Showing papers in "Journal of Non-Equilibrium Thermodynamics in 1999"
TL;DR: In this article, the authors reviewed the state-of-the-art of finite time thermodynamic theory and applications from the point of view of both physics and engineering, focusing on the performance optimization of thermodynamic processes and devices with finite-time and/or finite-size constraints.
Abstract: Abstract The historical background, research development, and the state-of-the-art of finite time thermodynamic theory and applications are reviewed from the point of view of both physics and engineering. The emphasis is on the performance optimization of thermodynamic processes and devices with finite-time and/or finite-size constraints, including heat engines, refrigerators, heat pumps, chemical reactions and some other processes, with respect to the following aspects: the study of Newton's law systems, an analysis of the effect of heat resistance and other irreversible loss models on the performance, an analysis of the effect of heat reservoir models on the performance, as well as the application for real thermodynamic processes and devices. It is pointed out that the generalized thermodynamic optimization theory is the development direction of finite thermodynamics in the future.
716 citations
TL;DR: In this article, the performance of an isothermal combined-cycle chemical engine with mass leak was analyzed and the relation between the optimal power output and the maximum energy efficiency was derived.
Abstract: The performance of an isothermal combined-cycle chemical engine with mass leak is analyzed in this paper. The relation between optimal power output and ef®ciency, the maximum power output and the corresponding ef®ciency, as well as the maximum ef®ciency and the corresponding power output are derived.
28 citations
TL;DR: In this paper, a general optimal control framework for a difficult class of work maximization in endoreversible multistage processes which yield mechanical work with finite rates and are characterized by multiple (vectorial) efficiencies is developed.
Abstract: Abstract We develop a general optimal control framework for a difficult class of problems of work maximization in endoreversible multistage processes which yield mechanical work with finite rates and are characterized by multiple (vectorial) efficiencies. Bellman's method of dynamic programming is used either to construct his recurrence equation or to arrive at a discrete maximum principle of Pontryagin's type, in which a Hamiltonian is maximized with respect to controls. Both these algorithms are powerful computational tools which serve to maximize the power output and evaluate optimal controls. Equations of dynamics which follow from energy and matter balances and transfer equations are difference constraints for optimizing work. Irreversibilities caused by the energy and mass transport are essential. Variation of efficiencies is analyzed in terms of heat and mass fluxes as natural control variables. Enhanced bounds for the work released from an engine system or added to a heat-pump system are evaluated. Lagrangians and Hamiltonians of work functionals and discrete canonical equations are effective; they reach their continuous counterparts in the limit of an infinite number of stages. For a finite-time passage of a resource fluid between two given thermodynamic states, an optimal process is shown to be irreversible. Its optimal intensity is characterized well by the Hamiltonian H. Characteristic functions which describe extremal work are found numerically in terms of final states, process duration and number of stages. An extension of classical exergy to nonisothermal separation systems with a finite number of stages and finite holdup time of the resource fluid is one of the main results. This extended exergy simplifies to the classical thermal exergy in the limit of infinite duration and an infinite number of stages. The extended exergy exhibits a hysteretic property as a decrease of maximum work received from a multistage engine system and an increase of minimum work added to a heat-pump system, two properties which are particularly important in high-rate regimes. This work is a significant step towards a realistic theory of nonisothermal chemical engines.
25 citations
TL;DR: In this paper, the authors examined the problem of energy-efficient production in an industrial process and showed that a distribution, that equipartitions the derivative of the local entropy production rate with respect to the local production, minimizes the entropy production.
Abstract: We examine the problem of energy-efficient production in an industrial process. By energy-efficient we mean minimum entropy production. We use the possibility to redistribute the production in different times or parts of the system for a given total production, and show that a distribution, that equipartitions the derivative of the local entropy production rate with respect to the local production, minimizes the entropy production. Equipartition in time implies stationary state production. Equipartition in space implies production for a given position independent force. The same constant derivative of the local entropy production rate is found if ones optimizes the production for a given total entropy production. Close of equilibrium the equipartition condition is found to reduce to the isoforce principle. Further from equilibrium, this reduction is extended to a whole class of nonlinear flux-force relations. We show that, when one increases the total production, the entropy production per unit produced starts to increase linearly, as a function of this total production. It is shown which process conditions give an optimum path with an equipartition of the entropy production rate. How this relates to the isoforce principle is discussed. In general constraints on process conditions restrict the freedom to optimize, and therefore make it impossible to realise the most favorable conditions. The importance of the Onsager relations for the systematic description of the optimization is discussed.
