This extended section can be found online at www.cambridge.org/kleinandnellis. The mathematical description of many interesting problems in thermodynamics and other areas of engineering involves ordinary differential equations (ODEs). In some cases, the ordinary differential equations are sufficiently simple that an analytical solution can be derived. However, in most cases this is not possible and therefore numerical solutions to the ODEs is required. This appendix provides an introduction to numerical techniques and a discussion of the use of the Integral command in EES.

Thermodynamics is a mature science. Many excellent engineering textbooks have been written on the subject, which leads to the question: Why yet another textbook on classical thermodynamics? There is a simple answer to this question: this book is different. The objective of this book is to provide engineers with the concepts, tools, and experience needed to solve practical real-world energy problems. With this in mind, the focus of this effort has been to integrate a computer tool with thermodynamic concepts in order to allow engineering students and practicing engineers to tackle problems that they would otherwise not be able to solve.

It is generally acknowledged that students need to solve problems in order to integrate concepts and skills. The effort required to solve a thermodynamics problem can be broken into two parts. First, it is necessary to identify the fundamental relationships that describe the problem. The set of equations that leads to a useful solution to a problem results from application of appropriate balances and rate relations, simplified with justified assumptions. Identifying the necessary equations is the conceptual part of the problem, and no computer program can provide this capability in general. Proper application of the First and Second Laws of Thermodynamics is at the heart of this process. The ability to identify the appropriate equations does not come easily to most thermodynamics students. This is an area in which problem-solving experience is helpful. A distinguishing feature of this textbook is that it presents detailed examples and discussion that explain how to apply thermodynamics concepts identify a set of equations that will provide solutions to non-trivial problems.

This extended section can be found on the website www.cambridge.org/kleinandnellis. Maple is an application that can be used to analytically solve algebraic and differential equations. The capability to differentiate, integrate and algebraically manipulate mathematical expressions in symbolic form can be a very powerful aid in solving many types of engineering problems, including some thermodynamics problems. Maple also provides a very convenient mathematical reference; if, for example, you've forgotten that the derivative of sine is cosine, it is easy to use Maple to quickly provide this information. Therefore, Maple can replace the numerous mathematical reference books that might otherwise be required to carry out all of the integration, differentiation, simplification, etc. that is required to solve many engineering problems. Maple and EES can be used effectively together; Maple can determine the analytical solution to a problem and these symbolic expressions can subsequently be copied (almost directly) into EES for convenient numerical evaluation and manipulation in the context of a specific application. This appendix summarizes the commands that are the most useful for thermodynamics problems.

Introduction

Chemical engineering is the field of applied science that employs physical, chemical, and biochemical rate processes for the betterment of humanity. This is a sweeping statement, and it contains two essential concepts: rate processes and betterment of humanity. The second is straightforward and is at the heart of all engineering. The engineer designs processes and tangible objects that meet the real or perceived needs of the populace. Some civil engineers design bridges. Some mechanical engineers design engines. Some electrical engineers design power systems. The popular perception of the chemical engineer is someone who designs and operates processes for the production of chemicals and petrochemicals. This is an historically accurate (if incomplete) image, but it describes only a small fraction of the chemical engineers of the early twenty-first century.

Let us turn first to the concept of rate processes, which is the defining paradigm of chemical engineering, and consider an example. Everyone is familiar with the notion that medication taken orally must pass through the digestive system and across membranes into the bloodstream, after which it must be transported to the relevant location in the body (a tumor, a bacterial infection, etc.) where it binds to a receptor or reacts chemically. The residual medication is transported to an organ, where it is metabolized, and the metabolic products are transported across still more membranes and excreted from the body, perhaps in the urine.

Introduction

Biotechnology is a major component of modern chemical engineering, and biotechnology appears to many observers to be a new thrust; yet, as noted in Chapter 1, biochemical engineering has been an essential part of chemical engineering since the development of the modern profession in the early part of the twentieth century. One important aspect of biotechnology, in fact its most traditional component, is the use of microorganisms to effect chemical change. We cited the microbiological production of acetone and penicillin as two classic examples in Chapter 1.

In terms of annual throughput, the activated sludge process for wastewater treatment is by far the most widely used biochemical process in the world, and it provides a useful framework for discussing some interesting features of bioreactor design and performance. The entire process flowsheet is shown schematically in Figure 8.1. The wastewater feed contains organic materials, commonly measured in toto as biological oxygen demand (BOD), that are used as nutrients by microorganisms; the organisms produce water and CO2 as metabolic products. The primary settler is there to remove large objects. The heart of the process is the aeration basin; this is a reactor in which a suspension of microorganisms in porous flocs is brought into contact with the BOD. The microorganisms are aerobic, meaning that they require oxygen for metabolism, so air or enriched air is added to keep the oxygen concentration in the water above a critical level of about 2 g/m3 (2 ppm).