net Fundamentals of Momentum, Heat, and Mass Transfer 5th Edition www.net Fundamentals of Momentum, Heat, and Mass Transfer 5th Edition James R.net Department of Mechanical Engineering Charles E. Wicks Department of Chemical Engineering Robert E. Wilson Department of Mechanical Engineering Gregory L. Rorrer Department of Chemical Engineering Oregon State University John Wiley & Sons, Inc.net ASSOCIATE PUBLISHER Daniel Sayre ACQUISITIONS EDITOR Jennifer Welter MARKETING MANAGER Christopher Ruel CREATIVE DIRECTOR Harry Nolan DESIGNER Michael St. Martine SENIOR MEDIA EDITOR Lauren Sapira SENIOR PRODUCTION EDITOR Patricia McFadden PRODUCTION MANAGEMENT SERVICES Thomson Digital www.net This book was set in by Thomson Digital and printed and bound by Hamilton Printing. The cover was printed by Lehigh Press, Inc. This book is printed on acid free paper. 1 Copyright # 2008 John Wiley & Sons, Inc. All rights reserved. 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ISBN-13 978-0470128688 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 www.net Preface to the 5th Edition The first edition of Fundamentals of Momentum, Heat, and Mass Transfer, published in 1969, was written to become a part of what was then known as the ‘‘engineering science core’’ of most engineering curricula. Indeed, requirements for ABET accreditation have stipulated that a significant part of all curricula must be devoted to fundamental subjects. The emphasis on engineering science has continued over the intervening years, but the degree of emphasis has diminished as new subjects and technologies have entered the world of engineering education. Nonetheless, the subjects of momentum transfer (fluid mechanics), heat transfer, and mass transfer remain, at least in part, important components www.net of all engineering curricula. It is in this context that we now present the fifth edition. Advances in computing capability have been astonishing since 1969. At that time, the pocket calculator was quite new and not generally in the hands of engineering students. Subsequent editions of this book included increasingly sophisticated solution techniques as technology advanced. Now, more than 30 years since the first edition, computer competency among students is a fait accompli and many homework assignments are completed using computer software that takes care of most mathematical complexity, and a good deal of physical insight. We do not judge the appropriateness of such approaches, but they surely occur and will do so more frequently as software becomes more readily available, more sophisticated, and easier to use. In this edition, we still include some examples and problems that are posed in English units, but a large portion of the quantitative work presented is now in SI units. This is consistent with most of the current generation of engineering textbooks. There are still some subdisciplines in the thermal/fluid sciences that use English units conventionally, so it remains necessary for students to have some familiarity with pounds, mass, slugs, feet, psi, and so forth. Perhaps a fifth edition, if it materializes, will finally be entirely SI. We, the original three authors (W3), welcome Dr. Greg Rorrer to our team. Greg is a member of the faculty of the Chemical Engineering Department at Oregon State University with expertise in biochemical engineering. He has had a significant influence on this edition’s sections on mass transfer, both in the text and in the problem sets at the end of Chapters 24 through 31. This edition is unquestionably strengthened by his contributions, and we anticipate his continued presence on our writing team. We are gratified that the use of this book has continued at a significant level since the first edition appeared some 30 years ago. It is our continuing belief that the transport phenomena remain essential parts of the foundation of engineering education and practice. With the modifications and modernization of this fourth edition, it is our hope that Fundamentals of Momentum, Heat, and Mass Transfer will continue to be an essential part of students’ educational experiences.net This page intentionally left blank www. Introduction to Momentum Transfer 1 1.1 Fluids