Fundamentals of Heat and Mass Transfer PDF

ffirs.qxd 3/6/06 11:11 AM Page iv ffirs.qxd 3/6/06 11:11 AM Page i SIXTH EDITION Fundamentals of Heat...

ffirs.qxd 3/6/06 11:11 AM Page iv ffirs.qxd 3/6/06 11:11 AM Page i SIXTH EDITION Fundamentals of Heat and Mass Transfer FRANK P. INCROPERA College of Engineering University of Notre Dame DAVID P. DEWITT School of Mechanical Engineering Purdue University THEODORE L. BERGMAN Department of Mechanical Engineering University of Connecticut ADRIENNE S. LAVINE Mechanical and Aerospace Engineering Department University of California, Los Angeles JOHN WILEY & SONS ffirs.qxd 3/6/06 11:11 AM Page ii ASSOCIATE PUBLISHER Daniel Sayre ACQUISITIONS EDITOR Joseph Hayton SENIOR PRODUCTION EDITOR Valerie A. Vargas MARKETING MANAGER Phyllis Cerys SENIOR DESIGNER Madelyn Lesure COVER and TEXT DESIGNER Karin Gerdes Kincheloe COVER ILLUSTRATIONS Carol Grobe SENIOR ILLUSTRATION EDITOR Sandra Rigby EDITORIAL ASSISTANT Mary Morgan-McGee MEDIA EDITOR Stefanie Liebman PRODUCTION SERVICES Ingrao Associates This book was set in 10/12 Times Roman by GGS Information Services and printed and bound by R.R. Donnelley. The cover was printed by Phoenix Color. This book is printed on acid-free paper.
Copyright © 2007 John Wiley & Sons, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc. 222 Rosewood Drive, Danvers, MA 01923, website www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201)748-6011, fax (201)748-6008, website http://www.wiley.com/go/permissions. To order books or for customer service, please call 1-800-CALL WILEY (225-5945). Library of Congress Cataloging-in-Publication Data Incropera, Frank P. Fundamentals of heat and mass transfer. / Frank P. Incropera... [et al.]. — 6th ed. / Frank P. Incropera... [et al]. p. cm. Includes bibliographical references and index. ISBN-13: *978-0-471-45728-2 (cloth) ISBN-10: 0-471-45728-0 (cloth) 1. Heat—Transmission. 2. Mass transfer. I. Title. QC320.145 2006 621.402
2–dc22 2005058360 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 ffirs.qxd 3/6/06 11:11 AM Page iii In Memory David P. DeWitt March 2, 1934–May 17, 2005 The year 2005 was marked by the loss of Dr. David P. DeWitt, a dear friend and col- league who contributed significantly to heat transfer technology and pedagogy throughout a distinguished 45-year career. Dave was educated as a mechanical engi- neer, receiving a BS degree from Duke University, an MS from MIT, and the PhD degree from Purdue University. His graduate studies at Purdue nucleated a strong interest in the fields of thermal physics and radiometry, in which he worked until illness made it impossible to continue. Dave was instrumental in developing radio- metric measurement standards at Purdue’s Thermophysical Properties Research Center, eventually becoming its deputy director and president of Technometrics Inc., an optical and thermal instrument design company. In 1973 he joined Purdue’s School of Mechanical Engineering at the rank of professor, where he taught and con- ducted research until his retirement in 2000. From 2000 to 2004, he worked in the Optical Technology Division of the National Institute of Technology and Standards. Dave was an excellent and demanding teacher, a good researcher and a superb engineer. In our nearly thirty-year collaboration, he provided complementary skills that contributed significantly to the success of the books we have co-authored. However, it is much more on a personal than a professional level that I have my fondest memories of this very special colleague. As co-authors, Dave and I spent thousands of hours working together on all facets of our books, typically in blocks of three to five hours. This time often in- volved spontaneous diversions from the task at hand, typically marked by humor or reflections on our personal lives. Dave and I each have three daughters of comparable ages, and we would often share stories on the joys and challenges of nurturing them. It’s hard to think about Dave without reflecting on the love and pride he had for his daughters (Karen, Amy, and Debbie). In 1990 Dave lost his first wife Jody due to cancer, and I witnessed first hand his personal character and strength as he supported her in battling this terrible disease. I also experienced the joy he felt in the relationship he developed with his second wife Phyllis, whom he married in 1997. I will always remember Dave as a sensitive and kind person of good humor and generosity. Dear friend, we miss you greatly, but we are comforted by the knowl- edge that you are now free of pain and in a better place. Frank P. Incropera Notre Dame, Indiana ffirs.qxd 3/6/06 11:11 AM Page iv ffirs.qxd 3/6/06 11:11 AM Page v Forward to Preface Not too long after finishing the previous editions of Fundamentals of Heat and Mass Transfer and Introduction to Heat Transfer, Dave DeWitt and I felt the need to plan for that time when we would no longer be able to add appropriate value to future editions. There were two matters of special concern. First, we were advanc- ing in years, and the potential for disruption due to declining health or our own mor- tality could not be ignored. But, perhaps more pertinent to maintaining freshness and vitality to the text books, we also recognized that we were becoming ever more distant from leading-edge activities in the field. In 2002, we concluded that we should proactively establish a succession plan involving the participation of additional co-authors. In establishing desired attrib- utes of potential candidates, we placed high priority on the following: a record of success in teaching heat and mass transfer, active involvement with research in the field, a history of service to the heat transfer community, and the ability to sustain an effective collaborative relationship. A large weighting factor was attached to this last attribute, since it was believed to have contributed significantly to whatever success Dave DeWitt and I have enjoyed with the previous editions. After reflecting long and hard on the many excellent options, Dave and I in- vited Ted Bergman and Adrienne Lavine, professors of Mechanical Engineering at the University of