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Warsaw University of Technology
Faculty of Chemical and Process Engineering
Warsaw, Poland
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The present volume responds to the need for a synthesizing book that throws light upon extensive fields of thermodynamics and entropy theory from the engineering perspective and applies basic ideas and results of these fields in engineering problems. The book is, in brief, a collection of reviews synthesizing important achievements of applied nonequilibrium thermodynamics in some important branches of mechanical, chemical, and biochemical engineering with a few excursions into environmental engineering.
Contemporary applications of thermodynamics, both reversible and irreversible, are broad and diverse. The range of thermodynamic applications is expanding and new areas finding a use for the theory are continually emerging. One of the main goals of this book is to outline the achievements in applied thermodynamics (both equilibrium and nonequilibrium) obtained within the recent 50 years. This goal is very broad since thermodynamics serves currently as a formal and substantive theory in applications involving analyses of physical, chemical, biological, and even economical systems. Dealing with such a broad goal within a single limited volume requires necessary elimination of many attractive mathematical aspects; consequently the book exploits the power of mathematical analysis to a lesser extent than many more specialized while narrower texts. Yet, this disadvantage is compensated by a vast literature analysis, which is a strong asset of the book to serve as a comprehensive reference text.
Let us shortly discuss several basic topics, most of which are analyzed in the present book. Thermodynamics provides theoretical tools to exclude improper kinetic equations or to improve empirical kinetic formulas. It may furnish thermodynamic equilibrium metrics and its disequilibrium extensions to measure a thermodynamic length. It may also help to describe reversible and irreversible dynamics in terms of energy-type Hamiltonians or related Lagrangians. The use of disequilibrium entropies serves to develop a wave theory of heat and mass transfer, applied to overcome the well-known paradox of infinite propagation speeds of thermal and material disturbances, implied by classical parabolic equations. Advanced thermodynamics can provide unifying theoretical framework for both classical and anomalous diffusion. The latter is usually treated by applying Tsallis’s (1988) theory for a generalized definition of entropy, consistent with both thermodynamics and statistical mechanics. Applied
in a chemical context, thermodynamics provides substantiation for the kinetic law of mass action consistent with suitable chemical resistance, a quantity useful in the analysis of chemical networks.
In fact, both classical and nonequilibrium thermodynamics predict the global stability of the thermodynamic equilibrium. However, for disequilibrium singular points and distributed steady states, sufficient stability conditions cannot be formulated in terms of entropy or other thermodynamic potentials, although, occasionally, some excess thermodynamic or quasi-thermodynamic potential can prove their utility as stability criteria (Lapunov functions).
The problem of thermodynamic stability criteria in disequilibrium systems has not yet been completely solved, despite extensive research in this area. Without doubt, thermodynamics may establish exact stability criteria for system trajectories approaching an equilibrium singular point. In this case one may apply the negative excess entropy W = Seq – S as a Lapunov functional for which the entropy density ρs is the same function of the thermodynamic state as prescribed by classical thermodynamics (local equilibrium assumption). Invoking the local form of the second law σ > 0 one obtains in the gradient-less case the conditions dW/dt < 0, which proves the stability of all system trajectories approaching the equilibrium singular point. This means that thermodynamics ensures the global stability of the thermodynamic equilibrium (Tarbell, 1982).
A practical question can be asked: In what sense can it be said that the distribution of the driving forces in one industrial configuration is better than in another? To answer this question realistic engineering examples, involving heat exchangers, plate distillation columns, chromatographic separators, etc., may be analyzed. When “a duty” (useful effect) for a process is defined, the following equipartition principle for the entropy production is advanced: “for a given duty, the best configuration of the process is that in which the entropy production rate is most uniformly distributed” (Tondeur and Kvaalen, 1987). A generalization of the principle may also be proposed for systems with a distributed design variable: “the optimal distribution of an investment is such that the investment in each element is equal to the cost of the energy degradation in this element”. Thus a uniform distribution of the ratio of these two quantities should be preserved. These results show the importance of irreversibility analysis in design.