and the Continuum 1 1.2 Properties at a Point 2 1.3 Point-to-Point Variation of Properties in a Fluid 5 1.6 Surface Tension 11 www.1 Pressure Variation in a Static Fluid 16 2.2 Uniform Rectilinear Acceleration 19 2.3 Forces on Submerged Surfaces 20 2. Description of a Fluid in Motion 29 3.1 Fundamental Physical Laws 29 3.2 Fluid-Flow Fields: Lagrangian and Eulerian Representations 29 3.3 Steady and Unsteady Flows 30 3.5 Systems and Control Volumes 32 4. Conservation of Mass: Control-Volume Approach 34 4.2 Specific Forms of the Integral Expression 35 4. Newton’s Second Law of Motion: Control-Volume Approach 43 5.1 Integral Relation for Linear Momentum 43 5.2 Applications of the Integral Expression for Linear Momentum 46 5.3 Integral Relation for Moment of Momentum 52 5.4 Applications to Pumps and Turbines 53 5. Conservation of Energy: Control-Volume Approach 63 6.1 Integral Relation for the Conservation of Energy 63 6.2 Applications of the Integral Expression 69 vii www.net viii Contents 6.3 The Bernoulli Equation 72 6. Shear Stress in Laminar Flow 81 7.1 Newton’s Viscosity Relation 81 7.2 Non-Newtonian Fluids 82 7.4 Shear Stress in Multidimensional Laminar Flows of a Newtonian Fluid 88 7. Analysis of a Differential Fluid Element in Laminar Flow 92 8.1 Fully Developed Laminar Flow in a Circular Conduit of Constant Cross Section 92 8.2 Laminar Flow of a Newtonian Fluid Down an Inclined-Plane Surface 95 8. Differential Equations of Fluid Flow 99 9.1 The Differential Continuity Equation 99 9.2 Navier-Stokes Equations 101 9. Inviscid Fluid Flow 113 10.1 Fluid Rotation at a Point 113 10.2 The Stream Function 114 10.3 Inviscid, Irrotational Flow about an Infinite Cylinder 116 10.4 Irrotational Flow, the Velocity Potential 117 10.5 Total Head in Irrotational Flow 119 10.6 Utilization of Potential Flow 119 10.7 Potential Flow Analysis—Simple Plane Flow Cases 120 10.8 Potential Flow Analysis—Superposition 121 10. Dimensional Analysis and Similitude 125 11.2 Dimensional Analysis of Governing Differential Equations 126 11.3 The Buckingham Method 128 11.4 Geometric, Kinematic, and Dynamic Similarity 131 11.net Contents ix 12.3 The Boundary-Layer Concept 144 12.4 The Boundary-Layer Equations 145 12.5 Blasius’s Solution for the Laminar Boundary Layer on a Flat Plate 146 12.6 Flow with a Pressure Gradient 150 12.7 von Kármán Momentum Integral Analysis 152 12.8 Description of Turbulence 155 12.9 Turbulent Shearing Stresses 157 12.10 The Mixing-Length Hypothesis 158 12.11 Velocity Distribution from the Mixing-Length Theory 160 12.12 The Universal Velocity Distribution 161 12.13 Further Empirical Relations for Turbulent Flow 162 12.14 The Turbulent Boundary Layer on a Flat Plate 163 12.15 Factors Affecting the Transition From Laminar to Turbulent Flow 165 12. Flow in Closed Conduits 168 13.1 Dimensional Analysis of Conduit Flow 168 www.2 Friction Factors for Fully Developed Laminar, Turbulent, and Transition Flow in Circular Conduits 170 13.3 Friction Factor and Head-Loss Determination for Pipe Flow 173 13.4 Pipe-Flow Analysis 176 13.5 Friction Factors for Flow in the Entrance to a Circular Conduit 179 13.2 Scaling Laws for Pumps and Fans 194 14.3 Axial and Mixed Flow Pump Configurations 197 14. Fundamentals of Heat Transfer 201 15.5 Combined Mechanisms of Heat Transfer 209 15. Differential Equations of Heat Transfer 217 16.1 The General Differential Equation for Energy Transfer 217 16.2 Special Forms of the Differential Energy Equation 220 16.3 Commonly Encountered Boundary Conditions 221 16. Steady-State Conduction 224 17.1 One-Dimensional Conduction 224 17.2 One-Dimensional Conduction with Internal Generation of Energy 230 17.3 Heat Transfer from Extended Surfaces 233 17.4 Two- and Three-Dimensional Systems 240 17. Unsteady-State Conduction 252 18.2 Temperature-Time Charts for Simple Geometric Shapes 261 18.3 Numerical Methods for Transient Conduction Analysis 263 18.4 An Integral Method for One-Dimensional Unsteady Conduction 266 18. Convective Heat Transfer 274 19.1 Fundamental Considerations in Convective Heat Transfer 274 www.2 Significant Parameters in Convective Heat Transfer 275 19.3 Dimensional Analysis of Convective Energy Transfer 276 19.4 Exact Analysis of the