# Transport Processes in Chemically Reacting Flow Systems (Dover Civil and Mechanical Engineering)

However, principles guiding systems that are far from equilibrium are still debatable. One of such principles is the maximum entropy production principle. In classical thermodynamics, the second law is a basic postulate applicable to any system involving heat energy transfer; in statistical thermodynamics, the second law is a consequence of the assumed randomness of molecular chaos. There are many versions of the second law, but they all have the same effect, which is to explain the phenomenon of irreversibility in nature.

The third law of thermodynamics is a statistical law of nature regarding entropy and the impossibility of reaching absolute zero of temperature. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy. Alternate definitions are, "the entropy of all systems and of all states of a system is smallest at absolute zero," or equivalently "it is impossible to reach the absolute zero of temperature by any finite number of processes".

An important concept in thermodynamics is the thermodynamic system , which is a precisely defined region of the universe under study. Everything in the universe except the system is called the surroundings. A system is separated from the remainder of the universe by a boundary which may be a physical boundary or notional, but which by convention defines a finite volume. Exchanges of work , heat , or matter between the system and the surroundings take place across this boundary.

In practice, the boundary of a system is simply an imaginary dotted line drawn around a volume within which is going to be a change in the internal energy of that volume. Anything that passes across the boundary that effects a change in the internal energy of the system needs to be accounted for in the energy balance equation. The volume can be the region surrounding a single atom resonating energy, such as Max Planck defined in ; it can be a body of steam or air in a steam engine , such as Sadi Carnot defined in ; it can be the body of a tropical cyclone , such as Kerry Emanuel theorized in in the field of atmospheric thermodynamics ; it could also be just one nuclide i.

Boundaries are of four types: fixed, movable, real, and imaginary. For example, in an engine, a fixed boundary means the piston is locked at its position, within which a constant volume process might occur. If the piston is allowed to move that boundary is movable while the cylinder and cylinder head boundaries are fixed.

For closed systems, boundaries are real while for open systems boundaries are often imaginary. In the case of a jet engine, a fixed imaginary boundary might be assumed at the intake of the engine, fixed boundaries along the surface of the case and a second fixed imaginary boundary across the exhaust nozzle. Generally, thermodynamics distinguishes three classes of systems, defined in terms of what is allowed to cross their boundaries:. As time passes in an isolated system, internal differences of pressures, densities, and temperatures tend to even out. A system in which all equalizing processes have gone to completion is said to be in a state of thermodynamic equilibrium.

Once in thermodynamic equilibrium, a system's properties are, by definition, unchanging in time. Systems in equilibrium are much simpler and easier to understand than are systems which are not in equilibrium. Often, when analysing a dynamic thermodynamic process, the simplifying assumption is made that each intermediate state in the process is at equilibrium, producing thermodynamic processes which develop so slowly as to allow each intermediate step to be an equilibrium state and are said to be reversible processes. When a system is at equilibrium under a given set of conditions, it is said to be in a definite thermodynamic state.

The state of the system can be described by a number of state quantities that do not depend on the process by which the system arrived at its state. They are called intensive variables or extensive variables according to how they change when the size of the system changes. The properties of the system can be described by an equation of state which specifies the relationship between these variables. State may be thought of as the instantaneous quantitative description of a system with a set number of variables held constant.

A thermodynamic process may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. It can be described by process quantities. Typically, each thermodynamic process is distinguished from other processes in energetic character according to what parameters, such as temperature, pressure, or volume, etc.

There are two types of thermodynamic instruments , the meter and the reservoir. A thermodynamic meter is any device which measures any parameter of a thermodynamic system. In some cases, the thermodynamic parameter is actually defined in terms of an idealized measuring instrument. For example, the zeroth law states that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other.

This principle, as noted by James Maxwell in , asserts that it is possible to measure temperature. An idealized thermometer is a sample of an ideal gas at constant pressure. Although pressure is defined mechanically, a pressure-measuring device, called a barometer may also be constructed from a sample of an ideal gas held at a constant temperature. A calorimeter is a device which is used to measure and define the internal energy of a system. A thermodynamic reservoir is a system which is so large that its state parameters are not appreciably altered when it is brought into contact with the system of interest.