Thermodynamics may help to predict selling prices and develop paraeconomic analyses and balances which involve unit exergies as measures of unit economic values. Interestingly, thermodynamics and especially exergy theory may be applied to define the so-called proecological tax, the quantity replacing actual personal taxes. A practical field related to thermodynamics is thermoeconomics. It defines the physical–mathematical background for energy–economic–ecological analyses which are made in different fields of knowledge. In this field the concept of exergetic cost is employed (Valero et al., 1994a,b); this is a concept close to that of embodied energy or cumulative exergy consumption (Szargut et al., 1988). The analysis of the exergetic cost focuses rigorously on the process of cost formation.
• alternative and unconventional energy sources (graduate)
• stability of chemical reactions and transport processes (graduate)
• thermoeconomics of solar energy conversion (graduate)
The content organization of the book is as follows. Chapters: Contemporary Thermodynamics for Engineering Systems and Variational Approaches to Nonequilibrium Thermodynamics outline main approaches and results obtained in applied disequilibrium thermodynamics, focusing on the methods and examples considered in the whole book. Chapter: Wave Equations of Heat and Mass Transfer shows the role of thermodynamics in setting a simple theory of wave equations for heat and mass transfer. Chapter: Classical and Anomalous Diffusion describes the significance of Tsallis’s (1988) theory for a generalized definition of entropy in the development of the generalized theory of diffusion, which includes diffusive phenomena, both classical and anomalous. Chapter: Thermodynamic Lapunov Functions and Stability displays some stability problems and related Lapunov’s functions derived from thermodynamics. Chapter: Analyzing Drying Operations on Thermodynamic Diagrams presents drying operations with granular solids on thermodynamic diagrams. Chapter: Frictional Fluid Flow through Inhomogeneous Porous Bed describes basic aspects of frictional fluid flow through both inhomogeneous and anisotropic porous media in which fluid streamlines are curved by a location dependent hydraulic conductivity. Chapter: Thermodynamics and Optimization of Practical Processes exposes the role of thermodynamics in optimization of applied processes undergoing in nonreacting systems. Chapter: Thermodynamic Controls in Chemical Reactors extends the related control ideas and results to chemical reactors. Chapter: Power Limits in Thermochemical Units, Fuel Cells, and Separation Systems offers a generalized treatment of power limits in various thermochemical engines, fuel cells, and separation systems. Chapter: Thermodynamic Aspects of Engineering Biosystems considers some basic thermodynamic properties of engineering biosystems. Chapter: Multiphase Flow Systems presents valuable selected results for multiphase flow systems, whereas Chapter: Radiation and Solar Systems—some recent results for applied radiation and solar systems. Chapter entitled Appendix: A Causal Theory of Hydrodynamics and Heat Transfer constitutes a supplementary text which shows the role of entropy four-flux in the dissipative relativistic phenomena and variety of disequilibrium temperatures obtained within a causal approach to hydrodynamics and heat transfer.
The author expresses his gratitude to the Polish Committee of National Research (KBN) and the Ministry of National Education of Poland under whose auspices a considerable part of his own research discussed in the book was performed in the framework of two grants: grant 3 T09C 02426 (Nonequilibrium thermodynamics and optimization of chemical reactions in physical and biological systems) and grant N N208 019434 (Thermodynamics and optimization of chemical and electrochemical energy generators and the related applications to fuel cells). A critical part of writing any book is the process of reviewing, thus the authors are very much obliged to the researchers who patiently helped them read through subsequent chapters and who made valuable suggestions. In preparing this volume the authors received help and guidance from Viorel Badescu (Polytechnic University of Bucharest, Romania), Ferenc Markus (Budapest University of Technology and Economics, Hungary), Alina Jeżowska (Rzeszów University of Technology, Poland), Andrzej B. Jarzębski (Institute of Chemical Engineering of Polish Academy of Science, and Faculty of Chemistry at the Silesian University of Technology, Gliwice), Lingen Chen (Naval University of Engineering, Wuhan, P. R. China), Piotr Kuran, Artur Poświata, and Zbigniew Szwast (Faculty of Chemical and Process Engineering at the Warsaw University of Technology), Elżbieta Sieniutycz (University of Warsaw), Anatolij M. Tsirlin (System Analysis Research Center, Pereslavl-Zalessky, Russia), and Anita Koch (Elsevier). We also acknowledge the scientific cooperation of many colleagues of the Institute of Fluid Flow Machinery in Gdańsk, Poland, the former Publisher of Archives of Thermodynamics. Finally, appreciations also go to the whole book’s production team in Elsevier for their cooperation, help, patience, and courtesy.