Connecticut and the University of California, Los Angeles, re- spectively, to join us as co-authors. We were grateful for their acceptance. Ted and Adrienne are listed as third and fourth authors for this edition, will move to first and second authors on the next edition, and will thereafter appear as sole authors. Ted and Adrienne have worked extremely hard on the current edition, and you will see numerous enhancements from their efforts, particularly in modern applica- tions related to subjects such as nano and biotechnology. It is therefore most appro- priate for Ted and Adrienne to share their thoughts in the following preface. Frank P. Incropera Notre Dame, Indiana ffirs.qxd 3/6/06 11:11 AM Page vi fpref.qxd 3/6/06 11:11 AM Page vii Preface Since the last edition, fundamental changes have occurred, both nationally and globally, in how engineering is practiced, with questions raised about the future of the profession. How will the practice of engineering evolve over the next decade? Will tomorrow’s engineer be more valued if he is a specialist, or more handsomely rewarded if she has knowledge of greater breadth but less depth? How will engi- neering educators respond to changing market forces? Will the traditional bound- aries that separate the engineering disciplines in the typical college or university remain in place? We believe that, because technology provides the foundation for improving the standard of living of all humankind, the future of engineering is bright. But, in light of the tension between external demand for generalization and intellectual satisfac- tion of specialization, how will the discipline of heat transfer remain relevant? What will the value of this discipline be in the future? To what new problems will the knowledge of heat transfer be applied? In preparing this edition, we attempted to identify emerging issues in technol- ogy and science in which heat transfer is central to the realization of new products in areas such as information technology, biotechnology and pharmacology, alterna- tive energy, and nanotechnology. These new applications, along with traditional ap- plications in energy generation, energy utilization, and manufacturing, suggest that the discipline of heat transfer is healthy. Furthermore, when applied to problems that transcend traditional boundaries, heat transfer will be a vital and enabling disci- pline of the future. We have strived to remain true to the fundamental pedagogical approach of previous editions by retaining a rigorous and systematic methodology for problem solving, by including examples and problems that reveal the richness and beauty of the discipline, and by providing students with opportunities to meet the learning objectives. fpref.qxd 3/6/06 11:11 AM Page viii viii Preface Approach and Organization From our perspective, the four learning objectives desired in any first course in heat transfer, detailed in the previous edition, remain as follows: 1. The student should internalize the meaning of the terminology and physical prin- ciples associated with the subject. 2. The student should be able to delineate pertinent transport phenomena for any process or system involving heat transfer. 3. The student should be able to use requisite inputs for computing heat transfer rates and/or material temperatures. 4. The student should be able to develop representative models of real processes and systems and draw conclusions concerning process/system design or perfor- mance from attendant analysis. As in the previous edition, learning objectives for each chapter are clarified to enhance the means by which they are achieved, as well as means by which achieve- ment may be assessed. The summary of each chapter highlights key terminology and concepts developed in the chapter, and poses questions to test and enhance stu- dent comprehension. For problems involving complex models and/or exploratory, what-if, and para- meter sensitivity considerations, it is recommended that they be addressed by using a computational equation-solving package. To this end, the Interactive Heat Transfer (IHT) package developed by Intellipro, Inc. (New Brunswick, New Jersey) and available in the previous edition has been updated. The seasoned user will find the technical content of IHT to be largely unchanged, but the computational capability and features have been improved significantly. Specifically, IHT is now capable of solving 300 or more simultaneous equations. The user interface has been updated to include a full-function workspace editor with complete control over formatting of text, copy and paste functionality, an equation editor, a new graphing subsystem, and enhanced syntax checking. In addition, the software now has the capability to export IHT-specific functions (e.g. properties and correlations) as Microsoft Excel add-ins. A second software package, Finite Element Heat Transfer (FEHT), developed by F-Chart Software of Middleton, Wisconsin, provides enhanced capabilities for solv- ing two-dimensional conduction heat transfer problems. As in the previous edition, many homework problems that involve a computer- based solution appear as extensions to problems that can be solved by hand calcula- tion. This approach is time tested and allows students to validate their computer predictions by checking the predictions with their hand solutions. They may then proceed with parametric studies that explore related design and operating conditions. Such problems are identified by enclosing the exploratory part in a red rectangle, as, for example (b) , (c) , or (d). This feature also allows instructors who wish to limit their assignments of computer-based problems to benefit from the richness of these problems. Solutions to problems for which the number itself is highlighted, as, for example, 1.26 , should be entirely computer based. We are aware that some instructors who use the text have not utilized IHT in their courses. We encourage our colleagues to dedicate, at a minimum, one-half hour of lecture or recitation time to demonstrate IHT as a tool for solving simultaneous equations, and for evaluating the thermophysical properties