When the reservoir is brought into contact with the system, the system is brought into equilibrium with the reservoir. For example, a pressure reservoir is a system at a particular pressure, which imposes that pressure upon the system to which it is mechanically connected. The Earth's atmosphere is often used as a pressure reservoir. If ocean water is used to cool a power plant, the ocean is often a temperature reservoir in the analysis of the power plant cycle. The central concept of thermodynamics is that of energy , the ability to do work. By the First Law , the total energy of a system and its surroundings is conserved.

Energy may be transferred into a system by heating, compression, or addition of matter, and extracted from a system by cooling, expansion, or extraction of matter. In mechanics , for example, energy transfer equals the product of the force applied to a body and the resulting displacement.

Conjugate variables are pairs of thermodynamic concepts, with the first being akin to a "force" applied to some thermodynamic system , the second being akin to the resulting "displacement," and the product of the two equalling the amount of energy transferred. The common conjugate variables are:. Thermodynamic potentials are different quantitative measures of the stored energy in a system. Potentials are used to measure the energy changes in systems as they evolve from an initial state to a final state. The potential used depends on the constraints of the system, such as constant temperature or pressure.

For example, the Helmholtz and Gibbs energies are the energies available in a system to do useful work when the temperature and volume or the pressure and temperature are fixed, respectively. Thermodynamic potentials can be derived from the energy balance equation applied to a thermodynamic system. Other thermodynamic potentials can also be obtained through Legendre transformation.

From Wikipedia, the free encyclopedia. The classical Carnot heat engine. Classical Statistical Chemical Quantum thermodynamics. Zeroth First Second Third. System properties. Note: Conjugate variables in italics. Work Heat. Material properties. Carnot's theorem Clausius theorem Fundamental relation Ideal gas law.

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Free energy Free entropy. History Culture. History General Entropy Gas laws. Entropy and time Entropy and life Brownian ratchet Maxwell's demon Heat death paradox Loschmidt's paradox Synergetics. Caloric theory Theory of heat. Heat ". Thermodynamics Heat engines. Note transition to turbulence within the thermal BL at Ra h -values based on plate length above ca.

Figure 6. Figure 7. Su Way Stewart Figure 8. Table 2. Table 3. Table 5. Rosner Table 6. Table 8. Gibbs remarked that the role of theory in any science is to find the perspective from which the subject appears in its simplest form. My purpose is to present in a simple language but rather general form, principles and approaches that have proven to be very fruitful, and that will doubtless remain so in solving the challenging problems still ahead of us.

Thus, while our perspective and scope is broader than that found in many previous transport textbooks especially those intended for undergraduates , the presentation here is deliberately concise and very selective, leaving many details for student exercises. I hope the result provides the dedicated reader with the fundamentally oriented yet up-to-date background needed to tackle more advanced, specialized topics. In any event, I am confident it will put the reader in a position to properly formulate and solve many important problems involving rates of energy, mass, or momentum transport in fluids that may be reacting chemically.

The pedagogical choice of combustion for many of the examples is not merely the result of my own research background. For the reasons outlined below I am convinced that combustion is an excellent prototype for presenting the important concepts of transport in chemically reacting fluid flows. First, it is perhaps the only area of chemically reacting flows not only common to chemical engineering, mechanical engineering, and aeronautical engineering, but also familiar in the daily experience of all applied scientists.

### 1st Edition

Second, while avoiding the dazzling variety of phases, states, and chemical species encountered in present-day ChE reactor applications, combustors exhibit all of the important qualitative features of nonideal, transport-limited, nonisothermal reactors used to synthesize valuable chemicals—indeed, many chemicals C2H2, HCl, P2O5, TiO2, etc. Finally, it should not be necessary to remind the reader of the economic importance of the efficient use of our remaining fossil fuels, and the prevention of combustion-related accidents.