Stanisław Sieniutycz Warszawa, August 2015
We begin with some information about the nature of thermodynamics as a macroscopic theory and then describe basic concepts and definitions in thermodynamics. Thermodynamics is a science that includes the study of energy transformations and relationships among the physical properties of substances that are affected by these transformations. The properties which really sets thermodynamics apart from other sciences are energy transformations through heat and work. It is clear that the aforementioned definition is broad and vague, and that various users will apply in their work different aspects of the thermodynamic theory. Chemical engineers typically focus on phase equilibria, stoichiometry, chemical reactions, catalysis, and so forth. Mechanical engineers are more interested in power generators, fuel cells, refrigeration devices, and nuclear reactors. Both users can apply in their research some common methods, such as optimal control theory thus contributing to the field called thermodynamic optimization.
Thermodynamic properties can be determined by studying either macroscopic or microscopic behavior of matter. Classical thermodynamics treats matter as a continuum and studies the macroscopic behavior of matter. Statistical thermodynamics investigates the statistical behavior of large groups of individual particles. It postulates that observed physical property (eg, temperature T, pressure P, energy E, etc.) is equal to the appropriate statistical average of a large number of particles. For a statistical theory of disequilibrium systems, see, for example, Kreuzer (1981). Thermodynamics is based upon experimental observation of macroscopic systems. Its power and beauty follows from a basic property of macrosystems composed of sufficiently large number of particles. Namely, as a consequence of the law of large numbers, these macrosystems can be described well (modulo to fluctuations) in terms of only several variables, for example, temperature, pressure and mole numbers.
Conclusions stemming from observations have been cast as postulates or laws. The study of thermodynamics considers five laws or postulates. Two of them deal with energy transformation and three deal with the physical properties.
Thermodynamic
3. State of a system
State, by definition, is a characteristic of a system. There are several types of states:
a. Thermodynamic state is the condition of the system as characterized by the values of its properties.
b. Stable equilibrium state is a state in which the system is not capable of finite spontaneous change to another state without a change in the state of the surroundings. Several types of equilibrium must be fulfilled: thermal, mechanical, phase, and chemical.
c. State postulate: The equilibrium state of a simple closed system can be completely characterized by two independent variables and the masses of the species within the system.
4. Thermodynamic process
A thermodynamic process is a transformation from one equilibrium state to another.
a. Quasistatic process is a process where every intermediate state is a stable equilibrium state.
b. Reversible process is one in which a second process could be performed so that the system and surroundings can be restored to their initial states with no change in the system or surroundings.
The following remarks can be made at this point. Reversible processes are quasistatic, but quasi-static processes are not necessarily reversible. A quasistatic process in a simple system is also reversible. Some factors which render processes irreversible are friction, unrestrained expansion of gasses, heat transfer through a finite temperature difference, mixing, chemical reaction, and so forth.
5. Thermodynamic path
Thermodynamic path is the specification of a series of states through which a system passes in a process. Various paths can be specified, such as: isothermal, ∆T = 0; isobaric, ∆P = 0; adiabatic, ∆Q = 0; polytropic, PVk = constant; isochoric, ∆V = 0; isentropic, ∆S = 0 (adiabatic and reversible); isenthalpic, ∆H = 0 (adiabatic and entirely irreversible, as in the throttling process). Path calculations usually involve the knowledge of the properties of gases and liquids (Reid et al., 1987).
6. Heat engines, refrigerators and HPs
Work may be converted to heat directly and completely, but converting heat to work requires the use of a special device called a heat engine. Heat engines may vary considerably from one another, but share the following characteristics: They operate on a cycle, they receive the driving heat from a high temperature source, they convert part of this heat to work, they reject the remaining waste heat to a low-temperature sink.
The work-generating device that fits the definition of a heat engine is the steam power plant, Fig. 1.1. The fraction of the heat input that is converted to network output is a measure of the performance of a heat engine, and is called the thermal efficiency. Most heat engines possess poor thermal efficiencies, with more than one half of the thermal energy supplied to the working fluid ending up in the environment (Naragchi, 2013).
borderline between classical and irreversible thermodynamics. Attention also should be paid to a concise and exact review of the theory and applications of classical thermodynamics and its relation to nonequilibrium theories (Mikielewicz, 1997, 2001).