23 citations
TL;DR: In this article, simple upper bound formulae for the efficiency of converting the energy of thermal radiation into mechanical work are derived, which refer to a large class of systems and are simple as they are functions of two parameters only, namely the temperatures of the energy sources.
Abstract: Abstract Simple upper bound formulae for the efficiency of converting the energy of thermal radiation into mechanical work are derived. They are upper bounds as they refer to a large class of systems. They are simple as they are functions of two parameters only, namely the temperatures of the energy sources. The original contributions are as follow: (1) Two sorts of “cold” thermal reservoirs are considered. (2) An endoreversible thermal engine is used here to convert radiation energy into work. A number of existing theories are particular cases of the present approach.
15 citations
TL;DR: In this article, the minimum free energy for a rigid dielectric with linear memory was given in terms of the Fourier transform of the variables, i.e., the minimum energy was defined as the squared of a norm in a suitable space of variables.
Abstract: The minimum free energy for a rigid dielectric with linear memory is found under isothermal conditions. The resulting expression is given in the frequency domain, i.e. in terms of the Fourier transform of the variables. By means of such a thermodynamic potential and of the ClausiusDuhem inequality an explicit formula of the dissipation is obtained. Thus the minimum free energy restores the customary relation between the dissipativity and the Clausius-Duhem inequality, that had been proved to fail when memory effects occur. Finally, by virtue of some properties of its, the minimum free energy is viewed as the squared of a norm in a suitable space of the variables.
12 citations
TL;DR: In this paper, the Soret coefficient of the binary liquid systems: benzene+nhexane, toluene +nheptane, and carbon tetrachloride with heptane and hexane, was measured with the thermogravitational method.
Abstract: Abstract We have measured with the thermogravitational method the Soret coefficient of the binary liquid systems: benzene+nhexane, toluene+nheptane and carbon tetrachloride with heptane and hexane, in a well characterized column used in a previous work to measure the systems benzene+nheptane and toluene+nhexane. The obtained results show that the Soret coefficient takes nearly the same value in the mixtures of each one of the components, benzene, toluene or carbon tetrachloride with hexane and heptane. For all the systems considered it varies slowly with the concentration and is nearly independent of temperature. The higher values of the thermal diffusion factor correspond to mixtures containing carbon tetrachloride. Previous results for these systems were obtained in an imperfect apparatus and must be disregarded.
11 citations
TL;DR: In this article, the validity of double layer compression as the mechanism which governs the stability of a nonaqueous suspension has been checked and another stability mechanism is claimed, based on positively charged polystyrene latexes.
Abstract: Abstract The validity of the double layer compression as the mechanism which governs the stability of a non-aqueous suspension has been checked. Positively charged polystyrene latexes have been used as model colloids. Another stability mechanism is claimed.
10 citations
TL;DR: In this paper, two versions of Clausius inequality for open discrete systems are derived, one formulated for the non-equilibrium system itself using contact quantities, the other one using equilibrium quantities belonging to the system's environment.
Abstract: Abstract We derive two versions of Clausius inequality for open discrete systems, one formulated for the non-equilibrium system itself using contact quantities, the other one using equilibrium quantities belongs to the system's environment. Consequently, Bhalekar's conjecture that there is no Clausius inequality for open systems is disproved.
9 citations
TL;DR: In this article, a general form for diagonal approximations is derived, which accounts for the requirement imposed by the special structure of the Stefan-Maxwell equation that such approximation be constructed in a reduced-dimensional subspace.
