thermal-fluid sciences 0.pdf

THERMAL-FLUID SCIENCESAn Integrated Approach

Thermal-Fluid Sciences is a truly integrated textbook for an engineering course covering thermodynamics, heattransfer, and fluid mechanics. This integration is based on the fundamental conservation principles of mass, energy,and momentum; a hierarchical grouping of related topics; and the early introduction and revisiting of practical deviceexamples and applications.

As with all textbooks the focus is on accuracy and pedagogy. To enhance the learning experience Thermal-FluidSciences features full-color illustrations. The robust pedagogy includes chapter learning objectives, overviews,historical vignettes, and numerous examples that follow a consistent problem-solving format, enhanced by innovativeself tests and color coding to highlight significant equations and advanced topics. Each chapter concludes with a briefsummary and a unique checklist of key concepts and definitions. Integrated tutorials show the student how to usemodern software including the NIST database (included on the in-text CD) to obtain thermodynamic and transportproperties.

Stephen R. Turns has been a Professor of Mechanical Engineering at The Pennsylvania State University sincecompleting his Ph.D. at the University of Wisconsin in 1979. Before that Steve spent five years in the Engine ResearchDepartment of General Motors Research Laboratories in Warren, Michigan. His active research interests include thestudy of pollutant formation and control in combustion systems, combustion engines, combustion instrumentation,slurry fuel combustion, energy conversion, and energy policy. He has published numerous referreed journal articleson many of these topics. Steve is a member of the ASME and many other professional organizations and has been anABET Program Evaluator since 1994. He is also a dedicated teacher, for which he has won numerous awardsincluding the Penn State Teaching and Learning Consortium, Hall of Fame Faculty Award; Penn State’s Milton S.Eisenhower Award for Distinguished Teaching; the Premier Teaching Award, Penn State Engineering Society; and theOutstanding Teaching Award, Penn State Engineering Society. Steve’s talent as a teacher is also reflected in his best-selling advanced undergraduate textbook Introduction to Combustion: Concepts and Applications, 2nd ed. Steve’scommitment to students and teaching is shown in the innovative approach and design of Thermal-Fluid Sciences: AnIntegrated Approach and its companion volume Thermodynamics, also published by Cambridge University Press.

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In lecturing on any subject, it seems to be the natural course to begin with a clear explanation

of the nature, purpose, and scope of the subject. But in answer to the question

“What is thermo-dynamics?” I feel tempted to reply

“It is a very difficult subject, nearly, if not quite, unfit for a lecture.”

Osborne Reynolds

On the General Theory of Thermo-dynamics

November 1883

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THERMAL-FLUIDSCIENCES

Stephen R. TurnsThe Pennsylvania State University

AN INTEGRATED APPROACH

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CAMBRIDGE UNIVERSITY PRESS

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo

CAMBRIDGE UNIVERSITY PRESS

40 West 20th Street, New York, NY 10011–4211, USA

www.cambridge.org

Information on this title:

© Stephen R. Turns 2006

This publication is in copyright. Subject to statutory exception

and to the provisions of relevant collective licensing agreements,

no reproduction of any part may take place without

the written permission of Cambridge University Press.

First published 2006

Printed in Hong Kong by Golden Cup Printing Co. Ltd.

A catalog record for this publication is available from the British Library.

Library of Congress Cataloging-in-Publication Data

Pages 1157–1158 constitute a continuation of the copyright page.

Turns, Stephen R.

Thermal-fluid sciences : an integrated approach / Stephen R. Turns.

p. cm.

Includes bibliographical references and index.

ISBN-13: 978-0-521-85043-8 (hardback : alk. paper)

ISBN-10: 0-521-85043-6 (hardback : alk. paper)

1. Thermodynamics. 2. Gas flow. 3. Heat–Transmission. I. Title.

QC311.T86 2005

536'.7–dc22

2005026545

ISBN-13 978 0 521 85043 8 hardback

ISBN-10 0 521 85043 6 hardback

Cambridge University Press has no responsibility

for the persistence or accuracy of urls for external or

third-party Internet websites referred to in this publication,

and does not guarantee that any content on such

websites is, or will remain, accurate or appropriate.

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This book is dedicated toMike, Matt, Sara, and Bryan

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Contents

Chapter 1 ● BEGINNINGS 2

LEARNING OBJECTIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.1 WHAT ARE THE THERMAL-FLUID SCIENCES? . . . 4

1.2 SOME APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2a Fossil-Fueled Steam Power Plants . . . . . . . . . . . . . . . . . . . 6

1.2b Solar-Heated Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.2c Spark-Ignition Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.2d Jet Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.2e Biological Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.3 PHYSICAL FRAMEWORKS FOR ANALYSIS . . . . . . 17

1.3a Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.3b Control Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.3c Integral versus Differential Analyses . . . . . . . . . . . . . . . . . 19

1.4 PREVIEW OF CONSERVATION PRINCIPLES . . . . . 21

1.4a Generalized Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.4b Motivation to Study Properties . . . . . . . . . . . . . . . . . . . . . . 22