7. Irreversible phenomena
The laws of irreversible evolution of macroscopic systems belong to the fundamental problems of contemporary science and engineering. They receive attention in a great number of papers in scientific journals with the topics ranging from the extensions and generalizations of the classical theory to diverse applications in fluid mechanics (Newtonian and non-Newtonian), heat and mass transfer, chemistry, electrochemistry, membrane technology, energy conversion, systems theory, biophysics, and so forth.
Entropy source or the amount of the entropy generated in the unit volume per unit time is the basic quantity characterizing the irreversibility in a continuum. In principle, the structure of the nonequilibrium thermodynamic theory can be analyzed in two ways.
The first (most popular) approach is based on the derivation of the entropy source by combining the conservation or balance laws and the Gibbs’ equation. This combining can be applied in the framework of either classical or extended thermodynamics, provided that a generalized form of the Gibbs’ equation is used in the extended case. The first approach is analyzed further on in this chapter. The first approach is well known, and it has been presented in detail in many books (Prigogine, 1947; Haase, 1969; Baranowski, 1974; Kestin, 1979; de Groot and Mazur, 1984; Keizer, 1987a, and many others). In particular, Kestin (1979, 1993) developed the theory of internal variables in the local equilibrium approximation, Kestin and Bataille (1980) set the thermodynamics of solids, and Kestin and Rice (1970) have described a number of paradoxes in the application of thermodynamics to strained solids. They gave an outline of a general method of the local state which allows us to extend our knowledge of uniform systems to include continuous systems. They paid particular attention to plastic deformation and to strain hardening, and concluded that the relation between the stress and the plastic strain rate does not seem to come within the scope of Onsager’s relations restricted to the small departures from the equilibrium. Muschik and Brunk (1977) defined a thermodynamic analogue of the temperature by the vanishing heat exchange between a nonequilibrium system and the heat reservoir. Properties of this analogue called contact temperature were discussed and illustrated graphically. Muschik and Papenfuss (1993) developed an evolution criterion of nonequilibrium thermodynamics and show its application to liquid crystals. Muschik et al. (2001) gave a sketch of continuum thermodynamics. Muschik and Restuccia (2002) demonstrated that in general constitutive equations depend on the motion of the material with respect to a chosen frame of reference. Despite this dependence of motion, the constitutive equations are isotropic functions on the state space. Muschik (2008) surveyed a number of branches of thermodynamics and proposed a classification of thermodynamic schools.
efficiencies of real heat engines. Chen and Sun (2004) review advances in FTT in the context of system’s analysis and optimization. Chen (2005) reviews achievements of FTT of irreversible processes and cycles. Bracco and Siri (2010) give an example of exergetic optimization of gas–steam power plants considering different objective functions.
Considering adiabatic processes in monoatomic gases, Carrera-Patino (1988) applies a kinetic model to predict the temperature evolution of a monatomic ideal gas undergoing an adiabatic expansion or compression at a constant finite rate, and it is then generalized to treat real gases. The effects of interatomic forces are considered, using as examples the gas with the square–well potential and the van der Waals gas. The model is integrated into a Carnot cycle operating at a finite rate to compare the efficiency’s rate–dependent behavior with the reversible result. Limitations of the model, rate penalties, and their importance are evaluated. Efficiency of the finite-rate process is expressed in the form η = ηC ∆, where ∆ is the correction retated to the finite rate. For a Carnot cycle operating with the piston velocity 20m/s, the efficiency of the cycle follows as 56% of the Carnot efficiency. This clearly shows the decreasing effect of the finite rate on the thermodynamic efficiency. This is the significant paper that introduces the effects of FTT by statistical approaches.
In FTT (Berry et al., 2000; Feidt, 1999), which served the present author as the topic for the complementary books (Sieniutycz and Jeżowski, 2009, 2013), extremal solutions for control thermodynamic processes constitute usually the main task of a mathematical analysis. In that case, extremum conditions lead to important in-principle limits (bounds) for control processes occurring in finite time and in systems of a finite size. The related analyses can lead to improved design for thermodynamic processes in engineering systems ranging from heat engines (Andresen et al., 1984; Andresen, 1983) to chemical plants (Månsson and Andresen, 1985; Månsson, 1985). Many other optimization problems set and solved within the FTT are discussed in chapter: Thermodynamics and Optimization of Practical Processes.