of various materials. We fpref.qxd 3/6/06 11:11 AM Page ix Preface ix have found that, once students have seen its power and ease of use, they will eagerly utilize IHT’s additional features on their own. This will enable them to solve prob- lems faster, with fewer numerical errors, thereby freeing them to concentrate on the more substantive aspects of the problems. What’s New in the 6th Edition Problem Sets This edition contains a significant number of new, revised, and renumbered end-of-chapter problems. Many of the new problems require relatively straightforward analyses, and many involve applications in nontraditional areas of science and technology. The solutions manual has undergone extensive revision. Streamlined Presentation The text has been streamlined by moving a small amount of material to stand-alone supplemental sections that can be accessed elec- tronically from the companion website. The supplemental sections are called out with marginal notes throughout the text. If instructors prefer to use material from the supplemental sections, it is readily available from the Wiley website (see below). Homework problem statements associated with the supplemental sections are also available electronically. Chapter-by-Chapter Content Changes To help motivate the reader, Chap- ter 1 includes an expanded discussion of the relevance of heat transfer. The rich- ness and pertinence of the topic are conveyed by discussion of energy conversion devices including fuel cells, applications in information technology and biological as well as biomedical engineering. The presentation of the conservation of energy requirement has been revised. New material on micro- and nanoscale conduction has been included in Chap- ter 2. Because in-depth treatment of these effects would overwhelm most students, they are introduced and illustrated by describing the motion of energy carriers in- cluding phonons and electrons. Approximate expressions for the effective thermal conductivity of thin films are presented and are explained in terms of energy carrier behavior at physical boundaries. The thermal conductivity of nanostructured versus conventional materials is presented and used to demonstrate practical applications of recent nanotechnology research. Microscale-related limitations of the heat diffu- sion equation are explained. The bioheat equation is introduced in Chapter 3, and its similarity to the heat equation for extended surfaces is pointed out in order to fa- cilitate its use and solution. The Chapter 4 discussion of conduction shape factors, applied to multidimen- sional steady-state conduction, is embellished with recent results involving the di- mensionless conduction heat rate. Although we have moved the graphical method to the supplemental material, discussion of two-dimensional isotherm and heat flow line distributions has been enhanced in order to assist students to conceptualize the con- duction process. Use of the dimensionless conduction heat rate is extended to tran- sient situations in Chapter 5. A new, unified approach to transient heat transfer is presented; easy-to-use approximate solutions associated with a range of geometries and time scales have been added. Recently, we have noted that few students use the graphical representations of the one-dimensional, transient conduction solutions (Heisler charts); most prefer to solve the approximate or exact analytical expressions. fpref.qxd 3/6/06 11:11 AM Page x x Preface Hence, we have relegated the graphical representations to the supplemental material. Because of the ease and frequency with which computational methods are used by students today, analytical solutions involving multidimensional effects have also been moved to the supplemental material. We have added a brief section on periodic heating and have demonstrated its relevance by presenting a modern method used to measure the thermophysical properties of nanostructured materials. Introduction to the fundamentals of convection, included in Chapter 6, has been simplified and streamlined. The description of turbulence and transition to turbu- lence has been updated. Proper accounting of the temperature-dependence of ther- mophysical properties is emphasized. Derivation of the convection transfer equations is now relegated to the supplemental material. The treatment of external flow in Chapter 7 is largely unchanged. Chapter 8 cor- relations for the entrance regions of internal flow have been updated, while the dis- cussion of heat transfer enhancement has been expanded by adding correlations for flow in curved tubes. Microsale-related limitations of the convective correlations for internal flow are presented. Chapter 9 correlations for the effective thermal conduc- tivity associated with free convection in enclosures have been revised in order to more directly relate these correlations to the conduction results of Chapter 3. Presentation of boiling heat transfer in Chapter 10 has been modified to im- prove student understanding of the boiling curve by relating aspects of boiling phe- nomena to forced convection and free convection concepts from previous chapters. Values of the constants used in the boiling correlations have been modified to re- flect the current literature. Reference to refrigerants that are no longer used has been eliminated, and replacement refrigerant properties have been added. Heat transfer correlations for internal two-phase flow are presented. Microscale-related limita- tions of the correlations for internal two-phase flow are discussed. A much-simpli- fied method for solution of condensation problems is presented. The use of the log mean temperature difference (LMTD) method is retained for de- veloping correlations for concentric tube heat exchangers in Chapter 11, but, because of the flexibility of the effectiveness-NTU method, the LMTD-based analysis of heat ex- changers of other types has been relegated to the supplemental material. Again, the sup- plemental sections can be accessed at the companion website. Treatment of radiation heat transfer in Chapter 12 and 13 has undergone modest revision and streamlining. The coverage of