Abstract: Mass diffusion in multicomponent gas mixtures is governed by a coupled system of linear equations for the diffusive mass fluxes in terms of thermodynamic driving forces, known as the generalized Stefan‐Maxwell equation. In computations of mass diffusion in multicomponent gas mixtures, this coupling between the different components results in considerable computational overhead. Consequently, simplified diffusion models for the diffusive mass fluxes as explicit functions of the driving forces are an attractive alternative. These models can be interpreted as an approximate solution to the Stefan‐Maxwell equation. Simplified diffusion models require the specification of ‘‘effective’’ diffusion coefficients which are usually expressed as functions of the binary diffusion coefficients of each species pair in the mixture. Current models for the effective diffusion coefficients are incapable of providing a priori control over the error incurred in the approximate solution. In this paper a general form for diagonal approximations is derived, which accounts for the requirement imposed by the special structure of the Stefan‐Maxwell equation that such approximations be constructed in a reduced-dimensional subspace. In addition, it is shown that current models can be expressed as particular cases of two general forms, but not all these models correspond to the general form for diagonal approximations. A new minimum error diagonal approximation (MEDA) model is proposed, based on the criterion that the diagonal approximation minimize the error in the species velocities. Analytic expressions are derived for the MEDA model’s effective diffusion coefficients based on this criterion. These effective diffusion coefficients automatically give the correct solution in two important limiting cases: for that of a binary mixture, and for the case of arbitrary number of components with identical binary diffusivities. Although these minimum error effective diffusion coefficients are more expensive to compute than existing ones, the approximation will still be cheaper than computing the exact Stefan‐Maxwell solution, while at the same time being more accurate than any other diagonal approximation. Furthermore, while the minimum error effective diffusion coefficients in this work are derived for bulk
8 citations
TL;DR: In this article, it was shown that there is a mathematical equivalence between the formulation of an extended thermodynamic theory with several fields where a relaxation time is successively set equal to zero and the direct formulation of a theory with a reduced number of independent fields, where a constitutive relation is postulated for the eliminated field.
Abstract: Abstract In this work it is rigorously shown that, even in the presence of highly nonlinear phenomena, provided that they belong to the thermodynamic branch, there is mathematical equivalence between the formulation of an extended thermodynamic theory with several fields where a relaxation time is successively set equal to zero and the direct formulation of a theory with a reduced number of independent fields where a constitutive relation is postulated for the eliminated field. This result is obtained as a consequence of the fact that for vanishing relaxation times of these fields the corresponding intrinsic Lagrange multipliers in the Liu procedure of Extended Thermodynamics also vanish, and of the fact that these multipliers can be chosen, together with the velocity, as global variables in Extended Thermodynamics.
TL;DR: In this paper, a novel kinetic phase diagrams for homogeneous nucleation during nun-equilibrium solidification of Ag-Cu alloys were evolved by stochastic modelling. But the calculated values were found to lie within the thermodynamically permissible limits determined through construction of non-isothermal metastability held diagrams.
Abstract: Novel kinetic phase diagrams for homogeneous nucleation during nun-equilibrium solidification of Ag-Cu alloys were evolved by stochastic modelling. The allowable undercoolings and the composition of the primary nucleating phase at any cooling rate and liquid composition could be read from these diagrams, The calculated values were found to lie within the thermodynamically permissible limits determined through construction of non-isothermal metastability held diagrams.
TL;DR: In this paper, the authors use an irreversible thermodynamics approach to derive hydrodynamic equations which govern the flow-induced concentration changes produced by inhomogeneous stresses in a viscoelastic binary mixture.
Abstract: Abstract We use an irreversible thermodynamics approach to derive hydrodynamic equations which govern the flow-induced concentration changes produced by inhomogeneous stresses in a viscoelastic binary mixture. The most relevant effects arising from these inhomogeneous flows are manifested in the migration of the dispersed phase and as flow-induced concentration fluctuations. Coupled constitutive equations for the mass flux and the stress tensor are derived self-consistently from our formalism. We show that our approach is consistent with different existing isothermal formalisms which predict the growth of concentration fluctuations and shear-induced diffusion of mass. Finally, we also comment on the possibility of extending our approach to incorporate nonisothermal effects and on the limitations and advantages of our description.