However, as indicated in Section 2. Therefore, it is appropriate that these underlying principles first be mastered in the context of either single-phase flows, or simple limiting cases of two-phase flows e. Thus, while we formulate and exploit the principles on which individual exchangers and chemical reactors are selected and designed e. While Chapters 4, 5, and 6 deal successively with momentum, energy, and mass transport, we clearly develop, state, and exploit useful quantitative analogies between these transport phenomena, including interrelationships that remain valid even in the presence of homogeneous or heterogeneous chemical reactions Sections 6.

Moreover, we include a separate chapter 7 on the use of transport theory in the systematization and generalization of experimental data on chemically reacting systems, emphasizing similitude methods that go far beyond ordinary dimensional analysis. Because of our present emphasis on the transport mechanisms of convection and diffusion, which operate for momentum, energy, and species mass, the somewhat singular subject of radiative energy transport Section 5.

While some chemical reactors are intended to produce photons e. These factors, together with the one-way nature of the fluid dynamics—radiative energy coupling in most engineering devices i. Nevertheless, what little is included is intended to indicate the nature of the radiative transport problem, and to suggest fruitful alternative approaches to deal with it. Following a concise overview Chapter 7, Summary of the main points of each chapter, many of these principles and methods are then brought together in a comprehensive numerical example Chapter 8 intended to also serve as a prototype see Appendix 8.

Unless otherwise specified they were developed by the author in connection with his previous teaching, research, and consulting; however, in some cases clearly cited , they are elaborations or revisions of similar problems included in earlier textbooks or treatises. While our preference is for metric units m-kg-s, or cm-g-s , some examples are deliberately included in other commonly used engineering unit systems for conversion factors, see Appendix 8. Most equations derived or quoted herein are either dimensionless or, if dimensional, stated in a form in which they are valid in any self-consistent unit set.

In summary, the principles developed and often illustrated here for combustion systems are important not only for the rational design and development of engineering equipment e. Indeed, while developed primarily for use as a graduate and undergraduate textbook in transport processes energy, mass, and momentum , our emphasis on fluids containing molecules capable of undergoing chemical reaction e. Specific sequences of topics in each of these possible courses are identified in Tables P1 and P2. In each case it is assumed that the relevant background in the underlying sciences of chemical thermodynamics and chemical kinetics can be provided via readily available texts in these classical areas.

By this time the reader will have noted that this text is concerned with the principles underlying the development of comprehensive rational computer models of chemically reacting flow systems, rather than the description of recently developed computer aids to engineering design. In this respect, the particular problems and solutions I have chosen to explicitly include here should be regarded merely as instructive prototypes for dealing with the challenging new engineering problems that face us.

Much of my own learning occurs in the process of doing research in the general area of transport processes in chemically reacting systems. Air Force and NASA-Lewis Research Laboratories for their financial support of research that has strongly influenced the orientation and content of this book. I am also indebted to many colleagues at Yale University and EXXON Corporation for their helpful comments, and to the members of Technion—Israel Institute of Technology for their hospitality during the Fall of , when this manuscript was essentially put into its present form.

However, the author takes full responsibility for any errors of commission or omission associated with this first edition, and will welcome the written feedback of students, faculty, and practicing engineers and applied scientists who use this book. The information needed to design and control engineering devices for carrying out chemical reactions will be seen below to extend well beyond the obviously relevant underlying sciences of:.

Even the basic data of these underlying sciences are generated by using idealized laboratory configurations e. This book deals with the role, in chemically reacting flow systems, of transport processes —particularly the transport of momentum, energy, and chemical species mass in fluids gases and liquids. The laws governing such transport will be seen to influence:. For systems in which only physical changes occur e.

Indeed, we will show that the transport laws governing nonreactive systems can often be used to make rational predictions of the behavior of analogous chemically reacting systems. For this reason, and for obvious pedagogical reasons, the simplest illustrations of momentum, energy, and mass transport in Chapters 4, 5, and 6, respectively will first deal with nonreacting systems, but using an approach and a viewpoint amenable to our later applications or extensions to chemically reacting systems.