mass transfer, Chapter 14, has been revised extensively. The chapter has been reorganized so that instructors can either cover the entire content or seamlessly restrict attention to mass transfer in stationary media. The latter approach is recommended if time is limited, and/or if interest is limited to mass transfer in liquids or solids. The new example problems of Chapter 14 reflect con- temporary applications. Discussion of the various boundary conditions used in mass transfer has been clarified and simplified. Acknowledgments We are immensely indebted to Frank Incropera and Dave DeWitt who entrusted us to join them as co-authors. We are especially thankful to Frank for his patience, thoughtful advice, detailed critique of our work, and kind encouragement as this edition was being developed. fpref.qxd 3/6/06 11:11 AM Page xi Preface xi Appreciation is extended to our colleagues at the University of Connecticut and UCLA who provided valuable input. Eric W. Lemmon of the National Institute of Standards and Technology is acknowledged for his generosity in providing proper- ties of new refrigerants. We are forever grateful to our wonderful spouses and children, Tricia, Nate, Tico, Greg, Elias, and Jacob for their love, support, and endless patience. Finally, we both extend our appreciation to Tricia Bergman who, despite all her responsibil- ities, somehow found the time to expertly and patiently process the solutions for the new end-of-chapter problems. Theodore L. Bergman ([email protected]) Storrs, Connecticut Adrienne S. Lavine ([email protected]) Los Angeles, California Supplemental and Website Material The companion website for the text is www.wiley.com/college/incropera. By click- ing on the ‘student companion site’ link, students may access the answers to the homework problems and the Supplemental Sections of the text. Material available for instructors only includes the instructor Solutions Man- ual, Powerpoint slides that can be used by instructors for lectures, and electronic versions of figures from the texts for those wishing to prepare their own materials for electronic classroom presentation. The instructor Solutions Manual is for use by instructors who are requiring use of the text for their course. Copying or distribut- ing all or part of the Solutions Manual in any form without the Publisher’s permis- sion is a violation of copyright law. Interactive Heat Transfer v3.0/FEHT with User’s Guide is available either with the text or as a separate purchase. This software tool provides modeling and computational features useful in solving many problems in the text, and enables what-if and exploratory analysis of many types of heat transfer problems. The CD/booklet package is available as a stand-alone purchase from the Wiley website, www.wiley.com, or through your local bookstore. Faculty interested in using this tool in their course may order the software shrinkwrapped to the text at a significant discount. Contact your local Wiley representative for details. fpref.qxd 3/6/06 11:11 AM Page xii ftoc.qxd 3/6/06 11:11 AM Page xiii Contents Symbols xxiii CHAPTER 1 Introduction 1 1.1 What and How? 2 1.2 Physical Origins and Rate Equations 3 1.2.1 Conduction 3 1.2.2 Convection 6 1.2.3 Radiation 9 1.2.4 Relationship to Thermodynamics 12 1.3 The Conservation of Energy Requirement 13 1.3.1 Conservation of Energy for a Control Volume 13 1.3.2 The Surface Energy Balance 25 1.3.3 Application of the Conservation Laws: Methodology 28 1.4 Analysis of Heat Transfer Problems: Methodology 29 ftoc.qxd 3/6/06 11:11 AM Page xiv xiv Contents 1.5 Relevance of Heat Transfer 32 1.6 Units and Dimensions 35 1.7 Summary 38 References 41 Problems 41 CHAPTER 2 Introduction to Conduction 57 2.1 The Conduction Rate Equation 58 2.2 The Thermal Properties of Matter 60 2.2.1 Thermal Conductivity 60 2.2.2 Other Relevant Properties 67 2.3 The Heat Diffusion Equation 70 2.4 Boundary and Initial Conditions 77 2.5 Summary 81 References 82 Problems 82 CHAPTER 3 One-Dimensional, Steady-State Conduction 95 3.1 The Plane Wall 96 3.1.1 Temperature Distribution 96 3.1.2 Thermal Resistance 98 3.1.3 The Composite Wall 99 3.1.4 Contact Resistance 101 3.2 An Alternative Conduction Analysis 112 3.3 Radial Systems 116 3.3.1 The Cylinder 116 3.3.2 The Sphere 122 3.4 Summary of One-Dimensional Conduction Results 125 3.5 Conduction with Thermal Energy Generation 126 3.5.1 The Plane Wall 127 3.5.2 Radial Systems 132 3.5.3 Application of Resistance Concepts 137 3.6 Heat Transfer from Extended Surfaces 137 3.6.1 A General Conduction Analysis 139 3.6.2 Fins of Uniform Cross-Sectional Area 141 3.6.3 Fin Performance 147 3.6.4 Fins of Nonuniform Cross-Sectional Area 150 3.6.5 Overall Surface Efficiency 153 3.7 The Bioheat Equation 162 3.8 Summary 166 References 168 Problems 169 ftoc.qxd 3/6/06 11:11 AM Page xv Contents xv CHAPTER 4 Two-Dimensional, Steady-State Conduction 201 4.1 Alternative Approaches 202 4.2 The Method of Separation of Variables 203 4.3 The Conduction Shape Factor and the Dimensionless Conduction Heat Rate 207 4.4 Finite-Difference Equations 212 4.4.1 The Nodal Network 213 4.4.2 Finite-Difference Form of the Heat Equation 214 4.4.3 The Energy Balance Method 215 4.5 Solving the Finite-Difference Equations 222 4.5.1 The Matrix Inversion Method 222 4.5.2 Gauss–Seidel Iteration 223 4.5.3 Some Precautions 229 4.6 Summary 234 References 235 Problems 235 4S.1 The Graphical Method W-1 4S.1.1 Methodology of Constructing a Flux Plot W-1 4S.1.2 Determination of the Heat Transfer Rate W-2 4S.1.3 The Conduction Shape Factor W-3 References W-6 Problems W-6 CHAPTER 5 Transient Conduction 255 5.1 The Lumped Capacitance Method 256 5.2 Validity of the Lumped Capacitance Method 259 5.3 General Lumped Capacitance Analysis 263 5.4 Spatial Effects 270 5.5 The Plane Wall with Convection 272 5.5.1 Exact Solution 272 5.5.2 Approximate Solution 273 5.5.3 Total Energy Transfer 274 5.5.4 Additional Considerations 275 5.6 Radial Systems with Convection 276 5.6.1 Exact Solutions 276 5.6.2 Approximate Solutions 277 5.6.3 Total Energy Transfer 277 5.6.4 Additional Considerations 278 5.7 The Semi-Infinite Solid 283 5.8 Objects with