ChE 686 – Chemical Engineering Analysis

  1998-2000 Catalog Data:      ChE 686 – Chemical Engineering Analysis; 3 credits.

Mathematical modeling of chemical engineering phenomena leading to total and partial differential equations requiring solution by use of series, transforms, as well as by digital computer techniques.  Applications to design and analysis of chemical engineering processes.

  Prerequisite by Topic:

Material and energy balances

Chemical kinetics and reactor design

Fluid flow, heat transfer, mass transfer, and separation operations

Calculus and an elementary course in differential equations

Computer tools and techniques

  Textbook:     R.G.Rice, D.D.Do, Applied Mathematics and Modeling for Chemical Engineers (1995) John Wiley & Sons, Inc., New York NY.

  Course Objectives:  Following this course, students will be able to:

Formulate problems that arise from chemical reactions, transport phenomena, separation operations, and process control

Obtain analytical solutions to finite difference equations arising from stage-wise processing

Obtain analytical solutions to linear or non-linear ordinary differential equations (ODEs), coupled or uncoupled, of first, second, or higher order with constant or variable coefficients

Understand the origins of, and complex solutions to, chaotic systems

Understand the nature of fractals at an introductory level

Obtain analytical solutions to linear partial differential equations (PDEs) via combination of variables, separation of variables, and integral transform techniques

Obtain approximate solutions to ODEs and PDEs via perturbation, weighted residuals, orthogonal collocation, and polynomial approximation techniques

Obtain (approximate) numerical solutions to ODEs and PDEs via finite difference techniques

  Topics Covered:

Formulation of physicochemical problems

Solution techniques for linear and non-linear ordinary differential equations (ODEs) of first, second, and higher order, whether coupled or not

Method of Frobenius for solving linear second order variable coefficient ODEs

Orthogonal functions and integral functions

Finite difference calculus

Inner, outer, and matched perturbation solutions of ODEs

Explicit, implicit, and predictor-corrector numerical solutions of ODEs

Weighted residuals and orthogonal collocation techniques to obtain approximate solutions to ODEs

Laplace, Fourier, and other integral transform techniques for solving linear ODEs or PDEs

Combination of variables and separation of variables techniques for solving linear PDEs

Polynomial approximation, singular perturbation, and orthogonal collocation techniques for solving PDEs

Finite difference solutions of PDEs in rectangular, cylindrical, and spherical coordinate systems

Class Schedule: Class meets 3 hours per week.

Contribution of course to meeting the professional component:

Understanding of advanced mathematical techniques for solving complex problems

Appreciation for approximate answers when rigorous solutions are not obtainable

Appreciation for the need to discover new techniques to advance the state-of-the-art