This strategy is virtually an educational necessity, since chemical reactions are now routinely encountered not only by chemical engineers, but also by many mechanical engineers, aeronautical engineers, civil engineers, and researchers in the applied sciences materials, geology, etc. Engineers frequently study momentum, energy, and mass transport in three separate, sequential, one-semester courses, as listed in the accompanying table.

Here the essential viewpoints and features of these three subjects will be concisely presented from a unified perspective Chapters 2 through 7 , with emphasis on their relevance to the quantitative understanding of chemically reacting flow systems Chapters 6 and 7. Our goal is to complete the foundation necessary for dealing with modern engineering problems and more specialized topics useful to:. For several reasons see the Preface we will illustrate the principles of chemically reacting flows and reactor design and analysis using examples drawn primarily from the field of combustion —i.

Combustion examples have the merits that:. Chemically Reacting Systems Flow systems with chemical reactions inevitably involve transport phenomena, since multicomponent mixtures with thermal and concentration gradients are present. These are generally extremely dif? Finally, in a two-volume treatise8c on solutions to the diffusion equation in catalytic systems was published by Aris, complete with literature references and bibliographical notes. All these are aimed at the design and operation of chemical reactors. A notable exception is that by Rosner,j which attempts to set forth the subject of transport phenomena for people working in the general area of combustion, shock waves, and?

This book makes full use of the equations of change, the thermodynamics of irreversible processes, and elementary ideas of turbulence. An introductory textbook by Bel? In addition, there are three review articlesl that cover the subjects of combustion and? Although not particularly devoted to the subject of transport phenomena, the comprehensive workm by Doraiswamy should be mentioned.

This massive reference work contains much useful information about experimental details and analysis of experiments, along with extensive bibliographical references. One area of research that makes full use of transport phenomena and chemical kinetics is that of chemical vapor depositionn and the simulation and design of CVD reactors. In the CVD process, chemically reacting gases form a thin solid? Homsy and Strohmano studied diffusion and chemical reaction in a tubular reactor with a non-newtonian annular?

Hougen and K. Sherwood and R. Sherwood, R. Pigford, and C. Rawlings and J. Bawn and C. Tipper, Ann. Wolfhard and D. Burger, Ann. Becker, Ann. Jensen, E.

## Transport Processes in Chemically Reacting Flow Systems

Einset, and D. Fotiadis, Ann. Homsy and R. Turbulence For an authoritative and readable summary of the turbulence literature for the last century, see the review article by Lumley and Yaglom. The book by Friedlander and Topper is a collection a dozen key classical papers on the statistical theory of turbulence. For turbulent shear? Despite the intense effort made in the past half-century on the fundamentals of turbulence, in many engineering calculations mixing-length theories or K, -theories are still being used, and with some success.

For example, the classical Prandtl mixing-length empiricism for the turbulent momentum? This same empiricism can also be used for predicting heat and mass transfer rates. Murphree, Ind. Then, at high Prandtl or Schmidt numbers, he showed that the Nusselt or Sherwood number is equal to a constant times the one-third power of the Prandtl or Schmidt number, plus another constant times the zero-th power of the Prandtl or Schmidt number, and so on.

This result checks well with the experimental datam of Shaw and Hanratty on mass transfer. A related analysis had been made earlier by Notter and Sleichern to deduce that the eddy diffusivity near a wall is proportional to the third power of the distance from the wall. In another effort to provide a useful equation for the Reynolds stresses, the classical von Karman-Prandtl universal log? Reynolds number curve in the turbulent region because of the presence of small amounts of high polymers. Other discussions of the turbulent heat transfer in drag-reducing? Seinfeldt has prepared an informative review of this topic, including a number of solutions to the turbulent diffusion equation.

