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Transport Analysis PDF

357 Pages·1973·5.129 MB·English
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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

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