3rd Edition

Applied Mathematical Methods for Chemical Engineers

By Norman W. Loney Copyright 2015
    566 Pages 47 B/W Illustrations
    by CRC Press

    Focusing on the application of mathematics to chemical engineering, Applied Mathematical Methods for Chemical Engineers addresses the setup and verification of mathematical models using experimental or other independently derived data. The book provides an introduction to differential equations common to chemical engineering, followed by examples of first-order and linear second-order ordinary differential equations. Later chapters examine Sturm–Liouville problems, Fourier series, integrals, linear partial differential equations, regular perturbation, combination of variables, and numerical methods emphasizing the method of lines with MATLAB® programming examples.

    Fully revised and updated, this Third Edition:

    • Includes additional examples related to process control, Bessel Functions, and contemporary areas such as drug delivery
    • Introduces examples of variable coefficient Sturm–Liouville problems both in the regular and singular types
    • Demonstrates the use of Euler and modified Euler methods alongside the Runge–Kutta order-four method
    • Inserts more depth on specific applications such as nonhomogeneous cases of separation of variables
    • Adds a section on special types of matrices such as upper- and lower-triangular matrices
    • Presents a justification for Fourier-Bessel series in preference to a complicated proof
    • Incorporates examples related to biomedical engineering applications
    • Illustrates the use of the predictor-corrector method
    • Expands the problem sets of numerous chapters

    Applied Mathematical Methods for Chemical Engineers, Third Edition uses worked examples to expose several mathematical methods that are essential to solving real-world process engineering problems.

    Differential Equations
    Model Development

    First-Order Ordinary Differential Equations
    Linear Equations
    Additional Information on Linear Equations
    Nonlinear Equations
    Problem Setup

    Linear Second-Order and Systems of First-Order Ordinary Differential Equations
    Fundamental Solutions of Homogeneous Equations
    Homogeneous Equations with Constant Coefficients
    Nonhomogeneous Equations
    Variable Coefficient Problems
    Alternative Methods
    Applications of Second-Order Differential Equations
    Systems of First-Order Ordinary Differential Equations

    Sturm–Liouville Problems
    Classification of Sturm–Liouville Problems
    Eigenfunction Expansion

    Fourier Series and Integrals
    Fourier Coefficients
    Arbitrary Interval
    Cosine and Sine Series
    Convergence of Fourier Series
    Fourier Integrals

    Partial Differential Equations
    Separation of Variables
    Nonhomogeneous Problem and Eigenfunction Expansion
    Laplace Transform Methods
    Combination of Variables
    Fourier Integral Methods
    Regular Perturbation Approaches

    Applications of Partial Differential Equations in Chemical Engineering
    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

    Dimensional Analysis and Scaling of Boundary Value Problems
    Classical Approach to Dimensional Analysis
    Finding the Πs
    Scaling Boundary Value Problems

    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
    Numerical Solution of Partial Differential Equations

    Elementary Properties of Determinants and Matrices
    Numerical Method of Lines Example Using MATLAB®
    Program for a Transport and Binding Kinetics Model of an Analyte
    Programmed Model of a Drug Delivery System


    Norman W. Loney is professor and was department chair of the Otto H. York Department of Chemical, Biological and Pharmaceutical Engineering at New Jersey Institute of Technology (NJIT). He has authored or coauthored more than 70 publications and presentations related to the use of applied mathematics to solve transport phenomena-related problems in chemical engineering since joining the department in 1991. Dr. Loney has been awarded several certificates of recognition from the National Aeronautics and Space Administration and the American Society for Engineering Education for research contributions. He has also been honored with the Newark College of Engineering Teaching Excellence award, the Saul K. Fenster Innovation in Engineering Education award, and the Excellence in Advising award. Dr. Loney is a fellow of the American Institute for Chemical Engineers. Prior to joining NJIT, Dr. Loney, a licensed professional engineer, practiced engineering at Foster Wheeler, M.W. Kellogg Company, Oxirane Chemical Company, and Exxon Chemical Company.