The onset of turbulence in falling liquid? The rather complete literature search with comments should be very helpful to workers in mass transfer. The interaction between homogeneous turbulence and chemical reactions has been reviewed by Hill. The gas enters the tube tangentially at sonic or supersonic velocity through a nozzle, and leaves at the two ends— one with a central ori?

Lumley and A. Yaglom, Flow, Turbulence, and Combustion, 66, — Tennekes and J. Monin and A. Friedlander and L. Topper, Turbulence, Interscience, New York Holmes, J. Lumley, and G. Lesieur, Turbulence in Fluids, Kluwer, Dordrecht, 3rd edition Aero Sci. Hanna, O. Sandall, and P. Mazet, AIChE Journal, 27, — , to make the turbulent viscosity be proportional to the third power of the distance from the wall; O. Sandall, O. Hanna, and P. Mazet, Canad. Wasan, C. Tien, and C. Stewart and D. Shaw and T. Notter and C. Barenblatt and A. Chorin, Proc. USA, 93, — Nieuwstadt and J.

Soldati and R. Monti , Springer, New York ; M. Graham, British Rheology Review, 2, 00 — 00 Hamersma and J. Fortuin and P. Klijn, Chem. Wells, Jr. Smith, G. Keuroghlian, P. Virk, and E. Seinfeld, Atmospheric Diffusion Theory, in Vol. Wei, K. Bischoff, T. Drew, and J.

Seinfeld, eds. Hoopes, T. Hill, Ann. Polymeric Liquids Chemical engineers, because of the growing importance of the plastics industry, were rather quick to jump into the emerging? The lengthy review article of Metznera identi? Various corotating coordinate systems have also been introduced. There is one important difference between the two types of problems: the non-Newtonian?

Several bookse,f,g,h,i have appeared in recent years that provide the molecular-continuum connection. The latter theories have been more highly developed, particularly as regards the formulation of the stress tensor and the heat and mass? Such cross effects have not been studied experimentally to any signi?

For a polymer in a dilute solution, the diffusivity of the polymer is proportional to the inverse square root of the molecular weight according to the theory of Kirkwood,k which has been con? The theory has been re? In this way he showed that the self diffusivity should be proportional to the inverse square of the molecular weight, more or less in agreement with experiment.

The DoiEdwards papers were received by the rheological community with considerable excitement. On closer examination, however, it appeared that the theory had some unfortunate defects;o these could be remedied by introducing additional assumptions into the theory, and a? To cite just one example, Neergaard and Schieberp have tested recently a modi? For some purposes, various dumbbell and chain models with nonlinear springs give plausible resultsq for a wide variety of phenomena. Williamsr reviewed the current status of molecular theories of rheology of polymers from the chemical and chemical engineering viewpoints in With regard to the experimental measurement of rheological properties of polymers, the works of Meissneru are highly recommended, and for both rheological and optical properties, the publications of Janeschitz-Kriegl.

Co and Stewarty solved the problem of the? In , Lodgee published his famous Elastic Liquids book, which provided an excellent organizational tool for the entire? The main de? Somewhat before, Spriggsaa had proposed his 4-constant model, which was inspired by the Rouse theory for dilute solutions; it proved to be reasonably good for describing the behavior of polymer melts. Metzner, in Advances in Chemical Engineering Vol. Oldroyd, Proc. Wedgewood, Rheol.

## Transport Processes in Chemically Reacting Flow Systems - 1st Edition

Acta, 38, 91—99 Bird, R. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, Vol. Bird, C. Curtiss, R. Doi and S. Bird, Adv. Curtiss, and K. Beers, Rheol. Acta, 36, — ; R. Bird and C. Curtiss, J. Ottinger, J. Today, 36, 33—39 Hassager, J. Lodge, J. Schieber, and R. Saab, R. Neergaard and J. Schieber, J. Zhou and R. Akhavan, J. Bird and H.

