09 Transport Phenomena A Unified Approach. Robert S. Brodkey. Harry C Hershey PDF

Preview

Summary

_I .T .- TRANSPORT PHENOMENA A Unified. Approach . . McGraw-Hill Chemical Engineering Series Editorial Advisory Board James J. Carbeny, Professor of Chemical Engineering, University of Notre Dame James R. Fair, Professor of Chemical Engineering, University of Texas, Austin William P. Schowalter, Pro...

Description

_I

.-

.T

TRANSPORT PHENOMENA

A Unified. Approach

.

.

McGraw-Hill Chemical Engineering Series Editorial Advisory Board James J. Carbeny, Professor of Chemical Engineering, University of Notre Dame James R. Fair, Professor of Chemical Engineering, University of Texas, Austin William P. Schowalter, Professor of Chemical Engineering, Princeton University Matthew ‘IkreU, Professor of Chemical Engineering, University of Minnesota James Wei, Professor of Chemical Engineering, Massachusetts Institute of Technology I&xx S. Peters, Emeritus Professor of Chemical Engineering, University of Colorado

BUILDING THE LITERATURE OF A PROFESSION Fifteen prominent chemical engineers first met in New York more than 60 years ago to plan a continuing literature for their rapidly growing profession. From industry came such pioneer practitioners as Leo H. Baekeland, Arthur D. Little, Charles L. Reese, John V. N. Dorr, M. C. Whitaker, and R. S. McBride. From the universities came such eminent educators as William H. Walker, Alfred H. White, D. D. Jackson, J. H. James, Warren K. Lewis, and Harry A. Curtis. H. C. Parmelee, then editor of Chemical and Metallurgical Engineering, served as chairman and was joined subsequently by S. D. Kirkpatrick as consulting editor. After several meetings, this committee submitted its report to the McGraw-Hill Book Company in September 1925. In the report were detailed specifications for a correlated series of more than a dozen texts and reference books which have since become the McGraw-Hill Series in Chemical Engineering and which became the cornerstone of the chemical engineering curriculum. From this beginning there has evolved a series of texts surpassing by far the scope and longevity envisioned by the founding Editorial Board. The McGraw-Hill Series in Chemical Engineering stands as a unique historical record of the development of chemical engineering education and practice. In the series one finds the milestones of the subject’s evolution: industrial chemistry, stoichiometry, unit operations and processes, thermodynamics, kinetics, and transfer operations. Chemical engineering is a dynamic profession, and its literature continues to evolve. McGraw-Hill and its consulting editors remain committed to a publishing policy that will serve, and indeed lead, the needs of the chemical engineering profession during the ars to come.

THE SERIES Bailey and Ouip: Biochemical Engineering Fundamentals Bennett and Myers: Momentum, Heat, and Mass Transfer Beveridge and Schechter: Optimization: Theory and Practice Brodkey and Hershey: Transport Phenomena: 4 fied Approach _, cprberry: Chemical and Catalytic Reaction En& iif&ig 1 ) Coughanowr and Koppel: Process Systems Analysis and Control Edgar and Himmelbhm: Optimization of Chemical Processes Fabien: Fundamentals o f Transport Phenomena FInlayson: Nonlinear Analysis in Chemical Engineering Gates, Katzer, and !3chuit: Chemistry of Catalytic Processes Holland: Fundamentals of Multicomponent Distillation Holland and Liipis: Computer Methods for Solving Dynamic Separation Problems Katz, Cornell, Kobayashi, Poettmann, Vary, Elenbaas, and Weinang: Handbook of Natural Gas Engineering King: Separation Processes Loyben: Process Modeling, Simulation, and Control for Chemical Engineers McCabe, Smith, J. C., and Harriott: Unit Operations of Chemical Engineering Mickley, Sherwood, and Reed: Applied Mathematics in Chemical Engineering Nelson: Petroleum Refinery Engineering Perry and Cbilton (Editors): Chemical Engineers’ Handbook Peters: Elementary Chemical Engineering Peters and Timmerhaus: Plant Design and Economics for Chemical Engineers Probstein and Hicks: Synthetic Fuels Reid, Prausnitz, and Shenvood: The Properties of Gases and Liquids Resnick Process Analysis and Design for Chemical Engineers Sattertield: Heterogeneous C?talysis in Practice Sherwood, Pigford, ind Wiie: Mass Transfer Smith, B. D.: Design of Equilibrium Stage Processes Smith, J. M.: Chemical Engineering Kinetics Smith, J. M., and Van Ness: Introduction to Chemical Engineering Thermodynamics Treybal: Mass Transfer Operations Valle-Riestraz Project Evolution in the Chemical Process Industries Van Ness and Abbott: Classical Thermodynamics of Nonelectrolyte Solutions: With Applications to Phase Equilibria Van Wile: Distillation Volk: Applied Statistics for Engineers Wdas: Reaction Kinetics for Chemical Engineers Wei, Russell, and Swartzlander: The Structure of the Chemical Processing Industries Whitwell and Toner: Conservation of Mass and Energy

