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HEAT TRANSFER
HANDBOOK
Adrian Bejan
J. A. Jones Professor of Mechanical Engineering

Department of Mechanical Engineering
Duke University
Durham, North Carolina
Allan D. Kraus
Department of Mechanical Engineering
University of Akron
Akron, Ohio
JOHN WILEY & SONS, INC.
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Designations used by companies to distinguish their products are often claimed as trademarks. In all
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Copyright © 2003 by John Wiley & Sons, Inc. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
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Library of Congress Cataloging-in-Publication Data:
Bejan, Adrian, 1948–
Heat transfer handbook / Adrian Bejan, Allan D. Kraus.
p. cm.
ISBN 0-471-39015-1 (cloth : alk. paper)
1. Heat—Transmission—Handbooks, manuals, etc. I. Kraus, Allan D. II. Title.
TJ250 .B35 2003
621.402'2—dc21 2002028857
Printed in the United States of America
10987654321
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To Warren Rohsenow and James Hartnett
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PREFACE
Heat transfer has emerged as a central discipline in contemporary engineering sci-
ence. The research activity of a few decades ago—the material reviewed in the first
handbooks—has distilled itself into textbook concepts and results. Heat transfer has
become not only a self-standing discipline in the current literature and engineering
curricula, but also an indispensable discipline at the interface with other pivotal and
older disciplines. For example, fluid mechanics today is capable of describing the
transport of heat and other contaminants because of the great progress made in mod-
ern convective heat transfer. Thermodynamics today is able to teach modeling, sim-
ulation, and optimization of “realistic” energy systems because of the great progress
made in heat transfer. Ducts, extended surfaces, heat exchangers, and other features
that may be contemplated by the practitioner are now documented in the heat transfer
literature.
To bring this body of results to the fingertips of the reader is one of the objectives
of this new handbook. The more important objective, however, is to inform the reader
on what has been happening in the field more recently. In brief, heat transfer marches
forward through new ideas, applications, and emerging technologies. The vigor of
heat transfer has always come from its usefulness. For example, the challenges of
energy self-sufficiency and aerospace travel, which moved the field in the 1970s,
are still with us; in fact, they are making a strong comeback. Another example is
the miniaturization revolution, which continues unabated. The small-scale channels
of the 1980s do not look so small anymore. Even before “small scale” became the
fashion, we in heat transfer had “compact” heat exchangers. The direction for the

future is clear.
The importance of optimizing the architecture of a flow system to make it fit into
a finite volume with purpose has always been recognized in heat transfer. It has been
and continues to be the driving force. Space comes at a premium. Better and better
shapes of extended surfaces are evolving into networks, bushes, and trees of fins. The
many surfaces designed for heat transfer augmentation are accomplishing the same
thing: They are increasing the heat transfer rate density, the size of the heat transfer
enterprise that is packed into a given volume.
The smallest features are becoming smaller, but this is only half of the story. The
other is the march toward greater complexity. More and more small-scale features
must be connected and assembled into a device whose specified size is always macro-
scopic. Small-scale technologies demand the optimization of increasingly complex
heat-flow architectures.
A highly distinguished group of colleagues who are world authorities on the
frontiers of heat transfer today have contributed to this new handbook. Their chapters
provide a bird’s-eye view of the state of the field, highlighting both the foundations
ix
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and, especially, the edifices that rest on them. Because space comes at a premium, we
have allocated more pages to those chapters dedicated to current applications. The
latest important references are acknowledged; the classical topics are presented more
briefly.
One feature of the handbook is that the main results and correlations are summa-
rized at the ends of chapters. This feature was chosen to provide quick access and
to help the flow of heat transfer knowledge from research to computer-aided design.
It is our hope that researchers and practitioners of heat transfer will find this new
handbook inspiring and useful.
Adrian Bejan acknowledges with gratitude the support received from Professor
Kristina Johnson, Dean of the Pratt School of Engineering, and Professor Kenneth
Hall, Chairman of the Department of Mechanical Engineering and Materials Science,
Duke University. Allan Kraus acknowledges the assistance of his wife, who has
helped in the proofreading stage of production.
Both authors acknowledge the assistance of our editor at John Wiley, Bob Argen-
tieri, our production editor, Milagros Torres, and our fantastic copy editor, known

only to us as Barbara from Pennsylvania.
Adrian Bejan
Allan D. Kraus
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EDITORIAL ADVISORY BOARD

Cristina Amon
Department of Mechanical
Engineering
Carnegie Mellon University
Pittsburgh, PA 15213-3980
Benjamin T. F. Chung
F. Theodore Harrington Emeritus
Professor
Department of Mechanical
Engineering
302 East Buchtel Mall
University of Akron
Akron, OH 44325-3903
Avram Bar-Cohen
Professor and Chair
Department of Mechanical
Engineering
2181B Martin Hall
University of Maryland
College Park, MD 20742-3035
Sadik Kakac
Department of Mechanical
Engineering
University of Miami
Coral Gables, FL 33124-0624
G. P. Peterson
Provost
Rensselaer Polytechnic Institute
110 Eighth Street
Troy, NY 12180-3590

