A companion book including interactive software for students and professional engineers who want to utilize problem-solving software to effectively and efficiently obtain solutions to realistic and complex problems. An Invaluable reference book that discusses and Illustrates practical numerical problem solving in the core subject areas of Chemical Engineering. Problem Solving in Chemical Engineering with Numerical Methods provides an extensive selection of problems that require numerical solutions from throughout the core subject areas of chemical engineering. Many are completely solved or partially solved using POLYMATH as the representative mathematical problem-solving software, Ten representative problems are also solved by Excel, Maple, Mathcad, MATLAB, and Mathematica. All problems are clearly organized and all necessary data are provided. Key equations are presented or derived. Practical aspects of efficient and effective numerical problem solving are emphasized. Many complete solutions are provided within the text and on the CD-ROM for use in problem-solving exercises.

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Current owners and new purchasers are able to obtain the very latest and significantly improved Educational Version of the POLYMATH Numerical Analysis Software at 1/2 of the usual Educational price.

POLYMATH is a proven computational system, which has been specifically created for educational or professional use. The various POLYMATH programs allow the user to apply effective numerical analysis techniques during interactive problem solving on personal computers. Results are presented graphically for easy understanding and for incorporation into papers and reports. Students, engineers, mathematicians, scientists, or anyone with a need to solve problems will appreciate the efficiency and speed of problem solution. The Version 5 software has been completely revised and reprogrammed for 32-bit WindowsTM operating systems. Capabilities include: Linear Equations (up to 200 with up to 64 via easy input), Nonlinear Equations (up to 200), Differential Equations (up to 200), Data Analysis and Regression (up to 600 data points)

Preface

Intended Audience

This book is for the chemical engineering student or the professional engineer who is interested in solving problems that require numerical methods by using mathematical software packages on personal computers. This book provides many typical problems throughout the core subject areas of chemical engineering. Additionally, the "nuts and bolts" or practical applications of numerical methods are presented in a concise form during example problem solving, which gives detailed solutions to selected problems.

Background

The widespread use of personal computers has led to the development of a variety of tools that can be utilized in the solution of engineering problems. These include mathematical software packages like MathCAD, Maple, Mathematica, Matlab,Polymath, and spreadsheets like Excel. While there is great potential in the hands of individual PC users, often this potential is not well developed in current engineering problem solving.

In the past the computer was used only for the difficult tasks of rigorous modeling and simulation of unit operations, processes, or control systems, while the routine calculations were carried out using hand-held calculators (or spreadsheet programs more recently), using essentially the same techniques that were used in the slide rule era. Limiting the use of the computer solely to the difficult tasks was justified before the introduction of interactive numerical packages because the use of the computer was very time consuming. A typical computer assignment in that era would require the student to carry out the following tasks: (1) Derive the model equations for the problem at hand, (2) find an appropriate numerical method to solve the model, (3) write and debug a FORTRAN program to solve the problem using the selected numerical algorithm, and (4) analyze the results for validity and precision.

It was soon recognized that the second and third tasks of the solution were minor contributions to the learning of the subject matter in most chemical engineering courses, but they were actually the most time consuming and frustrating parts of a computer assignment. The computer enables students to solve realistic problems, but the time spent on the technical details that were of minor relevancy to the subject matter was much too long.

The introduction of interactive numerical software packages brought about a major change in chemical engineering calculations. This change has been called a "paradigm shift" by Fogler.2 Using those packages the student's (or the practicing engineer's) main task is to set up the model equations. The interactive program provides accurate solutions to these equations in a short time, displaying the results in graphical and numerical forms. The meaning of the paradigm shift, however, is that using the old calculation techniques with the new computer tools brings very little benefit. This is emphasized in the following observation made by deNevers and Seader1: "Since the advent of digital computers, textbooks have slowly migrated toward computer solutions of examples and homework problems, but in many cases the nature of the examples and problems has been retained so that they can be solved with or without a computer."

In most of the examples and problems provided in this book, new solution techniques are presented that require the use of the computer. Thus the full benefits of a computer solution can be gained even for routine, simple problems, not just for complicated ones.