Constant Surface Temperatures or Surface Heat Fluxes 290 5.8.1 Constant Temperature Boundary Conditions 290 5.8.2 Constant Heat Flux Boundary Conditions 292 5.8.3 Approximate Solutions 293 5.9 Periodic Heating 299 ftoc.qxd 3/6/06 11:11 AM Page xvi xvi Contents 5.10 Finite-Difference Methods 302 5.10.1 Discretization of the Heat Equation: The Explicit Method 302 5.10.2 Discretization of the Heat Equation: The Implicit Method 310 5.11 Summary 317 References 319 Problems 319 5S.1 Graphical Representation of One-Dimensional, Transient Conduction in the Plane Wall, Long Cylinder, and Sphere W-8 5S.2 Analytical Solution of Multidimensional Effects W-13 References W-18 Problems W-18 CHAPTER 6 Introduction to Convection 347 6.1 The Convection Boundary Layers 348 6.1.1 The Velocity Boundary Layer 348 6.1.2 The Thermal Boundary Layer 349 6.1.3 The Concentration Boundary Layer 350 6.1.4 Significance of the Boundary Layers 352 6.2 Local and Average Convection Coefficients 352 6.2.1 Heat Transfer 352 6.2.2 Mass Transfer 353 6.2.3 The Problem of Convection 355 6.3 Laminar and Turbulent Flow 359 6.3.1 Laminar and Turbulent Velocity Boundary Layers 359 6.3.2 Laminar and Turbulent Thermal and Species Concentration Boundary Layers 361 6.4 The Boundary Layer Equations 364 6.4.1 Boundary Layer Equations for Laminar Flow 365 6.5 Boundary Layer Similarity: The Normalized Boundary Layer Equations 367 6.5.1 Boundary Layer Similarity Parameters 368 6.5.2 Functional Form of the Solutions 368 6.6 Physical Significance of the Dimensionless Parameters 374 6.7 Boundary Layer Analogies 377 6.7.1 The Heat and Mass Transfer Analogy 377 6.7.2 Evaporative Cooling 381 6.7.3 The Reynolds Analogy 384 6.8 The Convection Coefficients 385 6.9 Summary 385 References 386 Problems 387 6S.1 Derivation of the Convection Transfer Equations W-21 6S.1.1 Conservation of Mass W-21 6S.1.2 Newton’s Second Law of Motion W-22 6S.1.3 Conservation of Energy W-26 6S.1.4 Conservation of Species W-28 References W-33 Problems W-33 ftoc.qxd 3/6/06 11:11 AM Page xvii Contents xvii CHAPTER 7 External Flow 401 7.1 The Empirical Method 403 7.2 The Flat Plate in Parallel Flow 405 7.2.1 Laminar Flow over an Isothermal Plate: A Similarity Solution 405 7.2.2 Turbulent Flow over an Isothermal Plate 410 7.2.3 Mixed Boundary Layer Conditions 411 7.2.4 Unheated Starting Length 412 7.2.5 Flat Plates with Constant Heat Flux Conditions 413 7.2.6 Limitations on Use of Convection Coefficients 414 7.3 Methodology for a Convection Calculation 414 7.4 The Cylinder in Cross Flow 423 7.4.1 Flow Considerations 423 7.4.2 Convection Heat and Mass Transfer 425 7.5 The Sphere 433 7.6 Flow Across Banks of Tubes 436 7.7 Impinging Jets 447 7.7.1 Hydrodynamic and Geometric Considerations 447 7.7.2 Convection Heat and Mass Transfer 449 7.8 Packed Beds 452 7.9 Summary 454 References 456 Problems 457 CHAPTER 8 Internal Flow 485 8.1 Hydrodynamic Considerations 486 8.1.1 Flow Conditions 486 8.1.2 The Mean Velocity 487 8.1.3 Velocity Profile in the Fully Developed Region 488 8.1.4 Pressure Gradient and Friction Factor in Fully Developed Flow 490 8.2 Thermal Considerations 491 8.2.1 The Mean Temperature 492 8.2.2 Newton’s Law of Cooling 493 8.2.3 Fully Developed Conditions 493 8.3 The Energy Balance 497 8.3.1 General Considerations 497 8.3.2 Constant Surface Heat Flux 498 8.3.3 Constant Surface Temperature 501 8.4 Laminar Flow in Circular Tubes: Thermal Analysis and Convection Correlations 505 8.4.1 The Fully Developed Region 505 8.4.2 The Entry Region 512 8.5 Convection Correlations: Turbulent Flow in Circular Tubes 514 8.6 Convection Correlations: Noncircular Tubes and the Concentric Tube Annulus 518 8.7 Heat Transfer Enhancement 521 ftoc.qxd 3/6/06 11:11 AM Page xviii xviii Contents 8.8 Microscale Internal Flow 524 8.8.1 Flow Conditions in Microscale Internal Flow 524 8.8.2 Thermal Considerations in Microscale Internal Flow 525 8.9 Convection Mass Transfer 528 8.10 Summary 531 References 533 Problems 534 CHAPTER 9 Free Convection 559 9.1 Physical Considerations 560 9.2 The Governing Equations 563 9.3 Similarity Considerations 564 9.4 Laminar Free Convection on a Vertical Surface 566 9.5 The Effects of Turbulence 568 9.6 Empirical Correlations: External Free Convection Flows 571 9.6.1 The Vertical Plate 571 9.6.2 Inclined and Horizontal Plates 574 9.6.3 The Long Horizontal Cylinder 579 9.6.4 Spheres 583 9.7 Free Convection within Parallel Plate Channels 584 9.7.1 Vertical Channels 585 9.7.2 Inclined Channels 587 9.8 Empirical Correlations: Enclosures 587 9.8.1 Rectangular Cavities 587 9.8.2 Concentric Cylinders 590 9.8.3 Concentric Spheres 591 9.9 Combined Free and Forced Convection 593 9.10 Convection Mass Transfer 594 9.11 Summary 595 References 596 Problems 597 CHAPTER 10 Boiling and Condensation 619 10.1 Dimensionless Parameters in Boiling and Condensation 620 10.2 Boiling Modes 621 10.3 Pool Boiling 622 10.3.1 The Boiling Curve 622 10.3.2 Modes of Pool Boiling 624 10.4 Pool Boiling Correlations 627 10.4.1 Nucleate Pool Boiling 627 10.4.2 Critical Heat Flux for Nucleate Pool Boiling 629 10.4.3 Minimum Heat Flux 629 10.4.4 Film Pool Boiling 630 10.4.5 Parametric Effects on Pool Boiling 631 ftoc.qxd 3/6/06 11:11 AM Page xix Contents xix 10.5 Forced Convection Boiling 636 10.5.1 External Forced Convection Boiling 637 10.5.2 Two-Phase Flow 637 10.5.3 Two-Phase Flow in Microchannels 640 10.6 Condensation: Physical Mechanisms 641 10.7 Laminar Film Condensation on a Vertical Plate 643 10.8 Turbulent Film Condensation 646 10.9 Film Condensation on Radial Systems 651 10.10 Film Condensation in Horizontal Tubes 654 10.11 Dropwise Condensation 655 10.12 Summary 655 References 656 Problems 657 CHAPTER 11 Heat Exchangers 669 11.1 Heat Exchanger Types 670 11.2 The Overall Heat Transfer Coefficient 673 11.3 Heat Exchanger Analysis: Use of the Log Mean Temperature Difference 675 11.3.1 The Parallel-Flow Heat Exchanger 676 11.3.2 The Counterflow Heat Exchanger 679 11.3.3 Special Operating Conditions 679 11.4 Heat Exchanger Analysis: The Effectiveness–NTU Method 686 11.4.1 Definitions 686 11.4.2 Effectiveness–NTU Relations 688 11.5 Heat Exchanger Design and Performance