Transport Analysis

357 Pages·1973·5.129 MB·English

by  Daniel Hershey (auth.)

TRANSPORT ANALYSIS
TRANSPORT ANALYSIS '
Daniel Hershey
Department of Chemical Engineering
University of Cincinnati
Cincinnati, Ohio
A PLENUM/ROSETTA EDITION
Library of Congress Cataloging in Publication Data
Hershey, Daniel.
Transport analysis.
"A Plenum/Rosetta edition."
Includes bibliographical references.
1. Transport theory. I. Title.
[TP156.T7H47 1974] 660.2'842 73-23098
ISBN-13: 978-1-4615-8087-4 e-ISBN-13: 978-1-4615-8085-0
DOl: 10.1007/978-1-4615-8085-0
A Plenum I Rosetta Edition
Published by Plenum Publishing Corporation
227 West 17th Street, New York, N.Y. 10011
First paperback printing 1974
© 1973 Plenum Press, New York
A Division of Plenum Publishing Corporation
United Kingdom edition published by Plenum Press, London
A Division of Plenum Publishing Company, Ltd.
4a Lower John Street, London WIR 3PD, England
All rights reserved
No part of this publication may be reproduced in any form without
written permission from the publisher
Preface
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, I 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
Everyday Science.
To Anne Hagedorn, thanks for doing some of the typing.
To Gerry DenterIein, thanks for keeping tabs on the drawings.
To Edna Penn, special thanks for invaluable assistance in typing and
in many other ways.
vi
Contents
Part I. Introduction
Chapter 1. Some Mathematical Concepts
1.1. Elementary Transport Concepts 3
1.2. Elementary Calculus Concepts . . 5
1.3. Some Elementary Vector and Tensor Operations 9
1.4. Linear Operations with Functions, Vectors, and Matrices. 15
1.5. Matrix Solutions of Sets of Linear Equations . . . .. 19
1.6. Matrix Solutions of Linear Simultaneous Differential Equa-
tions .... 23
Assignments . . 29
Further Reading 30
Chapter 2. Laplace Transforms
2.1. Definitions and Basic Operations. . . . . . . . . . .. 31
2.2. The Inverse Laplace Transform ........... 36
2.3. Application of Laplace Transforms to Ordinary Differential
Equations . . . . . . . . . . . . . . . . . . . .. 38
2.4. Application of Laplace Transforms to Partial Differential
Equations . . . . . . . . . . . . . . . . . . . .. 42
2.5. Laplace Transforms Applied to Other Equation Forms.. 46
2.6. Complex Variables Applied to the Inverse Laplace Transform 50
2.7. Inverse Laplace Transforms by Integration in the Complex
Plane . . . . . . . . . . . . . . . . . 60
2.8. Solution of Partial Differential Equations . . -72
2.9. Laplace Transforms and Nonlinear Equations 78
Assignments . . 83
Further Reading . . . . 86
vii
viii Contents
Part II. Transport Analysis in Continuous Processes
Chapter 3. Derivation of the Momentum Transport Equations
3.1. The Equation of Continuity (Material Balance) . . . 89
3.2. The Equations of Motion (Rate of Momentum Balance) . 91
3.3. Non-Newtonian Fluid Behavior Applied to the Equations of
Motion 101
3.4. Generalized Representation of Newtonian and Non-New-
tonian Flow . . . . . . . . . . . . . . . 103
3.5. Alternative Forms of the Equations of Motion 106
Assignments . . 108
Further Reading . . . 109
Chapter 4. Transport Analysis in Fluid Flow Phenomena
4.1. Flow of Fluids in Thin Films 111
4.2. Flow in Circular-Shaped Conduits 114
4.3. Flow Equations Used in Viscometry 123
4.4. Periodic and Unsteady Flow Phenomena 128
4.5. Flow in Various Geometrical Configurations. 134
4.6. Macroscopic Flow, Friction Factors, and Turbulent Flow 140
4.7. Non-Newtonian Macroscopic Properties. 146
4.8. Viscoelastic Non-Newtonian Properties 153
4.9. Macroscopic Two-Phase Flow (Solid-Liquid) 155
4.10. Boundary Layer Flow Analysis 162
Assignments 177
Further Reading 183
Chapter 5. Derivation of the Mass Transport Equations
5.1. Governing Equation for Unsteady-State Diffusional Mass
Transport with Chemical Reaction and Convective Flow 185
5.2. Penetration Theories of Mass Transport. . . . . . . .. 196
5.3. Multicomponent and Turbulent Convection Mass Transport 199
5.4. Some Macroscopic Transport Approaches. 202
Assignments . . 206
Further Reading . . . . . . . . . . . . 206
Contents ix
Chapter 6. Transport Analysis in Mass Transport Phenomena
6.1. Diffusion Phenomena . . . . . . . . . . . . . . . 207
6.2. Unsteady-State One-Dimensional Diffusion . . . . . 209
6.3. Some More Diffusion Problems Solved by Laplace Transform
Techniques. . . . . . . . . . . . . . . . . . . . . 216
6.4. Some Diffusion Problems Solved by the Separation of Vari-
ables Technique . . . . . . 221
6.5. Moving-Front Diffusion Models . . . . . . . 225
6.6. Diffusion and Phase Changes . . . . . . . . 227
6.7. Diffusion with a Variable Diffusion Coefficient 228
6.8. Chemical Kinetics 232
6.9. Diffusion with Chemical Reaction 234
6.10. Complex Chemical Reactions in Reactors (Diffusion Is
Negligible) . . . . . . . . . . . . . . . . . . . . . 247
6.11. Diffusion, Convection, and Chemical Reaction in Thin Films
(Wetted-Wall Columns) . . . . . . . . . . . . . 251
6.12. Tubular Chemical Reactors . . . . . . . . . . . . 256
6.13. Macroscopic Analysis of Plug Flow Tubular Reactors. 271
6.14. Unsteady-State Response of Chemical Reactors 274
6.15. Miscellaneous Reactor Models 282
Assignments . . 286
Further Reading . . . . . . 295
Part III. Transport Analysis in Discrete Processes
Chapter 7. Finite Difference Calculus
7.1. Elementary Difference Operations 299
7.2. Interpolation and Extrapolation with Finite Differences. 302
7.3. The Difference Operator E. . . 304
7.4. Finite Difference Integration . . . . 305
7.5. Summation of Infinite Series by Finite Integration. 307
7.6. Finite Difference Integration Techniques. . . . . . 309
7.7. Solutions of First-Order Finite Difference Equations 312
7.8. Solutions of Higher-Order Linear Difference Equations. 316
7.9. Simultaneous Difference Equations . . . . . . . 324
7.10. Nonlinear Difference Equations of Higher Order 325
Assignments . . 326
Further Reading . . . . . . . . . . . . . . . 326
x Contents
Chapter 8. Transport Analysis in Cascaded Systems
8.1. Extraction . . . . . . . . . . . . . . 327
8.2. Stripping Columns . . . . . . . . . . 328
8.3. Unsteady-State Finite Difference Analysis 330
8.4. Cascaded Chemical Reactors at Steady State 333
8.5. Stirred Tank Reactors with Complex Chemical Reactions
(Unsteady State) . . . . . . . . . . . . . 335
8.6. Distillation Columns (Nonlinear Difference Equations). 338
8.7. Gas-Liquid Plate Reactors ...... . . . . 341
8.8. Difference Equations from Differential Equations 344
Assignments . . 348
Further Reading 350
Index ........ . 351
Part I
INTRODUCTION