dislocation density and flow stress at the steady state of high temperature deformation. For a material undergoing dynamic recovery and recrystallization, it is found that the total dislocation density can be expressed as ( )2 ρ = λε& b , where ε& is the strain rate, b is the magnitude of the Burgers vector and λ is a dynamic recovery and recrystallization related parameter.

CRYSTAL GROWTH AND THE THERMODYNAMICS OF IRREVERSIBLE PROCESSES

1959 ◽  
Vol 37 (6) ◽  
pp. 739-754 ◽  
Author(s):  
J. S. Kirkaldy
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Entropy Production ◽  
Dendritic Growth ◽  
Transport Processes ◽  
Irreversible Processes ◽  
Interface Morphology ◽  
Crystal Face ◽  
Thermodynamics Of Irreversible Processes ◽  
Alloy Crystal

The principle of minimum rate of entropy production is applied to steady-state transport processes in the neighborhood of an alloy crystal face growing into its melt. The procedure gives a satisfactory rationale of observed interface morphology. It is noted that segregation, which occurs in cellular or dendritic growth of alloys, is a direct manifestation of the system's attempt to minimize entropy production by conserving free energy. The general problems of growth of pure and impure single crystals from the melt and vapor are discussed.

A cybernetic view on learning curves and energy policy

Kybernetes ◽  
2015 ◽  
Vol 44 (6/7) ◽  
pp. 852-865 ◽  
Author(s):  
Clas-Otto Wene
Keyword(s):  
Steady State ◽  
Learning Curve ◽  
Learning Curves ◽  
Learning System ◽  
Minimum Entropy ◽  
Equilibrium Thermodynamics ◽  
Content Type ◽  
Technology Learning ◽  
Minimum Entropy Production ◽  
Non Equilibrium

Purpose – The purpose of this paper is to demonstrate that cybernetic theory explains learning curves and sets the curves as legitimate and efficient tools for a pro-active energy technology policy. Design/methodology/approach – The learning system is a non-trivial machine that is kept in non-equilibrium steady state at minimum entropy production by competitive, equilibrium markets. The system has operational closure and the learning curve expresses its eigenbehaviour. This eigenbehaviour is analysed not in calendar time but in the characteristic time of the system, i.e., its eigentime. Measured in eigentime, the minimum entropy production in the steady-state learning system is constant. The double closure mechanism described by Heinz von Förster makes it possible for the learning system to change (adapt) its eigenbehaviour without compromising its operational closure. Findings – By obeying basic laws of second order cybernetics and of non-equilibrium thermodynamics the learning system self-organises its learning to follow an optimal path described by the learning curve. The learning rates are obtained through an operator formalism and the results explain observed distributions. Application to solar cell (photo-voltaic) modules indicates that the silicon scarcity bubble 2005-2008 produced excess entropy corresponding to costs of the order of 100 billion US dollars. Research limitations/implications – Grounding technology learning and learning curves in cybernetics and non-equilibrium thermodynamics open up new possibilities to understand technology shifts through radical innovations or paradigm changes. Practical implications – Learning curves are legitimate and efficient tools for energy policy and industrial strategy. Originality/value – Grounding of technology learning and learning curves in cybernetic and thermodynamic theory provides a stable theoretical basis for applications in industry and policy.

scholarly journals Analysis of Existing Thermodynamic Models of the Liquid Drop Deposited on the Substrate—A Sufficient Condition of the Minimum Free Energy of the System

Coatings ◽  
2019 ◽  
Vol 9 (12) ◽  
pp. 791
Author(s):  
Torbus ◽  
Dolata ◽  
Jakiela ◽  
Michalski
Keyword(s):  
Free Energy ◽  
Liquid Droplet ◽  
Minimum Free Energy ◽  
Solid Substrate ◽  
Negative Energy ◽  
Contact Angles ◽  
Equilibrium Thermodynamics ◽  
Three Phase ◽  
The Moment ◽  
Non Equilibrium

On the basis of the principles of non-equilibrium thermodynamics, the following condition was determined: necessary and sufficient for the occurrence of a minimum free energy of a liquid droplet deposited on a solid substrate in a gaseous environment in an isothermal and isochoric system. Only for positive values of the energy of three-phase tension line (shrinking the wetting circumference) for small and large contact angles can the system not reach this minimum. Without exceeding a certain free energy limit, it is not possible for the drop to spontaneously spread over the surface. For zero and negative energy of three-phase tension line (stretching the wetting circumference), the system can always reach a minimum of free energy. The developed equations allow determining the change of free energy occurring between any two stationary states when the droplet volume and physicochemical parameters characterizing energies at the interfaces are known. For a known set of such parameters, the equations allow determining the trajectory of free energy changes in the system as a function of the contact angle from the moment the drop comes into contact with the substrate. The application of the principles of non-equilibrium thermodynamics makes it possible to treat a real system as one in which the drops do not evaporate. However, the system has to be isothermal.

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