Calculations: Using the Effectiveness–NTU Method 694 11.6 Compact Heat Exchangers 700 11.7 Summary 705 References 706 Problems 707 11S.1 Log Mean Temperature Difference Method for Multipass and Cross-Flow Heat Exchangers W-37 References W-41 Problems W-41 CHAPTER 12 Radiation: Processes and Properties 723 12.1 Fundamental Concepts 724 12.2 Radiation Intensity 727 12.2.1 Mathematical Definitions 727 12.2.2 Radiation Intensity and Its Relation to Emission 728 12.2.3 Relation to Irradiation 733 12.2.4 Relation to Radiosity 735 12.3 Blackbody Radiation 736 12.3.1 The Planck Distribution 737 12.3.2 Wien’s Displacement Law 737 ftoc.qxd 3/6/06 11:11 AM Page xx xx Contents 12.3.3 The Stefan-Boltzmann Law 738 12.3.4 Band Emission 739 12.4 Emission from Real Surfaces 744 12.5 Absorption, Reflection, and Transmission by Real Surfaces 752 12.5.1 Absorptivity 754 12.5.2 Reflectivity 755 12.5.3 Transmissivity 756 12.5.4 Special Considerations 757 12.6 Kirchhoff’s Law 762 12.7 The Gray Surface 764 12.8 Environmental Radiation 770 12.9 Summary 776 References 780 Problems 780 CHAPTER 13 Radiation Exchange Between Surfaces 811 13.1 The View Factor 812 13.1.1 The View Factor Integral 812 13.1.2 View Factor Relations 813 13.2 Radiation Exchange Between Opaque, Diffuse, Gray Surfaces in an Enclosure 822 13.2.1 Net Radiation Exchange at a Surface 823 13.2.2 Radiation Exchange Between Surfaces 824 13.2.3 Blackbody Radiation Exchange 830 13.2.4 The Two-Surface Enclosure 831 13.2.5 Radiation Shields 832 13.2.6 The Reradiating Surface 835 13.3 Multimode Heat Transfer 839 13.4 Radiation Exchange with Participating Media 842 13.4.1 Volumetric Absorption 843 13.4.2 Gaseous Emission and Absorption 843 13.5 Summary 847 References 849 Problems 849 CHAPTER 14 Diffusion Mass Transfer 879 14.1 Physical Origins and Rate Equations 880 14.1.1 Physical Origins 880 14.1.2 Mixture Composition 881 14.1.3 Fick’s Law of Diffusion 882 14.1.4 Mass Diffusivity 883 14.2 Mass Transfer in Nonstationary Media 885 14.2.1 Absolute and Diffusive Species Fluxes 885 14.2.2 Evaporation in a Column 888 14.3 The Stationary Medium Approximation 893 ftoc.qxd 3/6/06 11:11 AM Page xxi Contents xxi 14.4 Conservation of Species for a Stationary Medium 894 14.4.1 Conservation of Species for a Control Volume 894 14.4.2 The Mass Diffusion Equation 894 14.4.3 Stationary Media with Specified Surface Concentrations 897 14.5 Boundary Conditions and Discontinuous Concentrations at Interfaces 900 14.5.1 Evaporation and Sublimation 901 14.5.2 Solubility of Gases in Liquids and Solids 902 14.5.3 Catalytic Surface Reactions 905 14.6 Mass Diffusion with Homogeneous Chemical Reactions 908 14.7 Transient Diffusion 911 14.8 Summary 916 References 917 Problems 917 APPENDIX A Thermophysical Properties of Matter 927 APPENDIX B Mathematical Relations and Functions 959 APPENDIX C Thermal Conditions Associated with Uniform Energy Generation in One-Dimensional, Steady-State Systems 965 APPENDIX D The Convection Transfer Equations 973 D.1 Conservation of Mass 974 D.2 Newton’s Second Law of Motion 974 D.3 Conservation of Energy 975 D.4 Conservation of Species 976 APPENDIX E Boundary Layer Equations for Turbulent Flow 977 APPENDIX F An Integral Laminar Boundary Layer Solution for Parallel Flow over a Flat Plate 981 Index 985 ftoc.qxd 3/6/06 11:11 AM Page xxii ftoc.qxd 3/6/06 11:11 AM Page xxiii Symbols A A area, m2 Ėst rate of increase of energy stored within a Ab area of prime (unfinned) surface, m2 control volume, W Ac cross-sectional area, m2 e thermal internal energy per unit mass, Aff free-flow area in compact heat exchanger J/kg; surface roughness, m core (minimum cross-sectional area F force, N; heat exchanger correction available for flow through the core), m2 factor; fraction of blackbody radiation Afr heat exchanger frontal area, m2 in a wavelength band; view factor Ap fin profile area, m2 Fo Fourier number Ar nozzle area ratio Fr Froude number a acceleration, m/s2 f friction factor; similarity variable Bi Biot number G irradiation, W/m2; mass velocity, kg/s
m2 Bo Bond number Gr Grashof number C molar concentration, kmol/m3; heat Gz Graetz number capacity rate, W/K g gravitational acceleration, m/s2 CD drag coefficient gc gravitational constant, 1 kg
m/N
s2 or Cf friction coefficient 32.17 ft
lbm/lbf
s2 Ct thermal capacitance, J/K H nozzle height, m; Henry’s constant, Co Confinement number bars c specific heat, J/kg
K; speed of light, m/s h convection heat transfer coefficient, cp specific heat at constant pressure, J/kg
K W/m2
K; Planck’s constant cv specific heat at constant volume, J/kg
K hfg latent heat of vaporization, J/kg D diameter, m hsf latent heat of fusion, J/kg DAB binary mass diffusivity, m2/s hm convection mass transfer Db bubble diameter, m coefficient, m/s Dh hydraulic diameter, m hrad radiation heat transfer coefficient, E thermal plus mechanical energy, J; W/m2
K electric potential, V; emissive power, I electric current, A; radiation intensity, W/m2 W/m2
sr tot E total energy, J i electric current density, A/m2; enthalpy Ec Eckert number per unit mass, J/kg Ėg rate of energy generation, W J radiosity, W/m2 Ėin rate of energy transfer into a control Ja Jakob number volume, W J*i diffusive molar flux of species i relative Ėout rate of energy transfer out of control to the mixture molar average velocity, volume, W kmol/s
m2 ftoc.qxd 3/6/06 11:11 AM Page xxiv xxiv Symbols ji diffusive mass flux of species i relative Pe Peclet number (RePr) to the mixture mass average velocity, Pr Prandtl number kg/s
m2 p pressure, N/m2 jH Colburn j factor for heat transfer Q energy transfer, J jm Colburn j factor for mass transfer q heat transfer rate, W k thermal conductivity, W/m
K; q̇ rate of energy generation per unit Boltzmann’s constant volume, W/m3 k0 zero-order, homogeneous reaction rate q heat transfer rate per unit constant, kmol/s
m3 length, W/m k1 first-order, homogeneous reaction rate q
heat flux, W/m2 constant, s
1 q* dimensionless conduction heat rate k
1 first-order, homogeneous reaction rate R cylinder radius, m constant, m/s  universal gas constant L characteristic length, m Ra Rayleigh number Le Lewis number Re Reynolds number M mass, kg; number of heat transfer lanes Re electric resistance,  in a flux plot; reciprocal of the Rf fouling factor, m2