TL;DR: In this paper, a double-membrane system with boundary layer and membrane cell with horizontally mounted membranes has been studied and the validity of the model has been checked in the case of binary and ternary solutions.
Abstract: Abstract Non-equilibrium thermodynamic model equations describing transport properties of non-ionic and heterogeneous n-component solutions have been studied in a double-membrane system. The system is composed of two complexes: boundary layer/membrane/boundary layer. Definitions of hydraulic permeability (L̄ p), reflection (σ̄ *) and diffusive permeability (Ω̄) coefficients of the double-membrane system and relations between the coefficients of the double-membrane system (L̄ p, σ̄ *, Ω̄) and the respective quantities of the single membranes of the system (L p, σ*, Ω) are given. The validity of the model has been checked in the case of binary and ternary solutions, using a membrane cell with horizontally mounted membranes. The diffusive permeability and reflection coefficients were determined as functions of solution concentration and gravitational configuration.
TL;DR: The long term stability of open dissipative systems in either cyclic processes or in stationary states is due to their ability to export their surplus of entropy as mentioned in this paper, which is illustrated by selected examples from energy and environmental engineering, biology and global ecology.
Abstract: Abstract In ecology, economy and also in technology we are dealing with open dissipative systems. The long term stability of such systems in either cyclic processes or in stationary states is due to their ability to export their surplus of entropy. For this process valuable low entropy resources are consumed and transformed into waste. This mechanism determines to a large extent the efficiency of open dissipative systems. This is illustrated by selected examples from energy and environmental engineering, biology and global ecology.
TL;DR: In this article, it is shown how one can derive the impedance of a polarized electrode surface from irreversible thermodynamics, and a Nyquist diagram for the case that the electrode conducts by electrons only, and the electrolyte conducts by oxygen ions or vacancies.
Abstract: It is shown how one can derive the impedance of a polarized electrode surface from irreversible thermodynamics. The oxygen electrode is studied as an example. A Nyquist diagram is constructed for the case that the electrode conducts by electrons only, and the electrolyte conducts by oxygen ions or vacancies. The electrode surface contributes to the diagram with two semi-circles. One semi-circle is due to production of dipoles from adsorbed oxygen atoms. The other is due to the dipole moment of the ion-electron hole pair.
TL;DR: In this article, a numerical modeling of solute transport in non-saturated and non-isothermal porous media is dealt with by thermodynamics of irreversible processes, which enables us to consider the different kinds of transfer and the coupling, and every physical phenomenon as water phase transition and solute adsorption by the solid matrix can be taken into account.
Abstract: Abstract Modeling of solute transport in non-saturated and non-isothermal porous media is dealt with by thermodynamics of irreversible processes. This rigorous approach enables us to consider the different kinds of transfer and the coupling. Every physical phenomenon as water phase transition and solute adsorption by the solid matrix can be taken into account. The final model may be applied to several fields such as civil engineering, agronomy, pollution and the assessment of radioactive waste repositories. A numerical modeling taking into account the effect of temperature gradient on solute transport (“Soret effect”) is in the process of implementation in the French software “CESAR-LCPC” of the “Laboratoire Central des Ponts et Chaussées”.
TL;DR: In this article, the authors derived constitutive relations for the evolution of specific volume and specific enthalpy in amorphous glassy polymers after thermal treatment, and derived a nonlinear partial differential equation for the probability density of free volume.
Abstract: Abstract Constitutive relations are derived for the evolution of specific volume and specific enthalpy in amorphous glassy polymers after thermal treatment. The Robertson approach is extended to infinite ensembles of cells, and a nonlinear partial differential equation is developed for the probability density of free volume. This equation is resolved explicitly under plausible assumptions, whose validity is verified by comparison with observations for polystyrene. As a result, two ordinary differential equations are obtained for the excess specific volume and the excess specific enthalpy, which provide a molecular basis for the Kovacs phenomenological relations. It is demonstrated that in one-step thermal tests, the rate of change in the specific enthalpy exceeds by twice that for the specific volume. This conclusion is confirmed by experimental data for polycarbonate and polystyrene.