In spite of many available numerical problem-solving packages, advanced problem solving via personal computers continues to be under utilized in chemical engineering education. A recent survey by Jones5 has indicated that "across the country, computers are usually not used effectively in undergraduate engineering science courses. Often they are not used at all. Problem solving approaches and calculation methods are little influenced by the availability of computers." There are several major reasons for this situation.

First, many of the current engineering textbooks and reference books have been very slow to react to the enhanced problem-solving capabilities that are currently available. Unfortunately, the current textbooks in most engineering subject areas have been slow to react to this emerging capability. The lack of properly framed standard problems in various engineering disciplines is accompanied by a lack of faculty interest in the use of new tools and the creation of appropriate problems that utilize these tools.

Another important reason for the lack of mathematical software usage for advanced problem solving is the actual cost of the software for individual students. While there are many educational benefits to having problem solving close at hand on student-owned personal computers, often the cost to the individual students is prohibitively high. Fortunately, the costs to major colleges and universities for site licenses for the use of software only in computer labs is much more reasonable. However, this pricing structure forces students to use problem-solving software only in computer labs and does not allow interactive use of the software at other locations. Thus advanced problem-solving capabilities are not currently as close at hand as the nearest personal computer.

Finally, there is a significant learning curve to most of the advanced problem-solving software. This requires users to become familiar with a command structure that is often not intuitive and thus difficult to use. This is a significant impediment to student, professional, and faculty use of many packages.

Purposes of This Book

The main purpose of this book is to provide a comprehensive selection of chemical engineering problems that require numerical solutions. Many problems are completely or partially solved for the reader. This text is intended to be supplementary to most of the current chemical engineering textbooks, which do not emphasize numerical solutions to example and posed problems. This book is highly indexed, as indicated in Tables 1-9 at the end of this preface. The reader can only consider a particular subject area of interest or the application of a particular numerical method in actual problem solving. In either area, problems or methods, the book gives concise and easy-to-follow treatments.

The problems are presented in a general way so that various numerical problem-solving computer packages can be utilized. Many of the problems are completely solved so as to demonstrate a particular problem-solving approach. In other cases, problem-solving skills of the reader need to be applied. This book has been designed for use with any mathematical problem solving package. The reader is encouraged to use the mathematical software package of his or her choice to achieve problem solutions. However, the POLYMATH package has been used as an example package, and a complete version of POLYMATH is included in the CD-ROM that accompanies this text. This allows the convenient use of POLYMATH throughout the book, as many of the problems have some part of the solution in POLYMATH files that are available on the CD-ROM.

General Problem Format

All problems presented in the book have the same general format for the convenience of the reader. The concise problem topic is first followed by a listing of the chemical engineering concepts demonstrated by the problem. Then the numerical methods utilized in the solution are indicated just before the detailed problem statement. Typically a particular problem presents all of the detailed equations that are necessary for solution, including the appropriate units in a variety of systems, with Système International d'Unités (SI) being the most commonly used. Physical properties are either given directly in the problem or in the appendices.

Students

Students will find the chapter organization of the book, by chemical engineering subject areas, to be convenient. The problems are organized in the typical manner in which they are covered in most courses. Complete solutions are given to many of the problems that demonstrate the appropriate numerical methods in problem solving. Practice and application of various numerical methods can be accomplished by working through the problems as listed in Table 9.

Practicing Engineers

Engineers in the workplace face ever-increasing productivity demands. Thus the concise framework of the problems in this book should aid in the proper formulation of a problem solution using numerical methods.

Faculty

This book can assist faculty members in introducing numerical methods into their courses. This book is intended to provide supplementary problems that can be assigned to students. Many of the problems can be easily extended to open-ended problem solving so that critical thinking skills can be developed. The numerical solutions can be used to answer many "what if º " type questions so students can be encouraged to think about the implications of the problem solutions.

Chemical Engineering Departments

Departments are encouraged to consider adopting this book during the first introductory course in chemical engineering and then utilize the book as a supplement for many of the following courses in the curriculum. This allows an integrated approach to the use of numerical methods throughout the curriculum. This approach can be helpful in satisfying the Accreditation Board for Engineering and Technology (ABET) requirements for appropriate computer use in undergraduate studies. A first course in numerical methods can also utilize many of the problems as relevant examples. In this application, the book will supplement a standard numerical methods textbook. Students will find the problems in this book to be more interesting than the strictly mathematical or simplified problems presented in many standard numerical analysis textbooks.