K/W Fourier number for finite-difference Rm mass transfer resistance, s/m3 solutions Rm,n residual for the m, n nodal point Ṁi rate of transfer of mass for species, i, Rt thermal resistance, K/W kg/s Rt,c thermal contact resistance, K/W Ṁi,g rate of increase of mass of species i due Rt,f fin thermal resistance, K/W to chemical reactions, kg/s Rt,o thermal resistance of fin Ṁin rate at which mass enters a control array, K/W volume, kg/s ro cylinder or sphere radius, m Ṁout rate at which mass leaves a control r, , z cylindrical coordinates volume, kg/s r, ,  spherical coordinates Ṁst rate of increase of mass stored within a S solubility, kmol/m3
atm; shape factor control volume, kg/s for two-dimensional conduction, m;
i molecular weight of species i, kg/kmol nozzle pitch, m; plate spacing, m m mass, kg Sc solar constant ṁ mass flow rate, kg/s SD, SL, ST diagonal, longitudinal, and transverse mi mass fraction of species i,
i /
pitch of a tube bank, m N number of temperature increments in a Sc Schmidt number flux plot; total number of tubes in a Sh Sherwood number tube bank; number of surfaces in an St Stanton number enclosure T temperature, K NL,NT number of tubes in longitudinal and t time, s transverse directions U overall heat transfer coefficient, W/m2
Nu Nusselt number K; internal energy, J NTU number of transfer units u, v, w mass average fluid velocity Ni molar transfer rate of species i relative to components, m/s fixed coordinates, kmol/s u*, v*, w* molar average velocity components, N
i molar flux of species i relative to fixed m/s coordinates, kmol/s
m2 V volume, m3; fluid velocity, m/s Ṅi molar rate of increase of species i per v specific volume, m3/kg unit volume due to chemical reactions, W width of a slot nozzle, m kmol/s
m3 Ẇ rate at which work is performed, W Ṅ
i surface reaction rate of species i, We Weber number kmol/s
m2 X vapor quality n
i mass flux of species i relative to fixed X, Y, Z components of the body force per unit coordinates, kg/s
m2 volume, N/m3 ṅi mass rate of increase of species i per unit x, y, z rectangular coordinates, m volume due to chemical reactions, xc critical location for transition to kg/s
m3 turbulence, m P perimeter, m; general fluid property xfd,c concentration entry length, m designation xfd,h hydrodynamic entry length, m PL,PT dimensionless longitudinal and xfd,t thermal entry length, m transverse pitch of a tube bank xi mole fraction of species i, Ci /C ftoc.qxd 3/6/06 11:11 AM Page xxv Symbols xxv Greek Letters D diameter; drag  thermal diffusivity, m2/s; heat dif diffusion exchanger surface area per unit e excess; emission; electron volume, m2/m3; absorptivity evap evaporation  volumetric thermal expansion f fluid properties; fin conditions; saturated coefficient, K
1 liquid conditions  mass flow rate per unit width in film fc forced convection condensation, kg/s
m fd fully developed conditions  hydrodynamic boundary layer g saturated vapor conditions thickness, m H heat transfer conditions c concentration boundary layer h hydrodynamic; hot fluid; helical thickness, m i general species designation; inner p thermal penetration depth, m surface of an annulus; initial t thermal boundary layer thickness, m condition; tube inlet condition;  emissivity; porosity of a packed bed; incident radiation heat exchanger effectiveness L based on characteristic length f fin effectiveness l saturated liquid conditions  similarity variable lat latent energy f fin efficiency lm log mean condition o overall efficiency of fin array M momentum transfer condition  zenith angle, rad; temperature difference, m mean value over a tube cross section K max maximum fluid velocity absorption coefficient, m
1 mfp mean free path wavelength, m o center or midplane condition; tube outlet mfp mean free path length, nm condition; outer viscosity, kg/s
m ph phonon kinematic viscosity, m2/s; frequency of R reradiating surface radiation, s
1 r, ref reflected radiation
mass density, kg/m3; reflectivity rad radiation Stefan-Boltzmann constant; electrical S solar conditions conductivity, 1/
m; normal viscous s surface conditions; solid properties stress, N/m2; surface tension, N/m; sat saturated conditions ratio of heat exchanger minimum sens sensible energy cross-sectional area to frontal area sky sky conditions  viscous dissipation function, s
2 ss steady state  azimuthal angle, rad sur surroundings  stream function, m2/s t thermal  shear stress, N/m2; transmissivity tr transmitted  solid angle, sr; perfusion rate, s
1 v saturated vapor conditions x local conditions on a surface Subscripts spectral A, B species in a binary mixture
free stream conditions abs absorbed am arithmetic mean Superscripts b base of an extended surface; blackbody  fluctuating quantity c cross-sectional; concentration; cold fluid * molar average; dimensionless quantity cr critical insulation thickness cond conduction Overbar conv convection surface average conditions; time mean CF counterflow ftoc.qxd 3/6/06 11:11 AM Page xxvi c01.qxd 3/6/06 10:21 AM Page 1 C H A P T E R 1 Introduction c01.qxd 3/6/06 10:21 AM Page 2 2 Chapter 1
Introduction F rom the study of thermodynamics, you have learned that energy can be trans- ferred by interactions of a system with its surroundings. These interactions are called work and heat. However, thermodynamics deals with the end states of the process during which an interaction occurs and provides no information concerning the nature of the interaction or the time rate at which it occurs. The objective of this text is to extend thermodynamic analysis through study of the modes of heat trans- fer and through development of relations to calculate heat transfer rates. In this chapter we lay the foundation for much of the material treated in the text. We do so by raising several questions. What is heat transfer? How is heat transferred? Why is it important? One objective is to develop an appreciation for the fundamental concepts and principles that underlie heat transfer processes. A second objective is to illustrate the manner in which a knowledge of heat transfer may be used with the first law of thermodynamics (conservation of energy) to solve problems relevant to technology and society. 