General Information:

• Syllabus

Professor Frey's Transport Phenomena Course Lecture Notes:

·         Part 1: Review of Mathematical Fundamentals

·         Part 2: Basic Concepts in Fluid Mechanics

·         Part 3: Momentum Balance Basics

·         Part 4: General Momentum Balance

·         Part 5: Potential Flow and the Bernoulli Equation

·         Part 6: Creeping Flow

·         Part 7: Special Topics in Fluid Mechanics

·         Part 8: Heat Transfer

·         Part 9: Mass Transfer Basics

·         Part 10: Analogies Between Transport Modes and Film Model of Mass Transfer

·         Part 11: Brownian Motion

Problem Set Assignments in ENCH 630 for Spring 2024:

·         Problem Set 1: Basic Mathematical Methods  (Due 11:59 pm, Feb. 5, 2025)

Selected Course Handouts:

• The Reynolds transport theorem.
• A linear algebra approach to dimensional analysis with applications to the solution of partial differential equations.
• Dimensional Analysis, Modelling, and Invariance. This material is from the book Symmetries and Differential Equations by George W. Bluman and Sukeyuki Kumei
• Properties of Bessel functions. This material, and the material in the three links that follow, comes from the Handbook of Mathematical Functions by Milton Abramowitz and Irene Stegun.
• Properties of the modified Bessel functions I and K.
• Properties of gamma and related functions.
• Properties of hyperbolic functions.
• Brownian motion.
• Centrifugation.
• Electrophoresis.
• Chromatography.
• Spray drying and lyophilization 
• Membrane processes

COMSOL Multiphysics Simulation Software:

• COMSOL Multiphysics company website.  This company produces finite element modeling software for problems involving nearly any kind of chemical and physical process including most types of transport phenomena.
• COMSOL Multiphysics basic tutorial. Part 1.
• COMSOL Multiphysics basic tutorial. Part 2.
• COMSOL Multiphysics basic tutorial. Part 3.
• Example problem for COMSOL tutorial.

Fluid Mechanics Resources:  

• National Committee for Fluid Mechanics Films.  This series of 39 educational fluid mechanics films with accompanying film notes was produced by Ascher Shapiro at MIT in 1961. Despite their age, they definitely rate a "two thumbs up" and are worth viewing.
• Applied Aerodynamics: A Digital Textbook.  An on-line textbook from the Desktop Aerodynamics website that has an especially thorough description of wing theory. 

Heat and Mass Transfer Resouces:

• A Heat Transfer Textbook, 3rd ed.  This excellent textbook written by John H. Lienhard IV at the University of Houston and John H. Lienhard V at MIT can be downloaded for free and covers both heat and mass transfer.    
• Diffusion with Volume Change by R. F. Sekerka.  A thorough discussion of binary diffusion by Robert F. Sekerka at Carnegie Mellon University.    
• Notes on Brownian Motion by Albert Philipse.  This tutorial on Brownian motion was written by Albert Philipse at Utrecht Univerity in The Netherlands..   

Mathematics Tutorials:

• Chain Rule for Partial Derivatives.   A brief tutorial from Harvey Mudd College on this important concept.
• Elementary First Order Ordinary Differential Equations.  Another basic tutorial from Harvey Mudd College on first order ODEs.
• First-Order Ordinary Differential Equations in Applied Mathematics.  This tutorial, as well as the following three tutorials, come from Annette Bunge's applied mathematics course at Colorado School of Mines.
• Second-Order Ordinary Differential Equations.
• Separation of Variables Method for Partial Differential Equations.
• Combination of Variables Method for Partial Differential Equations.
• Symbolic Mathematics Using Matlab.  One option for doing symbolic mathematics on a computer is to use Matlab as described in this tutorial. Another option which might be better is to use Derive as described further below on this webpage.
• Tensors.  This simple tutorial comes from the Mathematical Physics section of the website of James Calvert at the University of Denver.

Class Photographs:

• Spring 2011
• Spring 2012
• Spring 2013
• Spring 2014
• Spring 2015
• Spring 2016
• Spring 2017
• Spring 2018

Additional Links of Interest for ENCH 630 Students:  

Centrifugation:

• Centrifugation tutorial from San Deigo State University

Electrophoresis:

• Electrophoresis tutorial from San Diego State University

Elmer finite element modeling software

• Elmer Software Website.  For those who are on a budget and can't affort COMSOL Multiphysics, Elmer provides a reasonable alternative for performing finite element modeling. Elmer is open source software that is available for free.

Mathematics on-line books

• Handbook of Mathematical Functions.   The classic reference book by Abramowitz and Stegun in an on-line format.

Mathematics websites

• EqWorld: The World of Mathematical Equations.  A thorough collection of solutions to mathematical equations, including most types of differential equations. 
• Wolfram MathWorld.  The (self-proclaimed) most extensive mathematics resource on the web. 
• SOS Mathematics: Basic Calculus.  
• SOS Mathematics: Matrix Algebra.   Learn the basics of matrix algebra.
• SOS Mathematics: Differential Equations.   Good review of methods for solving ODEs.