A numerical primer for the chemical engineer

✍ Scribed by Edwin Zondervan

• Publisher: CRC Press
• Year: 2015
• Tongue: English
• Leaves: 184
• Category: Library

✦ Synopsis

"This book emphasizes the deriviation and use of a variety of numerical methods for solving chemical engineering problems. The algorithms are used to solve linear equations, nonlinear equations, ordinary differential equations and partial differential equations. It also includes chapters on linear- and nonlinear regression and ond optimizaiton. MATLAB is adopted as the programming environment throughout the book. MATLAB is a high performance computing program. An introductory chapter on MATLAB basics has been added and Excel users can find a chapter on the implementation of numerical methods in Excel. Another chapter with worked out exaples are given in the Case study chapter to demonstrate the numerical techniques. Most of the examples were written in MATLAB and are compatible with the latest versions of MATLAB. It is important to mention that the main purpose of this book is to give the students a flavor of numerical methods and problem solving, rather than to be an in depth guide to numerical analysis. The chapters end with small exercises that students can use to familiarize them selves with the numerical methods. The material in this book has been used in undergraduate and graduate courses in the chemical engineering department of Eindhoven University of Technology. To aid lecturers and students course materials have also been made available on the web at http://webpage.com. The author would finally thank everybody who has been helpful and supportive in the creation of this book, especially some of the Ph.D. students at Eindhoven University that have assisted during lectures and directly influenced the content of this book: Juan Pablo Gutierrez, Esayas Barega and Arend Dubbelboer"-- �Read more...

✦ Table of Contents

Content: The role of models in chemical engineering Introduction The idea of a model Model building Model analysis Model solution strategies Summary Exercises Errors in computer simulations Introduction Significant digits Round off and truncation errors Break errors Loss of digits Ill conditioned problems (Un-)stable methods Summary Exercises Linear equations Introduction MATLAB Linear systems The inverse of a matrix The determinant of a matrix Useful properties Matrix ranking Eigenvalues and eigenvectors Spectral decomposition Summary Exercises Elimination methods Introduction MATLAB Gaussian elimination LU factorization Summary Exercises Iterative methods Introduction Laplace's equation LU factorization Iterative methods The Jacobi method Example for the Jacobi method Summary Exercises Nonlinear equations Introduction Newton's method D Newton's method D Reduced Newton step method Quasi Newton's method Summary Exercises Ordinary di erential equations Introduction Euler's method Accuracy and stability of Euler's method The implicit Euler method Stability of the implicit Euler method Systems of ODE's Stability of ODE systems Sti ness of ODE systems Higher order methods Summary Exercises Partial di erential equations 1 Introduction Types of PDE's The method of the lines Stability Summary Exercises Partial di erential equations 2 Introduction Transport PDE's Finite Volumes Discretizing the control volumes Transfer of heat to fluid in a pipe Simulation of the heat PDE Summary Exercises Data regression and curve fitting Introduction The least squares method Residual analysis ANOVA analysis Confidence limits Summary Exercises Optimization Introduction Linear programming Nonlinear programming Integer programming Summary Exercises Basics of Matlab Introduction The Matlab user interface The array structure Basic calculations Plotting Reading and writing data Functions and m-files Repetitive operations Numerical methods in Excel Introduction Basic functions in Excel The Excel solver Solving nonlinear equations in Excel Di erentiation Excel Curve fitting in Excel Case studies Introduction Modeling a separation system Modeling a chemical reactor system PVT behavior of pure substances Dynamic modeling of a distillation column Dynamic modeling of an extraction cascade (ODE's) Distributed parameter models for a tubular reactor Modeling of an extraction column Fitting of kinetic data Fitting of NRTL model parameters Optimizing a crude oil refinery Planning in a manufacturing line Bibliography
Abstract: "This book emphasizes the deriviation and use of a variety of numerical methods for solving chemical engineering problems. The algorithms are used to solve linear equations, nonlinear equations, ordinary differential equations and partial differential equations. It also includes chapters on linear- and nonlinear regression and ond optimizaiton. MATLAB is adopted as the programming environment throughout the book. MATLAB is a high performance computing program. An introductory chapter on MATLAB basics has been added and Excel users can find a chapter on the implementation of numerical methods in Excel. Another chapter with worked out exaples are given in the Case study chapter to demonstrate the numerical techniques. Most of the examples were written in MATLAB and are compatible with the latest versions of MATLAB. It is important to mention that the main purpose of this book is to give the students a flavor of numerical methods and problem solving, rather than to be an in depth guide to numerical analysis. The chapters end with small exercises that students can use to familiarize them selves with the numerical methods. The material in this book has been used in undergraduate and graduate courses in the chemical engineering department of Eindhoven University of Technology. To aid lecturers and students course materials have also been made available on the web at http://webpage.com. The author would finally thank everybody who has been helpful and supportive in the creation of this book, especially some of the Ph.D. students at Eindhoven University that have assisted during lectures and directly influenced the content of this book: Juan Pablo Gutierrez, Esayas Barega and Arend Dubbelboer"