Modern approaches involving extremum problems such as the maximum entropy formalism (Jaynes, 1957, 1963; Ingarden and Urbanik, 1962; Levine and Tribus, 1979; Jaworski, 1981; Grandy, 1983, 1988; Karkheck, 1986, 1989; Nettleton and Freidkin, 1989), thermodynamic geometry and related metric ideas (Ingarden, 1982; Weinhold, 1975, 1976; Ruppeiner, 1979; Nulton and Salamon, 1985; Sieniutycz and Berry, 1991), minimum entropy production theorems (Prigogine, 1947, 1949; Glansdorff and Prigogine, 1971; Essex, 1984; Salamon et al., 1980; Sieniutycz, 1980, 1994, 1997), and various macroscopic variational principles for heat conduction, hydrodynamics and thermohydrodynamics (Serrin, 1959; Biot, 1970; Bhattacharya, 1982; Caviglia, 1988; Muschik and Trostel, 1983; Markus and Gambar, 1991; Gambar and Mąrkus, 1994; 2003; Gambar et al., 1991; Nyiri, 1991; Van and Nyiri, 1999; Vázquez et al., 2009; Finlayson, 1972; Farkas et al., 2005; Kupershmidt, 1990, 1992; Lebon, 1976, 1986; Mornev and Aliev, 1995; Schechter, 1967; Schmid, 1970a, b; Seliger and Whitham, 1968;
Salmon, 1987a, b; Shiner and Sieniutycz, 1994; Shiner et al., 1996; Sieniutycz, 1977, 1979, 1980, 1982, 1983, 1984a, b, 1985, 1986, 1987a, b, 1988a, b, 1990, 1992a, b, 1994, 1995, 1997, 2000f, 2001d, f, 2002b) can lead to general results. In particular, significant progress has been achieved in extremum approaches to dynamic analysis of various thermal, hydrodynamic, radiative and porous systems (Markus and Gambar, 1991; Gambar and Markus, 1994; Salmon, 1987a; Essex, 1984; Sieniutycz, 2007a, 2008c). The essential role of action-type variables in the field theories of thermohydrodynamics have been recognized, making it possible to incorporate the entropy source and chemical changes into an extended Gibbs equation (Sieniutycz, 1994). The progress in variational and extremum formulations has been synthesized in a book (Sieniutycz and Farkas, 2005).
The topological network approach in network thermodynamics has proved to be a powerful tool improving many classical results and asking new questions (Peusner, 1986, 1990). A review of network thermodynamics in the context of the topological graph approach gives good information about the effectiveness of the method (Peusner, 1990). TNs are seen as specialized forms of directed graphs in which Kirchhoff’s laws hold. The approach has several advantages: it can incorporate both the equilibrium Gibbsian theory and the theory of engines in a single representation. It incorporates nicely the theory of thermodynamic transformations and the thermostatic metric, it integrates statistical and kinetic views, and it leads readily to nonequilibrium extensions. Examples are given which show that a variety of reversible and irreversible problems can be imbedded in a unified way using this approach.
Important generalizations in the context of maximum entropy approaches have been obtained for the statistical foundations of nonequilibrium thermodynamics (Jaynes, 1957; Lewis, 1967; Bedeaux, 1986, 1992; Callen, 1988; Garcia-Collin et al., 1984; Grandy, 1983, 1988; Jou, 1989; Jou and Llebot, 1980; Jou et al., 1988, 2001; Kreuzer, 1981; Keizer, J. 1987; Lavenda, 1985a, b; Nulton and Salamon, 1985, 1988; Nulton et al., 1985; Salamon et al., 1985; Wang, 2003) and in the stochastic theory of diffusion (Schlögl, 1974, 1980; Lavenda, 1985a, b). Benefits of nonequilibrium approaches are particularly visible in the diffusion processes (Compte and Jou, 1996). A generalized Onsager principle was found and its applications were presented for complex diffusion problems governed by memory kernels (Shter, 1973). Mechanism of stress-induced diffusion of macromolecules in solutions was worked out (Tirrell and Malone, 1977). Diffusion engines were designed and analyzed (Tsirlin et al., 2005). Balance equations of extensive quantities for a multicomponent fluid taking into account diffusion stresses were formulated and analyzed (Wiśniewski, 1984). A critical appraisal of the earlier theories of irreversible thermodynamics is available (Lavenda, 1978).
