This text is designed to teach you how to carry out quantitative analysis of physical phenomena important to chemical professionals. In the chemical engineering curriculum, this course is typically taught in the junior year. Students with adequate preparation in thermodynamics and reactor design should be successful at learning the material in this book. Students lacking a reactor design course, such as chemists and other professionals, will need to pay additional attention to the material in Chapter 2 and may need to carry out additional preparation by using the references contained in that chapter. This book uses the logic employed in the simple analysis of reacting systems for reactor design to develop the more complex analysis of mass and heat transfer systems.

Analysis is the process of developing a mathematical description (model) of a physical situation of interest, determining behavior of the model, comparing the behavior with data from experiment or other sources, and using the verified model for various practical purposes.

There are two parts in the analysis process that deserve special attention:

• developing the mathematical model, and

• comparing model behavior with data.

Our experience with teaching analysis for many years has shown that the model development step can be effectively taught by following well-developed logic. Just what constitutes agreement between model behavior and data is a much more complex matter and is part of the art of analysis.

In Part I of this text we developed the model equations for analyzing experiments and for the technically feasible design of laboratory-, pilot-, and commercial-scale processing equipment including reactors, heat exchangers, and mass contactors. Our organization in terms of the macroscale fluid motions in such equipment (Table 1.1) has broader applicability because many systems of interest in living organisms and in the natural environment can also be similarly analyzed.

The constitutive equations used in the model equations in Part I are summarized in Table 1.5. The overall heat transfer coefficient U and the mass transfer coefficient Km are engineering parameters defined by these constitutive equations. These transport coefficients depend on both the materials involved and the microscale and macroscale fluid motions of these materials, as well as their thermodynamic state (i.e., temperature and pressure). Our need to determine these parameters by experiment reflects our lack of understanding of the fluid mechanics affecting the transport of energy in a turbulent or laminar fluid to a solid surface, for example, or the transfer of a species at the interface between two phases with complex fluid motions. These boundary layers are critical regions at the fluid–fluid and fluid–solid interfaces where the dominant resistances to heat and mass transfer are located in flowing fluids. Transport coefficients deduced from analysis of existing equipment are accurate only if the model equations correctly describe the fluid motions in the experiment.

This book is designed to teach students how to become proficient in engineering analysis by studying mass and heat transfer, transport phenomena critical to chemical engineers and other chemical professionals. It is organized differently than traditional courses in mass and heat transfer in that more emphasis is placed on mass transfer and the importance of systematic analysis. The course in mass and heat transfer in the chemical engineering curriculum is typically taught in the junior year and is a prerequisite for the design course in the senior year and, in some curricula, also a prerequisite for a course in equilibrium stage design. An examination of most mass and heat transfer courses shows that the majority of the time is devoted to heat transfer and, in particular, conductive heat transfer in solids. This often leads to overemphasis of mathematical manipulation and solution of ordinary and partial differential equations at the expense of engineering analysis, which should stress the development of the model equations and study of model behavior. It has been the experience of the authors that the “traditional” approach to teaching undergraduate transport phenomena frequently neglects the more difficult problem of mass transfer, despite its being an area that is critical to chemical professionals.

At the University of Delaware, chemical engineering students take this course in mass and heat transfer the spring semester of their junior year, after having courses in thermodynamics, kinetics and reactor design, and fluid mechanics.

Hypothesis . The dramatic hypotheses (‘prefaces’ or ‘plot summaries’) which are preserved in the surviving medieval manuscripts and ancient papyri fall into three general categories (Zuntz (1955a) 129–52; cf. also van Rossum-Steenbeek (1998) 1–39; for the papyri, see Haslam (1975) 150–6, Diggle (2005)).

The first and most valuable are those derived from the Alexandrian edition of Aristophanes of Byzantium (cf. Pfeiffer (1968) 192–6, Mastronarde (1994) 168 n. 2). Although only fragments of these survive (occasionally combined with the two other types of hypothesis), we have enough material to be able to piece together the scope and typical features of Aristophanes’ introductory notes (for Eur., cf. Alc., Med., Hipp., Andr., Hec., Phoen., Or., Bacch., Rhes.). They combine basic points of scenography (e.g. where the play is set, the identity of the chorus and prologue speaker) with more scholarly information regarding such topics as the treatment of the myth by the other two tragedians, the date of the play, the titles of companion plays, and the results of the contest (Alc. second prize, Med. third prize, Hipp. first prize, Phoen. second prize).