“5

UNIVEiSIDAD DE GUADALAJ~EA LINIDAD DE BIBLIDTECAS CUCEI

21997

N o . ADQUlSlCION “..,...........*...“....“..*..-“----CLASIFICACION _..__....,.,...-.......,. . . . . . ...-... *--..-----I _ .._.... _ .__.__.... _.._ ._...... _I.-.. FACTURA .. . . .._....._.__..._.__ FECHA ____..______..._._..__.~~....~.....~. _ .__..... . _....._. m...;...E J . ._ . . . . . . . . . . ..._____... . _._ __... V . ______._ . . . . . . ..._...--..--... _-

“f

TRANSPORT PHENOMENA

A Unified Approach

Robert S. Brodkey The Ohio State Universi@

Harry C. Hershey The Ohio State University

McGraw-Hill Book Company New York St. Louis San Francisco Auckland BogotP Hamburg London Madrid Mexico Milan Montreal New Delhi Panama Paris SHo Paula Singapore Sydney Tokyo -Toronto

TRANSPORT PHENOMENA A Unified Approach INTERNATIONAL EDITION \ Copyright @ 1988 Exclusive rights by McGraw-Hill Book Co T Singapore for manufacture and export. This book cannot be re-exported from the country to which it is consigned by McGraw-Hill. 34567CM0943210 Copyright 0 1988 by McGraw-Hill Inc. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher. This book was set in Times Roman. The editor was B.J. Clark; the production supervisor was Denise L. Puryear; ’ Project supervision was done by Universities Press, Belfast. Library of Congress Cataloging-in-Publication Data Brodkey, Robert S. Transport phenomena. (McGraw-Hill chemical engineering series) Bibliography: p. Includes index. 1. Transport theory. I. Hershey Harry C. II. Title. III. Series TPI 56.T7B76 1988 660.2’842 86-34414 ISBN 0-07-007963-3 When ordering this title use ISBN 0-07-100152-2

Printed

in

Singapore

“{

CONTENTS

I

i Preface To the Instructor

xv

xvii

Part I Basic Concepts in Transport Phknomena 1 Introduction to Transport Phenomena 1.1 1.2 1.3 1.4 1.5

Transport Phenomena and Unit Operations Equilibrium and Rate Processes Fundamental Variables and Units The Role of Intermolecular Forces Simple Balances Problems References

2 Molecular Transport Mechanisms 2.1

2.2 2.3 2.4 2.5

The Analogy 2.1.1 The Case for Heat Transfer 2.1.2 The Case for Mass Transfer 2.1.3 The Case for Momentum Transfer 2.1.4 The Analogous Forms Heat Transfer Mass Transfer Momentum Transfer Heat, Mass and Momentum Diffusivities 2.51 Thermal Conductivity 2.5.2 Diffusion Coefficient 2.5.3 Viscosity

3 4 4 5 9 9 11 13

14 18 18 21 22 25 30 32 40 46 47 50 51

vii

.. . vul

CONTENTS

2.6

A Comparison of the Transports Problems References

53 55 59 60 62 64 65 66 67

3.4 The Continuity Equation 3.5 The General Property Balance for an Incompressible Fluid 3.6 Summary Problems

72 72 72 77 82 85 87 87

4 pI$ek&ar Transport and the General Property 90 4.1

Steady Transport in One Direction Involving Input-Output with no Generation 4.1.1 Constant-area Transport 4.1.2 Variable-area Transport 4.2 Steady State Transport With Generation 4.2.1 Heat or Mass Transport with Constant Generation 4.2.2 Momentum Transfer with Generation at Steady-State 4.2.3 Laminar Flow in a Tube 4.2.4 Laminar Flow Between Parallel Plates 4.2.5 Variable Generation 4.3 Concluding Remarks Problems References