Phenomenological theory for polymer diffusion has been developed for diffusion phenomena in nonhomogeneous velocity gradient flows and applied to continuum modeling of polyelectrolytes in solutions (Drouot and Maugin, 1983, 1985, 1987, 1988;
Jongschaap (1990) discusses the basic principles of some important models: continuum, bead-rod-spring, transient network, reptation and configuration tensor models. Emphasis has been put on a consistent treatment of the fundamentals of the various models and their interrelationship, rather than considering any of them in much detail. These synthesizing analyses performed in groups of applied mathematicians contributed significantly to the setting and development during the past 15 years of a two-bracket formalism of dissipative continuum physics called GENERIC (Grmela and Öttinger, 1997; Öttinger and Grmela, 1997; Öttinger, 2005). The formalism has been applied to different problems of continuum thermodynamics, often in this way, that a well-known problem was reformulated in GENERIC formalism. To learn some more about the GENERIC procedure, Muschik et al. (2000) attempted to compare GENERIC with rational nonequilibrium thermodynamics and other general methods. They consider a gas which is contained in a cylinder closed by a piston moving with friction. They treat this simple discrete system with rational nonequilibrium thermodynamics by using Liu’s method of Lagrange multipliers (Liu and I-Shih, 1972) and, for comparison, also with the GENERIC formalism. Both different procedures yield the same results, especially in the same entropy production. The researchers compare and discuss differences, similarities, and fundamental presuppositions of both formalisms. In particular, they show that GENERIC is more redundant than the rational theory, although the results for both are the same for the example under consideration.
An improved understanding of relaxation transients and oscillators has been obtained for both hydrodynamical and chemical systems (Velarde and Chu, 1990,1992; Sieniutycz and Salamon, 1990c). Chaos theory emerged and received its universal form since Feigenbaum’s (1979) development showing the role of functional equations to describe the exact local structure of bifurcated attractors of xn+1 = λ f (xn) independent of specific f. His discovery of universal metric properties of nonlinear transformations has prompted the understanding of chaos problems along with appropriate corrections to the turbulence theory in the newer editions of fluid mechanics (Landau and Lifshitz, 1987). Moreover, Zalewski (2005) and Zalewski and Szwast (2006) worked out a method to determine regimes of chaos for heterogeneous catalytic reactions in the presence of deactivating catalysts. Using Bateman’s Lagrangian (Bateman, 1929, 1931), containing its usual exponential term, Steeb and Kunick (1982) showed that a class of dissipative dynamical systems with limit-cycle and chaotic behavior can be derived from a Lagrangian function. Breymann et al. (1998) reviewed entropy balance, time reversibility and mass transport in dynamical systems modelling transport of mass or charge. The key ingredient of understanding entropy balance is the coarse graining of the local phase-space density. Their irreversible entropy production is proportional to the average growth rate of the local phase-space density. The average phase-space contraction rate measures the irreversible entropy production. They also show consistency of their results with thermodynamics. Gorban et al. (2001) developed a general method of constructing dissipative equations,
following Ehrenfest’s idea of coarse graining. The approach resolves the major issue of discrete time coarse graining versus continuous time macroscopic equations. Proof of the H theorem for macroscopic equations is given, several examples supporting the construction are presented, and generalizations are suggested. Coveney (1988) reviews the second law of thermodynamics from the standpoint of entropy, irreversibility, and dynamics. Dettmann et al. (1997) show how the irreversibility arises from reversible microdynamics. (See also ”Classical and Anomalous Diffusion)
Nonequilibrium thermodynamics of surfaces has been developed with applications in catalysis, adsorption theory and interface phenomena (Bedeaux, 1986, 1992). These improvements resulted in an amended description of thermal, hydrodynamic, and chemical behavior for many physical and industrial systems.