The second type of hypothesis is uniquely Euripidean, stemming from a collection of Euripidean plot summaries, arranged alphabetically by the first letter of the title, which was composed in the first or second century ad To gain scholarly respectability, the collection was ascribed to Aristotle's fourth-century bc pupil Dicaearchus of Messene. These Tales from Euripides (as Zuntz (1982) 358 called them) were, however, written for a popular audience, and their narratives were intended to be simple summaries of the plot.

All physical situations of interest to engineers and scientists are complex enough that a mathematical model of some sort is essential to describe them in sufficient detail for useful analysis and interpretation. Mathematical expressions provide a common language so different disciplines can communicate among each other more effectively. Models are very critical to chemical engineers, chemists, biochemists, and other chemical professionals because most situations of interest are molecular in nature and take place in equipment that does not allow for direct observation. Experiments are needed to extract fundamental knowledge and to obtain critical information for the design and operation of equipment. To do this effectively, one must be able to quantitatively analyze mass, energy, and momentum transfer (transport phenomena) at some level of complexity. In this text we define six levels of complexity, which characterize the level of detail needed in model development. The various levels are summarized in Table 1.1.

Level I, Conservation of Mass and/or Energy. At this level of analysis the control volume is considered a black box. A control volume is some region of space, often a piece of equipment, that is designated for “accounting” purposes in analysis. Only the laws of conservation of mass and/or energy are applied to yield the model equations; there is no consideration of molecular or transport phenomena within the control volume. It is a valuable approach for the analysis of existing manmade or natural systems and is widely employed.

Chemical engineers educated in the undergraduate programs of departments of chemical engineering have received an education that has been proven highly effective. Chemical engineering educational programs have accomplished this by managing to teach a methodology for solving a wide range of problems. They first did so by using case studies from the chemical process industries. They began case studies in the early part of the 20th century by considering the complete processes for the manufacture of certain chemicals and how they were designed, operated, and controlled. This approach was made much more effective when it was recognized that all chemical processes contained elements that had the same characteristics, and the education was then organized around various unit operations. Great progress was made during the 1940s and 1950s in experimental studies that quantified the analysis and design of heat exchangers and equilibrium stage operations such as distillation. The 1960s saw the introduction of reaction and reactor analysis into the curriculum, which emphasized the critical relationship between experiment and mathematical modeling and use of the verified models for practical design. We have built upon this approach, coupled with the tools of transport phenomena, to develop this text.

Our approach to teaching mass and heat transfer has the following goals:

1. Teach students a methodology for rational, engineering analysis of problems in mass and heat transport, i.e., to develop model equations to describe mass and heat transfer based on the relationship between experimental data and model.

2. Using these model equations, teach students to design and interpret laboratory experiments in mass and heat transfer and then to effectively translate this knowledge to the operation and design of mass and heat transfer equipment.

3. […]

A substantial portion of this chapter is taken from Introduction to Chemical Engineering Analysis by Russell and Denn (1972) and is used with permission.

This short chapter is a review of the analysis of simple reacting systems for chemical engineers. It is also designed to teach the fundamentals of analysis to other chemical professionals.

Reactor analysis is the most straightforward issue that chemical professionals encounter because rates of reaction can be obtained experimentally. The analysis of experimental data for reacting systems with mathematical models and the subsequent use of the verified model equations for design provide a template for the analysis of mass and heat transfer. We begin with simple reacting systems because the laboratory-scale experiments enable determination of reaction-rate constants that, with reasonable assumptions, can be used in model equations for design and operation of pilot- or commercial-scale reactors.

The same general principles apply to the design of mass contactors and heat exchangers, although it is more difficult to get the necessary values for mass and heat transfer coefficients from experiment. As we will see, mass transfer analysis is further complicated by the need to determine interfacial areas.

All chemical reaction and reactor analysis begins with experiment. Most experiments are carried out in batch equipment in a laboratory, and efforts are made to ensure the vessel is well mixed. In batch experiments, the concentrations of critical reacting species and products are measured over a given time period, sometimes until equilibrium is reached.

