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Book Overview This book provides extensive problem-solving instruction and suggestions, numerous examples, and many complete and partial solutions in the main sub- ject areas of chemical and biochemical engineering and related disciplines. Prob- lem solutions are clearly developed using fundamental principles to create mathematical models. An equation-oriented approach that enables computer- based problem solving on personal computers is utilized. Efficient and effective problem solving is introduced employing numerical methods for linear equations, nonlinear equations, ordinary and partial differential equations, linear and non- linear regressions, and polynomial curve fitting. Basic to advanced problem solv- ing is covered utilizing a novel integrated approach with three widely used mathematical software packages: POLYMATH, Excel, and MATLAB. Readers may choose to focus on one or more of these software packages or utilize another mathematical software package. The book and a dedicated web site ( www.problemsolvingbook.com ) fur- nish all necessary problem information, software files, and additional enrich- ment materials. For advanced applications, unique software tools are provided for solving complex problems such as parameter estimation in dynamic systems and solution of constrained systems of algebraic equations.
Intended Audience This book is intended for individuals who are interested in solving problems in chemical and biochemical engineering and in related fields by using mathemati- cal software packages on personal computers. It can serve as a textbook for stu- dents in conjunction with college- and university-level courses, and it can be a companion reference book for individual students. For professionals, it can be an invaluable reference book that also allows extensive self-study in problem solv- ing using the most widely used software packages.
Background Prior to the introduction of the personal computers and mathematical software packages in the early 1980’s, desktop calculations for engineering problem solv- ing were mainly carried out with hand-held calculators. Sometimes mainframe computers were utilized, which required source code programming. Since then the emphasis has gradually moved to computer-based (or computer-enhanced) problem solving or CBPS on desktop or notebook computers. By the time the first edition of this book was published in 1999, it became evident that CBPS can be a
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very important, or possibly the most important, application of the computer in scientific and engineering education and in industrial practice. The first edition of this book provided examples to the use of CBPS in core chemical engineering subject areas using the POLYMATH software package. Shortly after the publication of the first edition, we carried out several compari- son studies in order to determine what types of software packages should be included in the “toolbox” of the engineering student and the practicing engineer that would enable the effective and efficient solution of practical problems. We arrived at the conclusion that three types of software are needed. There is a need for a numerical problem solver, such as POLYMATH, that accepts the model equations close to their mathematical forms and provides their numerical solu- tion with very minimal user intervention. Additionally, there is also a need to be able to use spreadsheet software, such as Excel, because of its wide use in busi- ness and industry. Software like Excel is also used for the organization and pre- sentation of information in tabular and graphical forms and for database management-related operations. Software packages that support programming, such as MATLAB, are needed to implement algorithms which are required in graduate research and advanced mathematics, programming, control, and numerical analysis courses. It is increasingly important for today’s engineering student and forward- looking engineering professionals to be proficient in the use of several software packages, and thus we greatly expanded the book so that it now includes solu- tions in Excel and MATLAB, in addition to POLYMATH. New problems have been introduced that demonstrate how the special capabilities of each of these packages can best be utilized for efficient and effective problem solving.
The POLYMATH Numerical Computation Package The POLYMATH package provides convenient solutions to most numerical anal- ysis problems, including the problems that are presented in this book. We authored and published the first PC version of POLYMATH in 1984, and it has been in use since then in over one hundred universities and selected industrial sites world wide. The version available at the time of the publication of the book, POLYMATH 6.1, was released in 2006. This 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. Equa- tions are entered in standard form with user-defined notation. Results are pre- sented in graphical or tabular form. A sophisticated calculator and a general unit conversion utility are available within POLYMATH. The new and unique capability of the latest POLYMATH to automatically export any problem to Excel and MATLAB with a single keypress is extensively
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Engineering faculty can use the book to introduce numerical methods into an individual course, a sequence of courses, or an entire departmental curricu- lum. This book provides supplementary problems that can be assigned to stu- dents in order to introduce numerical problem solving which is avoided in most textbooks. 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 ” type questions so that students can be encouraged to think about the implications of the problem solutions. The book can also be used as a companion textbook for an introductory computer program- ming course or a comprehensive course in numerical analysis.