5 Transport with a Net Convective Flux 5.1

Convective Flux Caused by Forced Convection 5.1.1 The Balance Equation 51.2 Coordinate Systems 51.3 Relationship Between Shear Stress and Shear Rate 51.4 The Continuity Equation 51.5 The Energy Balance 5.1.6 The Navier-Stokes Equation 5.1.7 The Boundary Layer 5.2 Convected Coordinates 5.3 Mass Diffusion Phenomena 5.3.1 Mass Flwes in Stationary and Convected Coordinates

93 95 95 103 104 108 113 119 124 125 126 128 129 132 134 134 135 138 142 146 157 160 161 161

CONTENTS

5.4

5.5

5.3.2 Total Flux and Fick’s Law 5.3.3 Binary Mass Diffusion in Gases 5.3.4 Binary Mass Diffusion in Liquids 5.3.5 Diffusion in Solids 53.6 Diffusion due to a Pressure Gradient 53.7 Diffusion with Three or More Components Less Common Types of Mass and Thermal Transport 5.4.1 Heat Transport 5.4.2 Mass Transport Summary Problems References

6 Flow Turbulence 6.1

6.2

6.3

6.4 6.5 6.6

Transitional and Turbulent Flow 6.1.1 The Reynolds Experiment 6.1.2 Transitional Flow 6.1.3 Fully Developed Turbulent Flow The Equations for Transport under Turbulent Conditions 6.2.1 Reynolds Rules of Averaging 6.2.2 Reynolds Equation for Incompressible Turbulent Flow 6.2.3 Reynolds Stresses 6.2.4 Turbulent Flow in Channels and Pipes Turbulence Models 6.3.1 The Boussinesq Theory 6.3.2 The Prandtl Mixing Length Theory 6.3.3 Analogies 6.3.4 Film and Penetration Theories The Velocity Distribution Friction Factor Summary Problems References

7 Ink ral Methods of Analysis 7.1

7.2

7.3

The 8eneral Integral Balance 7.1.1 The Integral Mass Balance 7.1.2 The Integral Balance on an Individual Species 7.1.3 The Integral Momentum Balance 7.1.4 The Integral Energy Balance 7.1.5 The Mechanical Energy Equation and the Engineering Bernoulli Equation Fluid Statics : 7.2.1 Manometers 7.2.2 Buoyant Forces 7.2.3 Variation of Pressure with Depth Recapitulation

ix 168 172 179 180 182 186 186 187 187 188 189 193 195 198 198 201 206 210 214 220 223 225 227 227 229 234 236 240 257 260 261 263 265 268 270 273 275 286 295 305 305 316 319 321

x

coN-rENTs Problems References

8 Methods of Analysis 8.1 Inspection of the Basic Differential Equations 8.2 Dimensional Analysis 8.2.1 Rayleigh Method of Analysis 8.2.2 Buckingham Method 8.2.3 Completeness of Sets 8.3 Modeling Problems References

323 326 327 330 335 339 346 350 353 355 356

Part II Applications of Transport Phenomena

9 Agitation 9.1 9.2 9.3 9.4 9.5 9.6

9.7

Introduction to Agitation Equipment Geometric Similarity and Scale-up Design Variables Dimensionless Numbers Scale-up 9.6.1 Scale-up Procedures for Turbulent Flow with Three or More Test Volumes 9.6.2 Scale-up Procedures for Turbulent Flow with Two Test Volumes 9.6.3 Scale-up Procedures for Turbulent Flow with a Single Test Volume 9.6.4 Scale-up Procedure for Laminar Flow 9.6.5 Scale-up Without Geometric Similarity Summary Problems References

1 0 Transport in Ducts 10.1

10.2

Review 10.1.1 Laminar Pipe Flow 10.1.2 Turbulent Pipe Flow Piping Systems 10.2.1 Roughness 10.2.2 Pressure Drop in Rough Pipes 10.2.3 von Karman Number 10.2.4 Solutions of Large Molecules 10.2.5 The Velocity Head Concept 10.2.6 Curved Tubes 10.2.7 Expansion and Contraction Losses 10.2.8 Pipe Fittings and Valves

