Transport Analysis

It has been my experience in teaching graduate and undergraduate courses that if the students are conversant with the pertinent mathematical proce­ dures, and can "think mathematically," there is almost no limit to their comprehension. Most courses that are considered difficult by students are either poorly taught or require a degree of mathematical sophistication that the students do not possess. In Transport Analysis, J have culled some basic momentum transport (fluid flow) and mass transport phenomena and explicitly revealed the derivation of the governing equations. There is no mystery, no omitted steps or "it can be shown" phrases that are usually the bane of the student. There are chapters that review basic calculus, vector and matrix concepts, Laplace transform operations, and finite difference calculus. Ordinary dif­ ferential and partial differential equations are derived and solved. This book is intended for undergraduates and graduate students in engineering, chemistry, physics, and even biology and medicine. It is also intended for my non-engineering colleagues with whom I have collaborated during our cooperative research in the life sciences. If they knew what is contained in Transport Analysis, they probably wouldn't need me. v Acknowledgments To Barbara and Michael, who helped keep me alert, happy, and ful­ filled. To Barbara, who deserves belated thanks for doing the drawings in E1'eryday Science. To Anne Hagedorn, thanks for doing some of the typing. To Gerry Denterlein, thanks for keeping tabs on the drawings. I. Introduction.- 1. Some Mathematical Concepts.- 1.1. Elementary Transport Concepts.- 1.2. Elementary Calculus Concepts.- 1.3. Some Elementary Vector and Tensor Operations.- 1.4. Linear Operations with Functions, Vectors, and Matrices.- 1.5. Matrix Solutions of Sets of Linear Equations.- 1.6. Matrix Solutions of Linear Simultaneous Differential Equations.- Assignments.- Further Reading.- 2. Laplace Transforms.- 2.1. Definitions and Basic Operations.- 2.2. The Inverse Laplace Transform.- 2.3. Application of Laplace Transforms to Ordinary Differential Equations.- 2.4. Application of Laplace Tra Front Matter....Pages i-x Front Matter....Pages 1-1 Some Mathematical Concepts....Pages 3-30 Laplace Transforms....Pages 31-86 Front Matter....Pages 87-87 Derivation of the Momentum Transport Equations....Pages 89-109 Transport Analysis in Fluid Flow Phenomena....Pages 111-183 Derivation of the Mass Transport Equations....Pages 185-206 Transport Analysis in Mass Transport Phenomena....Pages 207-296 Front Matter....Pages 297-297 Finite Difference Calculus....Pages 299-326 Transport Analysis in Cascaded Systems....Pages 327-350 Back Matter....Pages 351-353