Book Organization
All the chapters of the book, except the introductory Chapter 1, are built around problems that serve to provide practical applications in a particular subject area. Most of the problems presented in the book have the same general format for the convenience of the reader. The concise problem topic is followed by a listing of the engineering concepts demonstrated by the problem. Then the numerical methods utilized in the solution are indicated just before the detailed problem statement. Each of the problems presents the detailed equations and parameter values that are necessary for solution, including the appropriate units in a variety of sys- tems, with Systéme International d’Unités (SI) being the most commonly used. 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. Physical properties are either given directly in the problem or in the appendices.
The book is divided into two parts. In the first part, which includes the first six chapters, subjects of general interest are presented, some on an introductory level and some on an advanced level. In Chapter 1, Introduction, the history of CBPS is briefly reviewed and guidelines are provided for categorizing problems according to the numerical techniques that should be used for their solution. Chapter 2, 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 demonstrates the use of POLYMATH for solving simple problems belonging to the main categories dis- cussed in the book, namely single nonlinear algebraic equations, systems of lin- ear algebraic equations, linear and polynomial regression, and systems of ordinary differential equations (ODEs). In Chapter 3, Regression and Correla- tion of Data, the application of POLYMATH for analysis and regression of data using advanced statistical techniques is demonstrated. Chapter 4, Problem Solv- ing with Excel, introduces the reader to the engineering and scientific problem solving capabilities of Excel using problems belonging to the same categories as in Chapter 2. The automatic export capabilities of POLYMATH to Excel are dis- cussed. More advanced topics such as solution of systems of nonlinear algebraic equations (NLEs) and optimization with constraints (nonlinear programming) are also presented. In Chapter 5, Problem Solving with MATLAB, MATLAB is
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used to solve the problems presented in Chapter 4. The capability of POLY- MATH to automatically generate MATLAB m-files are presented and provided templates for MATLAB problem solutions are demonstrated and utilized. In Chapter 6, Advanced Techniques in Problem Solving, the problem solutions deal with advanced topics such as two-point boundary value problems, systems of dif- ferential-algebraic equations, partial differential equations, and parameter esti- mation in systems of differential equations. The second part of the book (Chapters 7 through 14) is organized according to the particular subject areas such as Thermodynamics (Chapter 7), Fluid Mechanics (Chapter 8), and so forth. The content of these chapters is presented in the typical order of coverage in college or university-level courses.
New Content in the Second Edition The contents of the book were almost doubled by adding six new chapters to the eight chapters of the first edition. The introductory Chapter 1 was added in order to help the reader in a very critical step of the problem solving—the character- ization of the problem in terms of the solution method that has to be used. After studying and verifying the importance of various software packages in effective and efficient problem solving, the two chapters dealing with the use of Excel and MATLAB were added. These chapters also introduce the new capa- bility of the POLYMATH software to automatically convert a problem solution into Excel worksheets and MATLAB m-files. This considerably shortens the learning curve associated with the initial use of these packages. Since the first edition was published, biochemical engineering has gained importance and is now being taught in most colleges and universities. The new bio- chemical engineering chapter and selected problems in other chapters provide a wide selection of problems in this important subject area. New chapters on “Phase Equilibria and Distillation” (Chapter 12) and “Process Dynamics and Control” (Chapter 13) have been added.
Companion Web Site Readers of the book are encouraged to make full use of the companion web site that will be maintained and extended by the book’s authors. This web site enable downloads of programs files which are used in the various book chapters for the three software packages: POLYMATH, Excel, and MATLAB. Additional educational problems, learning resources, corrections and updates to this book, and new materials are provided.
www.problemsolvingbook.com/ The web site also allows book owners to purchase and immediately down- load the latest POLYMATH software at significant discounts from the already highly discounted POLYMATH Educational version software. This enables book users to have the very latest software at very reasonable cost. Instructors who are using the book have special access to all problems as well as substantial educational and enrichment materials through the compan- ion web site. This include suggestions as to the book use in individual courses, sequences of courses, and throughout a departmental curriculum. Details about this access are provided in Chapter 1 from the authors.
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13. Process Safety: References No. 7, 10, and 12 in Table 1. 14. Environmental Engineering: Reference No. 11 in Table 1. 15. Introduction to Computer Based Problem Solving: This course can compli- ment or replace the traditional programming course. This book can serve as the primary textbook for such a course. Content can include Chapters 1 and 2, Problems 3.3, 3.4, 3.5, 3.6, 4.1, 4.2, 4.4, 5.1, 5.2, and 5.4. Problems 2. and 8.8 can be used to introduce NLEs and ODEs at the introductory level as replacements for Problems 4.3 and 5.3.