Helen has often been misunderstood and undervalued because of its apparent refusal to follow the ‘rules’ of its genre, yet in fact it embodies the variety and dynamism of fifth-century Athenian tragedy perhaps more than any other surviving play. The story of an exemplary wife (not an adulteress) who went to Egypt (not to Troy), Euripides' ‘new Helen’ skilfully transforms and supplants earlier currents of literature and myth. Nevertheless, Euripides uses his unorthodox heroine and her phantom double to explore many of the central issues connected to her more traditional self: the role of the gods in human suffering, the limits of mortal knowledge, the importance of reputation, the consequences of overwhelming beauty and desire, among others. By turns playful and serious, Helen is an extraordinarily exuberant and inventive drama that deserves to be read (and performed) more widely. To that end, this edition of the play aims to discuss a broad spectrum of issues (intellectual context, stagecraft, language, style, reception, etc.) in an easily accessible manner. Like many other tragedies, Helen has suffered from being interpreted anachronistically: as a tragicomedy, for example, or as an indictment of war; the Introduction therefore seeks to reconstruct the original audience's core values and expectations as a more accurate guide to understanding the play. As a result, the Introduction is comparatively long for this series, but the many preconceptions about Helen (and Euripidean tragedy more generally) therein addressed are of such pervasive and continuing influence as to merit detailed analysis.

In our study of mass transfer, we noted that both technically feasible analysis and design were complicated by the need to estimate two parameters in the rate expression: the mass transfer coefficient (Km) and the interfacial area (a). In Chapter 6 theoretical and correlative methods for estimating mass transfer coefficients were discussed for those cases in which transfer of some species was limited by a well-defined boundary layer, such as at a solid or liquid surface. Correlations were identified relating the Sherwood number to the Reynolds and Schmidt numbers, with the functionality specific to the geometry and type of flow (i.e., laminar or turbulent). Complications arise in applying these developments when estimating Km in liquid–liquid or gas–liquid mass contactors. We need estimates of bubble or drop size and some knowledge of the fluid motions in the vicinity of the bubbles or drops to calculate the Reynolds and Sherwood numbers. Furthermore, as shown in Section 6.5, resistances to mass transfer may occur in both phases, necessitating knowledge of the fluid motions inside the bubbles or drops. In this chapter we examine methods for estimating these quantities. This is an active research area requiring Level VI two-phase fluid motion modeling and experiment and is not understood nearly as well as its single-phase counterpart. For this reason, most handbooks and textbooks alike provide only empirical correlations of the product Kma specific to particular process equipment and do not address the problem of interfacial area determination independently from the prediction of mass transfer coefficients.

EURIPIDES AND ATHENS

Life and works

Euripides appears to us as one of the most vivid and recognizable poets of the fifth century bc. Compared to Aeschylus and Sophocles, more than twice as many of his plays have survived complete, while the greater quantity both of quotations in ancient authors and of sizeable papyrus fragments of the lost plays (reflecting his popularity throughout antiquity) gives us a more detailed picture of his dramatic oeuvre. In addition, we possess a variety of sources purporting to chronicle the life of the poet, who even appears as a character in three of the surviving comedies of Aristophanes (Acharnians, Women at the Thesmophoria, Frogs). Yet the very abundance of ancient ‘evidence’ for Eur.'s life and character has had a paradoxically confusing impact on the interpretation of his works (on which more below). For with the exception of a few details securely based on the Athenian didascalic records, all the surviving evidence is of highly dubious reliability, and the bulk of it is little more than anecdote based on naïve ‘inference’, whether from the plays themselves or from the absurd caricatures of Eur.'s art and life generated by Aristophanes and other comic poets.

In fact we have very little reliable evidence for Eur.'s dramatic career and know almost nothing about his life. He was evidently dead by the time of the first production of Aristophanes' Frogs at the Lenaea (in early January) of 405, and the Marmor Parium (a marble stele from Paros inscribed c. 264/3 with various dates from Greek history) puts his death in 407/6 and his birth in 485/4, dates which are as reasonable as any preserved in the sources.