Educational Resources on CD-ROM

A CD-ROM is provided that contains additional learning resources including a complete operational version of the POLYMATH Numerical Computation Package which can be installed on a reader's personal computer to enable efficient interactive problem solving. All illustrative solved problems are available from the CD-ROM for execution and modification using POLYMATH. Ten representative book problems have also been solved by knowledgeable professionals with Excel, Maple, Mathcad, Mathematica, MATLAB, and POLYMATH. Detailed writeups and the files to solve these problems with these packages are included on the CD-ROM. The icon at the beginning of this paragraph is used to designate a CD-ROM resource throughout the book. For many problems, tabulated data for individual problems are provided as input files to POLYMATH, thereby eliminating time-consuming data entry. The complete details on the CD-ROM are given in Appendix F.

Book Organization

Chapter 1, "Basic Principles and Calculations," serves a dual purpose. The chapter introduces the reader to the subject material that is typically taught in a first chemical engineering course (in most universities called Material and Energy Balance, or Stoichiometry). Additionally, this chapter introduces numerical solutions that are presented using the POLYMATH Numerical Computation Package. This material can also be used in a separate "Introduction to Personal Computers" course that can be given in parallel to the first chemical engineering course. For the past three years at Ben-Gurion University, the material from Chapter 1 of this book has been taught in the second semester of the first year, in parallel with the second part of the material and energy balance course. The students are introduced to the POLYMATH software in two two-hour lectures and two one-hour computer lab sessions. During the lectures and lab sessions, Problems 1.1, 1.3 and 1.13 are presented to introduce students to the different programs of POLYMATH. After this workshop, students are expected to use POLYMATH without additional help.

Chapters 2 and 3 are not associated with any particular required course in the chemical engineering curriculum. Chapter 2, "Regression and Correlation of Data," presents advanced statistical techniques for regression of experimental data. Students can be encouraged to complete this chapter as part of a statistics course or as preparation for the chemical engineering laboratory. Chapter 3, "Advanced Techniques in Problem Solving," provides the background necessary for solution of more complicated problems, such as stiff differential equations, two-point boundary value problems, and systems of differential-algebraic equations using interactive numerical software packages. This chapter can be integrated into the curriculum or covered as part of a separate numerical analysis course. The titles of the remaining chapters clearly indicate in which courses the problems can be used.

The fully or partially solved problems demonstrate solution methods that are not included in regular textbooks. Some of them also show advanced solution techniques that may not be obvious to the casual user. Table 3 lists these special techniques and the problem numbers in which they are demonstrated or required.

Book Notation

Because of the wide variety of problems posed in this book, the notation used has been standardized according to one of the major Prentice Hall textbooks in the various subject areas whenever possible. These books are summarized in Table 10.

The POLYMATH Numerical Computation Package

We have authored the POLYMATH package to provide convenient solutions to many numerical analysis problems, including the chemical engineering problems that are presented in this book. The first PC version of POLYMATH was published in 1984, and it has been in use since then in over one hundred universities and selected industrial sites mainly in the United States and Israel. The initial version included with this book, POLYMATH 4.02, was released in May of 1998. This version executes in computers with DOS (and Windows) operating systems. The package contains the following programs:

Ordinary Differential Equations Solver

Nonlinear Algebraic Equations Solver

Linear Algebraic Equations Solver

Polynomial, Multiple Linear, and Nonlinear Regression Program

The programs are extremely easy to use, and all options are menu driven. Equations are entered in standard form with user-defined notation. Results are presented in graphical or tabular form. No computer language is used, and a manual is not required. All problems can be stored on disk for future use. A sophisticated calculator and a general unit conversion utility are available from within POLYMATH upon request.

Current information on the latest POLYMATH software is available from polymath-software/.

Web Site:

polymath-software/book

This site on the World Wide Web (WWW) will be maintained by the book authors to provide any corrections or updates to this book. The site will also provide information about where the CD-ROM may be reordered in the event that it has become damaged, outdated, or lost. Details on the latest POLYMATH software will also be available on the WWW, allowing inexpensive software upgrades to be downloaded. Additionally, the site may provide computer files for various solved prob...

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