Progress in applications accompanies progress in the theory. With the help of theories of irreversible processes, many nonequilibrium systems have successfully been modelled and implemented, including, for example, complex heat and mass exchangers, thermal, acoustic and solar-driven engines, convection cells, radiation-emitting fluids, viscoelastic continua (especially polymeric fluids), ion-selective membranes, diffusional separators, thermocouples, semiconductor devices, and so forth. These applications have promoted a deeper understanding of the irreversible theory, and have in turn led to valuable improvements in the design of related industrial devices. Extended thermodynamics has been formulated (Garcia-Collin et al., 1984; Jou, 1988, 1989) as a theory based on extended Gibbs equations including fluxes as independent variables. It has evolved to the status of a mature theory, summarized in a book (Jou et al., 2001) and capable of dealing with a vast variety of nonequilibrium continua. An extended thermodynamic description is important especially for systems involving high fluxes, steep gradients, and highly unsteady transients.
Progress in the theoretical and applied irreversible thermodynamics has been summarized in the corresponding project of Advances in Thermodynamics Series (series editor A. Mansoori), in the form of several edited volumes (Sieniutycz and Salamon, 1990a, c, 1992a, c). Their contents are outlined subsequently.
Volume 3 of the series entitled General Theory and Extremum Principles (Sieniutycz and Salamon, 1990a) is the first of four multiauthored volumes on the theory and applications of nonequilibrium thermodynamics. This volume offers a collection of papers dealing with nonequilibrium theory and extremum principles. Various theories of nonequilibrium thermodynamics are discussed in a quasi-historical context. The significance of the extremum, variational and geometric formulations for nonequilibrium theory is analyzed. A variety of nonequilibrium theories are considered including Onsagerian, rational, Meixnerian, network, information-theoretic, Mullerian, finite-time and extended. A perspective is given on the phenomenon of spacial and temporal structure formation in self-organizing systems, and self-organizing criteria are presented which show that
information is an important concept. Some recent results in network thermodynamics are also reviewed. Geometric theories originating from Riemannian thermostatic curvature are extended to nonequilibrium situations. Selected statistical and stochastic aspects of the theory of nonequilibrium systems are analyzed, and their macroscopic consequences are shown in the form of generalizations of the so-called governing variational principle of dissipative processes and the associated extremum principles. An emphasis is put on variational principles of considerable generality, involving nondissipative and dissipative nonequilibrium continua containing matter or radiation. Radiation processes are treated on both statistical and phenomenological levels and the nonequilibrium thermodynamic theory of emitting and absorbing media is developed.
Volume 4 entitled Finite-Time Thermodynamics and Thermoeconomics (Sieniutycz and Salamon, 1990c) deals with applications of nonequilibrium thermodynamics and availability theory to mostly lumped systems where a certain external control can be applied in order to achieve improved performance. Approaches from nonequilibrium thermodynamics are capable of providing quite realistic performance criteria and bounds for real processes occurring in a finite time. Model systems have been developed which incorporate friction, heat loss, inertial effects, and finite heat conductance for real energy conversion processes. Finite-time thermodynamics, exergy analysis, and thermoeconomics seek the best adjustable parameters of various engines (thermal, solar, combustion, acoustic, convection cells, etc.), unit operations and unit processes (distillation, evaporation, chemical reactions, etc.) and systems of these operations or processes in chemical plants working under definite operational constraints. Optimal paths (or a set of optimal steady-state parameters) and optimal controls (for instance temperatures maximizing chemical efficiency) have been found. The role of optimization approaches and in particular optimal control theory is essential when solving these problems. The optimization results for a few important ecological and industrial systems are given.
Volume 5 of the series entitled Analytic Thermodynamics with Applications in Energy Conversion Systems supplements the previous results and gives a number of extra examples.
Volume 6 entitled Flow, Diffusion, and Rate Processes (Sieniutycz and Salamon, 1992a) reviews valuable results obtained for the nonequilibrium thermodynamics of transport and rate processes. Kinetic equations, conservation laws and transport coefficients are obtained for multicomponent mixtures. Thermodynamic principles are used in the design of experiments predicting heat and mass transport coefficients. Highly nonstationary conditions are analyzed in the context of transient heat transfer, nonlocal diffusion in stress fields and thermohydrodynamic oscillatory instabilities. Unification of the dynamics of chemical systems with other sorts of processes (eg, mechanical) is given. Thermodynamics of reacting surfaces is developed. Admissible reaction paths are studied and a consistency of chemical kinetics with thermodynamics is shown. Oscillatory reactions are analyzed in a unifying approach showing explosive, conservative or damped behavior. A