Table 1 Additional Problem References
No. Title and Reference 1 “Exothermic CSTR’s—Just How Stable are the Multiple Steady States?” Chem. Eng. Educ. , 28 (1), 30-35 (1994).
2 “Numerical Experiments in Fluid Mechanics with a Tank and Draining Pipe,” Comput. Appl. Eng. Educ , 2 (3), 175-183 (1994).
3 “Correlation and Over-correlation of Heterogeneous Reaction Rate Data,” Chem. Eng. Educ. , 29 (1) 22-25, 45 (1995).
4 “The Wind-Chill Paradox: Four Problems in Heat Transfer,” Chem. Eng. Educ. , 30 (4), 256-261 (1996).
5 “Replacing the Graph Paper by Interactive Software in Modeling and Analysis of Experimental Data,” Comput. Appl. Eng. Educ. , 4 (3), 241-251 (1996).
6 “What To Do If Relative Volatilities Cannot Be Assumed To Be Constant?—Differen- tial-Algebraic Equation Systems in Undergraduate Education,” Chem. Eng. Educ. , 31 (2), 86-93 (1997).
7 “Prediction and Prevention of Chemical Reaction Hazards—Learning by Simulation,” Chem. Eng. Educ. , 35 (4), 268-273 (2001).
8 Letter to the Editor Concerning “An Undergraduate Course in Applied Probability and Statistics,” Chem. Eng. Educ. , 36 (4), 263, 277 (2002).
9 “An Exercise for Practicing Programming in the ChE Curriculum—Calculation of Thermodynamic Properties Using the Redlich-Kwong Equation of State,” Chem. Eng. Educ. , 27 (2), 148 (2003).
10 Letter to the Editor Concerning “Evaluations of Kinetic Parameters and Critical Run- away Conditions in the Reaction System of Hexamine-Nitric Acid to Produce RDX in a Non-Isothermal Batch Reactor,” Journal of Loss Prevention in the Process Indus- tries , 17 (6), 513-514 (2004). 11 “Applications of Mathematical Software Packages for Modeling and Simulations in Environmental Engineering Education,” Environment Modeling and Software , 20 , 1307-1313 (2005).
12 “Combining HAZOP with Dynamic Simulation—Applications for Safety Education,” Journal of Loss Prevention in the Process Industries, 19 , 754 (2006).
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Chemical and Biochemical Engineering Departments Academic departments are encouraged to consider adopting this book during the first introductory course in chemical and/or biochemical engineering and then utilizing the book as a supplement for many of the following courses in the cur- riculum. This allows an integrated approach to the use of numerical methods throughout the curriculum. This approach can be helpful in satisfying the 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 pre- sented in many standard numerical analysis textbooks.
Acknowledgments We would like to express our appreciation to our wives and families who have shared the burden of this effort which took longer than anticipated to complete. We particularly thank Professor H. Scott Fogler for his encouragement with this book effort and with the continuing development of the POLYMATH package. Many thanks are due to Professor Neima Brauner for her help in developing many of the problems. Additionally, we appreciate the input and many suggestions of our stu- dents, who have been subjected to preliminary versions of the problems and have endured the various pre-release versions of the POLYMATH software over the years. During the twenty-three years that POLYMATH has been in use, many of our colleagues provided advice and gave us help in revising and improving this software package. In particular, we would like to acknowledge the assistance of Professors N. Brauner, B. Carnahan, D. J. Cooper, H. S. Fogler, D. M. Himmel- blau, D. S. Kompala, S. E. LeBlanc, E. M. Rosen, and J. D. Seader. H. S. Fogler has also provided some of the problems included in the book. Continuing development of the POLYMATH program has been a continu- ing process. The initial programming and algorithm implementations were car- ried out and maintained for the first ten years by Orit Shacham. She spent many hours and most of her vacations fixing bugs and writing new code for still another version of POLYMATH. She always amazed us by the speed and preci- sion with which she converted ideas into computer code. For the last seven years, POLYMATH has been coauthored and pro- grammed by Michael Elly. He has developed a very intuitive and user-friendly interface for interactive problem solving. He has also exhibited a unique capabil- ity for effectively implementing rather difficult algorithmic challenges. His cre- ativity, organization, speed, and accuracy continue to impress us. We are happy to have him as a continuing member of our team. The first draft of the first edition this book was typed (and retyped) by Michal Shacham. She took several months of vacation from her job to learn to use various word processors and graphical programs. The draft she typed became the basis for class testing and refinement of the book. Nancy Neborsky