359 362 364 371 372 374 383 384 385 386 395 396 396 397 398 400 403 403 406 409 409 413 417 420 421 422 424 430

CoNreNTs

10.3 10.4

10.5 10.6

10.2.9 Gases 10.2.10 Complex Fluid Flow Systems Noncircular Conduits Measurement of Fluid Flow 10.4.1 Orifice Meter 10.4.2 Venturi and Nozzle 10.4.3 Rotameter 10.4.4 Pitot Tube 10.45 Other Flow Metering Devices Measurement of Pressure Measurement of Temperature and Concentration Problems References

11.2 11.3

11.4

11.5

11.6

489 493 493 493 494 494 504 505 506 506 510 512 512 512 516 520 526 528 530 532 535. 539 539 541 546 547 549

Review and Extensions 11.1.1 Radiation 11.1.2 Convection 11.1.3 Conduction 11.1.4 The Resistance Concept 11.15 Slope at the Wall 11.1.6 Bulk and Film Temperatures Laminar Pipe Flow 11.2.1 Fully Developed Transfer 11.2.2 Entry Region Heat and Mass Transfer During Turbulent Flow 11.3.1 Review of Turbulence Models 11.3.2 Correlations for Fully Developed HOW 11.3.3 The Analogies 11.3.4 Other Methods Double-pipe Heat Exchangers 11.4.1 The Overall Heat Transfer Coefficient 11.4.2 Contact Resistance and Fouling Factors 11.4.3 Design Equations 11.4.4 Simple Solutions Multipass Heat Exchangers 11.51 Equipment 11.5.2 Design Equations Other Topics Problems References

I2 Transport Past Immersed Bodies 12.1

The Boundary Layer and the Entry Region 12.1.1 The Laminar Boundary Layer 12.1.2 The Turbulent Boundary Layer 12.1.3 Heat and Mass Transfer During Boundary Layer Past a Flat Plate

i

442 443 455 459 460 469 471 476 479 481 482 484 487

11 Heat and Mass Transfer in Duct Flow 11.1

x

551 556 557 566 Flow

571

xii CONrENTs 12.2

12.3

12.4

I.3

Flow Over Cylinders and Spheres 12.2.1 Ideal Flow (Nonviscous Fluids) 12.2.2 Stokes Flow Past a Sphere 12.2.3 Drag Coefficient Correlations Flow Phenomena with Solids and Fluids 12.3.1 Introduction to Fluidization 12.3.2 Gas-Solid Fhridization 12.3.3 Liquid-Solid Fluidization 12.3.4 Packed Beds 12.35 Single-Cylinder Heat Transfer 12.3.6 Banks of Tubes Flow Phenomena with Gas-Liquid and Liquid-Liquid Mixtures Problems References

578 578 587 591 600 601 606 6 1 3 619 623 626 634 63.5 637

Unsteady-state Transport

640 644 645 646 646 647 652 654 665 669 685 696 696 698 701 702 703 706

13.1 Basic Equations 13.1.1 Heat Transfer Equation 13.1.2 Mass Transfer 13.1.3 Error Function 13.1.4 Heat Transfer with Negligible Internal Resistance 13.2 Finite Slab and Cylinder 13.2.1 Fourier Series Solution 13.2.2 Lapiace Transform Solution 13.2.3 Generalized Chart Solution 13.2.4 Numerical Solution 13.3 Other Geometries 13.3.1 Infinite Slab 13.3.2 Semi-infinite Slab 13.3.3 Cylinder 13.3.4 Sphere Problems References

Part III Transport Property 14 Estimation of Transport Coefficients 14.1

14.2

14.3 14.4

Cases 14.1.1 Kinetic Theory of Gases 14.1.2 Nonuniform Gas Theory 14.1.3 Empirical Correlations for Gases Liquids 14.2.1 Viscosity 14.2.2 Thermal Conductivity 14.2.3 Diffusion Coefficient Solids Measurement of the Transport Properties