Laminar Boundary Layer 279 19.5 Approximate Integral Analysis of the Thermal Boundary Layer 283 19.6 Energy- and Momentum-Transfer Analogies 285 19.7 Turbulent Flow Considerations 287 19. Convective Heat-Transfer Correlations 297 20.2 Forced Convection for Internal Flow 305 20.3 Forced Convection for External Flow 311 20. Boiling and Condensation 323 21. Heat-Transfer Equipment 336 22.1 Types of Heat Exchangers 336 22.2 Single-Pass Heat-Exchanger Analysis: The Log-Mean Temperature Difference 339 22.3 Crossflow and Shell-and-Tube Heat-Exchanger Analysis 343 22.4 The Number-of-Transfer-Units (NTU) Method of Heat-Exchanger Analysis and Design 347 22.5 Additional Considerations in Heat-Exchanger Design 354 22.net Contents xi 23. Radiation Heat Transfer 359 23.1 Nature of Radiation 359 23.3 The Intensity of Radiation 361 23.4 Planck’s Law of Radiation 363 23.5 Stefan-Boltzmann Law 365 23.6 Emissivity and Absorptivity of Solid Surfaces 367 23.7 Radiant Heat Transfer Between Black Bodies 370 23.8 Radiant Exchange in Black Enclosures 379 23.9 Radiant Exchange in Reradiating Surfaces Present 380 23.10 Radiant Heat Transfer Between Gray Surfaces 381 23.11 Radiation from Gases 388 23.12 The Radiation Heat-Transfer Coefficient 392 23. Fundamentals of Mass Transfer 398 www.1 Molecular Mass Transfer 399 24.2 The Diffusion Coefficient 407 24.3 Convective Mass Transfer 428 24. Differential Equations of Mass Transfer 433 25.1 The Differential Equation for Mass Transfer 433 25.2 Special Forms of the Differential Mass-Transfer Equation 436 25.3 Commonly Encountered Boundary Conditions 438 25.4 Steps for Modeling Processes Involving Molecular Diffusion 441 25. Steady-State Molecular Diffusion 452 26.1 One-Dimensional Mass Transfer Independent of Chemical Reaction 452 26.2 One-Dimensional Systems Associated with Chemical Reaction 463 26.3 Two- and Three-Dimensional Systems 474 26.4 Simultaneous Momentum, Heat, and Mass Transfer 479 26. Unsteady-State Molecular Diffusion 496 27.1 Unsteady-State Diffusion and Fick’s Second Law 496 27.2 Transient Diffusion in a Semi-Infinite Medium 497 27.3 Transient Diffusion in a Finite-Dimensional Medium Under Conditions of Negligible Surface Resistance 500 27.4 Concentration-Time Charts for Simple Geometric Shapes 509 27.net xii Contents 28. Convective Mass Transfer 517 28.1 Fundamental Considerations in Convective Mass Transfer 517 28.2 Significant Parameters in Convective Mass Transfer 519 28.3 Dimensional Analysis of Convective Mass Transfer 521 28.4 Exact Analysis of the Laminar Concentration Boundary Layer 524 28.5 Approximate Analysis of the Concentration Boundary Layer 531 28.6 Mass, Energy, and Momentum-Transfer Analogies 533 28.7 Models for Convective Mass-Transfer Coefficients 542 28. Convective Mass Transfer Between Phases 551 29.2 Two-Resistance Theory 554 29. Convective Mass-Transfer Correlations 569 www.1 Mass Transfer to Plates, Spheres, and Cylinders 569 30.2 Mass Transfer Involving Flow Through Pipes 580 30.3 Mass Transfer in Wetted-Wall Columns 581 30.4 Mass Transfer in Packed and Fluidized Beds 584 30.5 Gas-Liquid Mass Transfer in Stirred Tanks 585 30.6 Capacity Coefficients for Packed Towers 587 30.7 Steps for Modeling Mass-Transfer Processes Involving Convection 588 30. Mass-Transfer Equipment 603 31.1 Types of Mass-Transfer Equipment 603 31.2 Gas-Liquid Mass-Transfer Operations in Well-Mixed Tanks 605 31.3 Mass Balances for Continuous Contact Towers: Operating-Line Equations 611 31.4 Enthalpy Balances for Continuous-Contact Towers 620 31.5 Mass-Transfer Capacity Coefficients 621 31.6 Continuous-Contact Equipment Analysis 622 31.7 Closure 636 Nomenclature 641 APPENDIXES A. Transformations of the Operators = and =2 to Cylindrical Coordinates 648 B. Summary of Differential Vector Operations in Various Coordinate Systems 651 C. Symmetry of the Stress Tensor 654 D. The Viscous Contribution to the Normal Stress 655 E. The Navier–Stokes Equations for Constant r and m in Cartesian, Cylindrical, and Spherical Coordinates 657 F. Charts for Solution of Unsteady Transport Problems 659 www.net Contents xiii G. Properties of the Standard Atmosphere 672 H. Physical Properties of Solids 675 I. Physical Properties of Gases and Liquids 678 J.