1.1 What and How? A simple, yet general, definition provides sufficient response to the question: What is heat transfer? Heat transfer (or heat) is thermal energy in transit due to a spatial temperature difference. Whenever there exists a temperature difference in a medium or between media, heat transfer must occur. As shown in Figure 1.1, we refer to different types of heat transfer processes as modes. When a temperature gradient exists in a stationary medium, which may be a solid or a fluid, we use the term conduction to refer to the heat transfer that will occur across the medium. In contrast, the term convection refers to heat trans- fer that will occur between a surface and a moving fluid when they are at different Conduction through a solid Convection from a surface Net radiation heat exchange or a stationary fluid to a moving fluid between two surfaces T1 > T2 Ts > T∞ T1 T2 Surface, T1 Moving fluid, T∞ Surface, T2 q" q"1 q" Ts q"2 FIGURE 1.1 Conduction, convection, and radiation heat transfer modes. c01.qxd 3/6/06 10:21 AM Page 3 1.2
Physical Origins and Rate Equations 3 temperatures. The third mode of heat transfer is termed thermal radiation. All sur- faces of finite temperature emit energy in the form of electromagnetic waves. Hence, in the absence of an intervening medium, there is net heat transfer by radiation between two surfaces at different temperatures. 1.2 Physical Origins and Rate Equations As engineers it is important that we understand the physical mechanisms which un- derlie the heat transfer modes and that we be able to use the rate equations that quantify the amount of energy being transferred per unit time. 1.2.1 Conduction At mention of the word conduction, we should immediately conjure up concepts of atomic and molecular activity, for it is processes at these levels that sustain this mode of heat transfer. Conduction may be viewed as the transfer of energy from the more energetic to the less energetic particles of a substance due to interactions be- tween the particles. The physical mechanism of conduction is most easily explained by considering a gas and using ideas familiar from your thermodynamics background. Consider a gas in which there exists a temperature gradient and assume that there is no bulk, or macroscopic, motion. The gas may occupy the space between two surfaces that are maintained at different temperatures, as shown in Figure 1.2. We associate the tem- perature at any point with the energy of gas molecules in proximity to the point. This energy is related to the random translational motion, as well as to the internal rota- tional and vibrational motions, of the molecules. T T1 > T2 xo q"x q"x x T2 FIGURE 1.2 Association of conduction heat transfer with diffusion of energy due to molecular activity. c01.qxd 3/6/06 10:21 AM Page 4 4 Chapter 1
Introduction Higher temperatures are associated with higher molecular energies, and when neighboring molecules collide, as they are constantly doing, a transfer of energy from the more energetic to the less energetic molecules must occur. In the presence of a temperature gradient, energy transfer by conduction must then occur in the direction of decreasing temperature. This would even be true in the absence of collisions, as is evident from Figure 1.2. The hypothetical plane at xo is constantly being crossed by molecules from above and below due to their random motion. However, molecules from above are associated with a larger temperature than those from below, in which case there must be a net transfer of energy in the posi- tive x direction. Collisions between molecules enhance this energy transfer. We may speak of the net transfer of energy by random molecular motion as a diffusion of energy. The situation is much the same in liquids, although the molecules are more closely spaced and the molecular interactions are stronger and more frequent. Simi- larly, in a solid, conduction may be attributed to atomic activity in the form of lat- tice vibrations. The modern view is to ascribe the energy transfer to lattice waves induced by atomic motion. In an electrical nonconductor, the energy transfer is ex- clusively via these lattice waves; in a conductor it is also due to the translational motion of the free electrons. We treat the important properties associated with con- duction phenomena in Chapter 2 and in Appendix A. Examples of conduction heat transfer are legion. The exposed end of a metal spoon suddenly immersed in a cup of hot coffee will eventually be warmed due to the conduction of energy through the spoon. On a winter day there is significant energy loss from a heated room to the outside air. This loss is principally due to conduction heat transfer through the wall that separates the room air from the out- side air. It is possible to quantify heat transfer processes in terms of appropriate rate equations. These equations may be used to compute the amount of energy being transferred per unit time. For heat conduction, the rate equation is known as T Fourier’s law. For the one-dimensional plane wall shown in Figure 1.3, having a temperature distribution T(x), the rate equation is expressed as T1 dT q"x T(x) q
x
k (1.1) dx T2 The heat flux q
x (W/m2) is the heat transfer rate in the x direction per unit area per- x pendicular to the direction of transfer, and it is proportional to the temperature gra- L dient, dT/dx, in this direction. The parameter k is a transport property known as the thermal conductivity (W/m
K) and is a characteristic of the wall material. The FIGURE 1.3 One-dimensional heat minus sign is a consequence of the fact that heat is transferred in the direction of de- transfer by conduction creasing temperature. Under the steady-state conditions shown in Figure 1.3, where (diffusion of energy). the temperature distribution is linear, the temperature gradient may be expressed as dT T2  T1
dx L and the heat flux is then T2  T1 q
x
k L c01.qxd 3/6/06 10:21 AM Page 5 1.2
Physical Origins and Rate Equations 5