Applied Mathematical Methods for Chemical Engineers, Second Edition

Focusing on the application of mathematics to chemical engineering, Applied Mathematical Methods for Chemical Engineers, Second Edition addresses the setup and verification of mathematical models using experimental or other independently derived data. An expanded and updated version of its well-respected predecessor, this book uses worked examples to illustrate several mathematical methods that are essential in successfully solving process engineering problems. The book first provides an introduction to differential equations that are common to chemical engineering, followed by examples of first-order and linear second-order ordinary differential equations (ODEs). Later chapters examine Sturm–Liouville problems, Fourier series, integrals, linear partial differential equations (PDEs), and regular perturbation. The author also focuses on examples of PDE applications as they relate to the various conservation laws practiced in chemical engineering. The book concludes with discussions of dimensional analysis and the scaling of boundary value problems and presents selected numerical methods and available software packages. New to the Second Edition · Two popular approaches to model development: shell balance and conservation law balance · One-dimensional rod model and a planar model of heat conduction in one direction · Systems of first-order ODEs · Numerical method of lines, using MATLAB® and Mathematica where appropriate This invaluable resource provides a crucial introduction to mathematical methods for engineering and helps in choosing a suitable software package for computer-based algebraic applications.

Table of Contents:
DIFFERENTIAL EQUATIONS Introduction Ordinary Differential Equations Model Development References FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS Linear Equations Additional Information on Linear Equations Nonlinear Equations Problem Setup Problems References LINEAR SECOND-ORDER AND SYSTEMS OF FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS Introduction Fundamental Solutions of the Homogeneous Equation Homogeneous Equations with Constant Coefficients Nonhomogeneous Equations Variable Coefficient Problems Alternative Methods Summary Applications of Second-Order Differential Equations Systems of First-Order Ordinary Differential Equations Problems References STURM–LIOUVILLE PROBLEMS Introduction Classification of Sturm–Liouville Problems Eigenfunction Expansion Problems References FOURIER SERIES AND INTEGRALS Introduction Fourier Coefficients Arbitrary Interval Cosine and Sine Series Convergence of Fourier Series Fourier Integrals Problems References PARTIAL DIFFERENTIAL EQUATIONS Introduction Separation of Variables The Nonhomogeneous Problem and Eigenfunction Expansion Laplace Transform Methods Combination of Variables Fourier Integral Methods Regular Perturbation Approaches Problems References APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS IN CHEMICAL ENGINEERING Introduction Heat Transfer Mass Transfer Comparison between Heat and Mass Transfer Results Simultaneous Diffusion and Convection Simultaneous Diffusion and Chemical Reaction Simultaneous Diffusion, Convection, and Chemical Reaction Viscous Flow Problems References DIMENSIONAL ANALYSIS AND SCALING OF BOUNDARY VALUE PROBLEMS Introduction A Classical Approach to Dimensional Analysis Finding the Πs Scaling Boundary Value Problems Problems References SELECTED NUMERICAL METHODS AND AVAILABLE SOFTWARE PACKAGES Introduction and Philosophy Solution of Nonlinear Algebraic Equations Solution of Simultaneous Linear Algebraic Equations Solution of Ordinary Differential Equations Solution of Partial Differential Equations Summary Problems References APPENDIX A APPENDIX B INDEX