711 714 714 721 731 733 733 736 738 745 745

coNl?wrs

14.4.1 Viscosity Measurements 14.4.2 Thermal Conductivity 14.4.3 Diffusion Coefficient Measurements Problems References

1 5 Non-Newtonial Phenomena 15.1

15.2

15.3 15.4 15.5 15.6

Rheological Characteristics of Materials 15.1.1 Time-Independent Behavior 151.2 Time-Dependent Behavior 15.1.3 Viscoelastic Behavior Rheological Measurements 15.2.1 Capillary Viscometer 15.2.2 Rotational Viscometers Turbulent Flow Agitation of Non-Newtonian Fluids Heat Transfer in Pipe Flow Summary Problems References

.. . xlu

745 746 746 747 749 752 755 756 761 762 770 771 777 778 783 784 786 786 788

Appendixes A Properties of Materials A.1

A.2

B

Properties of Water and Air Table A.1 Thermophysical Properties of Saturated Water Table A.2 Thermophysical Properties of Dry Air Prediction of Transport Properties Table A.3 Constants in the Lennard-Jones 12-6 Potential as Determined from Viscosity Data Table A.4 Le Bas Atomic and Molar Volumes at the Normal Boiling Point

Mechanical Characteristics of Pipe and Tubing Table B.l Table B.2

C

Standard Steel Pipe Dimensions, Capacities, and Weights Condenser and Heat-Exchanger Tube Data

Physical Constants, Units, and Conversion Tables Table C.l Physical Constants Table C.2 SI Base and Supplementary Quantities and Units Table C.3 Derived Units of SI Which Have Special Names

791 791 792 794 796 797 799 802 8 0 805

806 807 807 808

3

xiv CONTENTS Table C.4 SI Prefixes Table C.5 Density (or Specific Volume) Table C.6 Diffusivity Table C.7 Force Table C.8 Gravitational Conversion Constant Table C.9 Heat Capacity Table C.10 Heat Transfer Coefficient Table C.ll Length Table C.12 Mass Table C. 13 Mass Transfer Coefficient Table C.14 Power Table C. 15 Pressure or Momentum Flux or Shear Stress Table C.16 Thermal Conductivity Table C. 17 Viscosity Table C.18 Volume Table C.19. Work, Energy, and Torque Table C.20 Miscellaneous

D Vector Mathematics D. 1 Introduction D.2 Scalar Quantities and Vectors D.3 Tensors

E Computer Programs E. 1

Table E. 1

Index

Index of Computer Programs

808 809 809 809 809 809 810 810 810 810 811 811 811 812 812 812 813 814 814 814 816 817 817 818

PREFACE

After publication of the pioneering book Transport Phenomena by Bird, Stewart, and Lightfoot in 1960, educators everywhere recognized that the previous “unit operations-unit processes” organization of material for the curricula of chemical engineers was inadequate for modern engineering education. Many schools found that the 1960 book was suitable for graduate courses and an excellent reference, but too difficult for most undergraduates, especially if the course was offered early in the curriculum. Others followed this pioneering effort by writing simpler versions. This book was designed to provide an integrated treatment of the three areas of transport: momentum, heat, and mass. The similarities and the differences of the three transports are clearly stated at a level suitable for second-semester sophomores and first-semester juniors in engineering or the other sciences where the mathematics requirement is similar. Many of the basic equations are mathematically identical, when expressed in terms of the generalized flux and property variables. This identity helps the student understand transport phenomena and forms the basis for the organization of the material here. A typical curriculum teaches momentum transfer before heat and mass because a complete treatment of these latter two is not possible without a prior discussion of fluid dynamics. This text allows heat transfer, which is encountered daily by everyone and easily visualized, to explain by analogy momentum transfer, which is not easily visualized or understood by neophytes. Transport is rapidly becoming more widely used in most branches of engineering, and this text provides all engineering disciplines with a readable and otherwise useful treatment of this difficult subject. In most of the other books on this subject, these topics are covered separately. We believe that this text provides a solid foundation for engineering design and research. At the same time, some interesting and important problems are solved. A study of transport phenomena does not replace unit operations, but understanding of transport phenomena provides deeper insight xv

XVi P R E F A C E

into the fundamental processes occurring in the unit operations. The engineer who masters the material in this text will be better able to analyze the unit operations he or she encounters. McGraw-Hill and the authors would like to express their thanks for the many useful comments and suggestions provided by colleagues who reviewed this text during the...