Ottinger, Ann. Bird and J. Wiest, Ann. Truesdell and R. Flugge, ed. Meissner, Ann. Co and W. Spriggs, Chem. Denson, W. Prest, Jr. Tadmor and C. Chapman,c and then the? This article includes a description of a number of effects along with some photographs and line drawings. DiBenedetto and Lightfoot,g in a publication that combined theoretical analysis and experiment, veri? Crosser, Powers, and Prabhudesaih analyzed the separation that occurs in a thermoelectrogravitational electrophoresis column.

Newman, Ind. Melcher and G.

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Taylor, Ann. Saville, Ann. DiBenedetto and E. Lightfoot and E. Crosser, J. Powers, and R. Surface and Interfacial Phenomena When discussing interfacial phenomena, a whole new set of physical properties has to be taken into account, the most important of which is the interfacial tension,a which was studied in from the point of view of the principle of corresponding states. A method of measuring the surface tension from the shape of the meniscus was developed by Biery. In Chapter VII of the?

Then, in and publicationsd appeared by Sternling and Scriven, dealing with the Marangoni effect. In , another effect, evaporative convection,e was discussed in some detail. In these phenomena, one has to deal with the interaction of interfacial dynamics,? The hydrodynamic stability of Marangoni? A review article in by Kumar and Kuloor,g and a monograph by Clift, Grace, and Weberh in are devoted to the subject of the formation and behavior of Vol.

Transport Phenomena in Electrolytic Solutions When dealing with ionic systems, one needs not only the equations of change for mass, momentum, and energy, but also a statement of electric neutrality for the solution, and the Maxwell equations of electromagnetism usually in abbreviated form.

Also, the equation of motion may need to be modi? Most general textbooks on transport phenomena do not discuss ionic systems, notable exceptions being those of Probsteina and Plawsky. In the latter, heat- and mass-transfer effects, internal circulation, motions near con? Brock and R. Slattery, L. Sagis, and E. Edwards, H. Brenner, and D. Sternling and L. Scriven, Chem. Berg, A. Acrivos, and M. Boudart, Evaporative Convection, in Vol. Ludviksson and E. AIChE Journal, 17, — Kumar and N. Vermeulen , Academic Press, New York Clift, J. Grace, and M. This was followed by a comprehensive article by Brenner,b and thereafter many more.

The Happel-Brenner book was supplemented later by the monographc of Kim and Karilla. The book covers various kinds of averaging and possible methods for modeling suspensions.

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An extensive review of the rheological properties of suspensions of neutrally buoyant particles was published by Jeffrey and Acrivos. The rheology of suspensions has been discussed by Brennerg and by Adler, Nadim, and Brenner. None of these references deal with heat and mass transfer. An extensive review article by Brownl deals with the role of transport phenomena in crystal growth from the molten state. Greenkornm prepared a review article on the?

Whitakern studied diffusion in packed beds of porous particles, and described how to extract the particle effective-diffusivity from the overall effective-diffu February sivity of a packed bed. Lin and Slatteryo studied the two-phase? This is the? In porous media problems, there is always the problem of what kind of boundary condition to be used at the interface between the porous medium and the external? Sy, Taunton, and Lightfootq have solved the equations of motion for the motion of a solid sphere or a spherical gas bubble embedded in an external medium, starting from rest and accelerating to steady state.

Wagner and Slatteryr studied the? They used a third-order? Another problem is that of the liquid? They investigated the stability of the interface. Mixing, with or without diffusion and chemical reactions, is important in many of the unit operations of chemical engineering. In , a key paper by Ottino, Ranz, and Macoskot was published, based on the principles of continuum mechanics, which established the mathematical framework for future work in this subject. Happel and H. Brenner, Advances in Chemical Engineering, Vol. Vermeulen, G. Kim and S. Karilla, Microhydrodynamics, Butterworth-Heinemann, Boston Drew and S.

Jeffrey and A. Hunter, Foundations of Colloid Science 2 vols. Brenner, Ann. Adler, A. Nadim, and H. Bischoff, and J. Cox and S. Mason, Ann Rev. Marble, Ann. Brady and G. Bossis, Ann. Lin and J. Sy, J. Taunton, and E. Sy and E.