James Welty
Department of Mechanical
Engineering
Rogers Hall
Oregon State University
Corvallis, OR 97330
Michael M. Yovanovich
Department of Mechanical
Engineering
University of Waterloo
Waterloo, Ontario N2L 3G1
Canada
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CONTRIBUTORS
A. Aziz, Department of MechanicalEngineering, Gonzaga University, Spokane, WA
99258-0026
Avram Bar-Cohen, Department of Mechanical Engineering, University of Min-
nesota, Minneapolis, MN 55455-0213
Current address: Glenn L. Martin Institute of Technology, A. James Clark School
of Engineering, Department of Mechanical Engineering, 2181 Glenn L. Martin
Hall, College Park, MD 20742-3035
Adrian Bejan, J. A. Jones Professorof Mechanical Engineering, Department of Me-
chanical Engineering and Materials Science, Duke University, Durham, NC 27708-
0300
Robert F. Boehm, University of Nevada–Las Vegas, Las Vegas, NV 89154-4027
J. C. Chato, Department of Mechanical and Industrial Engineering, University of
Illinois–Urbana-Champaign, Urbana, IL 61801
C. Haris Doumanidis, Department of Mechanical Engineering, Tufts University,
Medford, MA 02150
R. T Jacobsen, Idaho National Engineering and Environmental Laboratory, Idaho
Falls, ID 83415-3790
Yogesh Jaluria, Mechanical and Aerospace Engineering Department, Rutgers Uni-
versity, New Brunswick, NJ 08901-1281

Yogendra Joshi, George W. Woodruff School of Mechanical Engineering, Georgia
Institute of Technology, Atlanta, GA 30332-0405
M. A. Kedzierski, Building and Fire Research Laboratory, National Institute of
Standards and Technology, Gaithersburg, MD 20899
Allan D. Kraus, University of Akron, Akron, OH 44325-3901
José L. Lage, Laboratory of Porous Materials Applications, Mechanical Engineer-
ing Department, Southern Methodist University, Dallas, TX 75275-0337
E. W. Lemmon, Physical and Chemical Properties Division, National Institute of
Standards and Technology, Boulder, CO 80395-3328
R. M. Manglik, Thermal-Fluids and Thermal Processing Laboratory, Department
of Mechanical, Industrial and Nuclear Engineering, University of Cincinnati, 598
Rhodes Hall, P.O. Box 210072, Cincinnati, OH 45221-0072
xiii
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xiv CONTRIBUTORS
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E. E. Marotta, Senior Engineer/Scientist, Thermal Technologies Group, IBM Cor-
poration, Poughkeepsie, NY 12801
Michael F. Modest, Professor of Mechanical and Nuclear Engineering, College of
Engineering, Pennsylvania State University, University Park, PA 16802-1412
Wataru Nakayama, Therm Tech International, Kanagawa, Japan 255-0004
Pamela M. Norris, Associate Professor, Department of Mechanical and Aerospace
Engineering, University of Virginia, Charlottesville, VA 22903
Jay M. Ochterbeck, College of Engineering and Science, Department of Mechani-
cal Engineering, Clemson University, Clemson, SC 29634-0921
S. G. Penoncello, Center for Applied Thermodynamic Studies, College of Engineer-
ing, University of Idaho, Moscow, ID 83844-1011
Ranga Pitchumani, Department of Mechanical Engineering, University of Con-
necticut, Storrs, CT 06269-3139
Ravi S. Prasher, Intel Corporation, Chandler, AZ 85225
T. J. Rabas, Consultant, Downers Grove, IL 60516
Z. Shan, Center for Applied Thermodynamic Studies, College of Engineering, Uni-
versity of Idaho, Moscow, ID 83844-1011

Andrew N. Smith, Department of Mechanical Engineering, United States Naval
Academy, Annapolis, MD 21402-5000
Richard N. Smith, Department of Mechanical Engineering, Aeronautical Engineer-
ing and Mechanics, Rensselaer Polytechnic Institute, Troy, NY 12180-3590
John R. Thome, Laboratory of Heat and Mass Transfer, Faculty of Engineering Sci-
ence, Swiss Federal Institute of Technology Lausanne, CH-1015 Lausanne, Switzer-
land
Abhay A. Watwe, Intel Corporation, Chandler, AZ 85225
N. T. Wright, Department of Mechanical Engineering, University of Maryland,
Baltimore, MD 21250
M. M. Yovanovich, Distinguished Professor Emeritus, Department of Mechanical
Engineering, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
CONTENTS
Preface ix
Contributors xi
1. Basic Concepts 1
Allan D. Kraus
2. Thermophysical Properties of Fluids and Materials 43
R. T Jacobsen, E. W. Lemmon, S. G. Penoncello, Z. Shan, and N. T. Wright
3. Conduction Heat Transfer 161
A. Aziz
4. Thermal Spreading and Contact Resistances 261
M. M. Yovanovich and E. E. Marotta
5. Forced Convection: Internal Flows 395
Adrian Bejan
6. Forced Convection: External Flows 439
Yogendra Joshi and Wataru Nakayama
7. Natural Convection 525
Yogesh Jaluria
8. Thermal Radiation 573

Michael F. Modest
9. Boiling 635
John R. Thome
10. Condensation 719
M. A. Kedzierski, J. C. Chato, and T. J. Rabas
11. Heat Exchangers 797
Allan D. Kraus
12. Experimental Methods 913
José L. Lage
13. Heat Transfer in Electronic Equipment 947
Avram Bar-Cohen, Abhay A. Watwe, and Ravi S. Prasher
14. Heat Transfer Enhancement 1029
R. M. Manglik
vii

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