TL;DR: In this paper, the relation between local and global thermodynamic stability is analyzed in a simple system and shown how the global stability can be understood in terms of the structures existent in the local dynamics.
Abstract: Abstract We analyze in a simple system the relation between local and global thermodynamic stability. This example shows how the global stability can be understood in terms of the structures existent in the local dynamics.
TL;DR: In this paper, a brief analysis of the classical derivation of the continuity equation in general relativity is presented, and the consequences of the equation obtained are reviewed and compared with similar results related with the conservation of particles (baryons and leptons).
Abstract: Abstract A brief analysis of the classical derivation of the continuity equation in general relativity is presented. The consequences of the equation obtained are reviewed and compared with similar results related with the conservation of particles (baryons and leptons). Emphasis is made on the fact that different transport equations may be derived from the possible choices of the mass balance equation in non-equilibrium formalisms. Nevertheless, the continuity equation is not at odds with the notion of particle conservation.
TL;DR: In this article, the authors present an application of Linear Irreversible Thermodynamics to the problem of diffusion among miscible incompressible fluids, assuming that the mixture density is a function of the volume fractions.
Abstract: Abstract In this work we present an application of Linear Irreversible Thermodynamics to the problem of diffusion among miscible incompressible fluids. First, we suppose that the mixture density is a function of the volume fractions. This hypothesis allows us to reformulate the interface diffusion problem in terms of transport equations for the concentrations or the mass-volume fractions, the momentum balance equations for the diffusion flux and the energy balance equations for the relative internal energies, respectively. The transport equations so obtained are generalized equations of the classical diffusion equations obtained by means of fluctuating hydrodynamics and the H model of critical dynamics. Afterwards we apply linear irreversible thermodynamics in order to get the entropy production and then assume a linear relation between fluxes and forces, obtaining the constitutive equations for the diffusion flux, the heat flux, the stress tensor for each component. Finally, from this choice we compare our results with those originated from fluctuating hydrodynamics and continuum theory. We also show that the constitutive equation for diffusion flux is a Maxwell-Cattaneo's type relaxation equation and therefore a generalization of Fick's law. Also the stress tensor constitutive equation generalizes the Korteweg de Vries stress tensor equations and we present how to arrive at a telegrapher type hyperbolic equation for the concentrations or the mass-volume fractions.
TL;DR: In this paper, a phenomenological theory for a polarizable and magnetizable plasma in an electromagnetic field is proposed within the framework of Extended Irreversible Thermodynamics (EIT) and the dispersion relation for plane weak electromagnetic disturbances is derived.
Abstract: Abstract Within the framework of Extended Irreversible Thermodynamics (EIT) a phenomenological theory is proposed for a polarizable and magnetizable plasma in an electromagnetic field. In particular, for the polarization a transport equation is proposed generalizing the well-established Debye's law for dielectric relaxation. For the magnetization a transport equation is proposed generalizing the well-established Langevin's law for magnetic relaxation. The present equations correspond to those obtained by Dixon involving also coupling terms with the heat flux. Finally, in the special case in which cross-effects are not taken into account, the dispersion relation for plane weak electromagnetic disturbances is derived.
TL;DR: In this article, the problem of phonon transport, referring to heat conduction in the micro-scale regime, is formulated in terms of the displacements of atoms from their equilibrium positions.
Abstract: Abstract Consideration is given to a microscale structure consisting of a thin porous medium filled with interstitial Ouid or a microscale regime with binary species of atoms. An example is a cellular membrane. This paper treats a one-dimensional model consisting of atoms of heavier mass M alternating with atoms of lighter mass m arranged in a series. Like photons, elastic vibrations of atoms or phonons propagate as waves. The problem of phonon transport, referring to heat conduction in the microscale regime, is formulated in terms of the displacements of atoms from their equilibrium positions. With the displacements treated as a wave motion, the frequency-wave number relationship for the heterogeneous-atomic membrane is obtained. Two modes of wave transport are obtained and their roles in phonon transport are discussed.