1.5 KEY CONCEPTS AND DEFINITIONS . . . . . . . . . . . . . 23

1.5a Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

1.5b States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

page vii

PART ONE: FUNDAMENTALS 1

SAMPLE SYLLABI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii

PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxiii

ABOUT THE AUTHOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxvii

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxix

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1.5c Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

1.5d Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

1.5e Equilibrium and the Quasi-Equilibrium Process . . . . . . . . . 27

1.5f Local Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

1.6 SOME GENERAL CHARACTERISTICS OF REAL FLOWS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

1.7 DIMENSIONS AND UNITS . . . . . . . . . . . . . . . . . . . . . . 31

1.8 PROBLEM-SOLVING METHOD . . . . . . . . . . . . . . . . . 34

1.9 HOW TO USE THIS BOOK . . . . . . . . . . . . . . . . . . . . . . 34

SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

KEY CONCEPTS & DEFINITIONS CHECKLIST . . . . . . . . . 36

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

QUESTIONS AND PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . 38

APPENDIX 1A: SPARK-IGNITION ENGINES . . . . . . . . . . . . 44

Chapter 2 ● THERMODYNAMIC PROPERTIES, PROPERTYRELATIONSHIPS, AND PROCESSES 46


OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.1 KEY DEFINITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.2 FREQUENTLY USED THERMODYNAMIC PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

2.2a Properties Related to the Equation of State . . . . . . . . . . . . 50

Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Number of Moles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Specific Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

2.2b Properties Related to the First Law and Calorific Equation of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Internal Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Specific Heats and Specific-Heat Ratio . . . . . . . . . . . . . . . 61

2.2c Properties Related to the Second Law . . . . . . . . . . . . . . . . 64

Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Gibbs Free Energy or Gibbs Function . . . . . . . . . . . . . . . . 65

Helmholtz Free Energy or Helmholtz Function . . . . . . . . . 65

2.3 CONCEPT OF STATE RELATIONSHIPS . . . . . . . . . . 66

2.3a State Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

2.3b P–v–T Equations of State . . . . . . . . . . . . . . . . . . . . . . . . . . 66

2.3c Calorific Equations of State . . . . . . . . . . . . . . . . . . . . . . . . 66

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2.3d Temperature–Entropy (Gibbs) Relationships . . . . . . . . . . . 67

2.4 IDEAL GASES AS PURE SUBSTANCES . . . . . . . . . . . 67

2.4a Ideal Gas Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

2.4b Ideal-Gas Equation of State . . . . . . . . . . . . . . . . . . . . . . . . 68

2.4c Processes in P–v–T Space . . . . . . . . . . . . . . . . . . . . . . . . . 71

2.4d Ideal-Gas Calorific Equations of State . . . . . . . . . . . . . . . . 74

2.4e Ideal-Gas Temperature–Entropy (Gibbs) Relationships . . . 80

2.4f Ideal-Gas Isentropic Process Relationships . . . . . . . . . . . . 83

2.4g Processes in T–s and P–v Space . . . . . . . . . . . . . . . . . . . . . 84

2.4h Polytropic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

2.5 NONIDEAL GAS PROPERTIES . . . . . . . . . . . . . . . . . . 90

2.5a State (P–v–T) Relationships . . . . . . . . . . . . . . . . . . . . . . . . 90

Tabulated Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

TUTORIAL 1—How to Interpolate . . . . . . . . . . . . . . . . . . . . . 94

Other Equations of State . . . . . . . . . . . . . . . . . . . . . . . . . . 96

Generalized Compressibility . . . . . . . . . . . . . . . . . . . . . . . 98

2.5b Calorific Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

2.5c Second-Law Relationships . . . . . . . . . . . . . . . . . . . . . . . . . 102

2.6 PURE SUBSTANCES INVOLVING LIQUID AND VAPOR PHASES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

2.6a State (P–v–T ) Relationships . . . . . . . . . . . . . . . . . . . . . . . 102

Phase Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

A New Property—Quality . . . . . . . . . . . . . . . . . . . . . . . . . 105

Property Tables and Databases . . . . . . . . . . . . . . . . . . . . . 108

TUTORIAL 2—How to Use the NIST Software . . . . . . . . . . . 111

TUTORIAL 3—How to Define a Thermodynamic State . . . . . 115

T–v Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

P–v Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

2.6b Calorific and Second-Law Properties . . . . . . . . . . . . . . . . . 123

T–s Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

h–s Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

2.7 LIQUID PROPERTY APPROXIMATIONS . . . . . . . . . 130

2.8 SOLIDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

2.9 IDEAL-GAS MIXTURES . . . . . . . . . . . . . . . . . . . . . . . . 134

2.9a Specifying Mixture Composition . . . . . . . . . . . . . . . . . . . . 135

2.9b State (P–v–T ) Relationships for Mixtures . . . . . . . . . . . . . 135

2.9c Standardized Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

2.9d Calorific Relationships for Mixtures . . . . . . . . . . . . . . . . . 141

2.9e Second-Law Relationships for Mixtures . . . . . . . . . . . . . . . 141

2.10 SOME PROPERTIES OF REACTING MIXTURES . . 142

2.10a Enthalpy of Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . 142

2.10b Heating Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

2.11 TRANSPORT PROPERTIES . . . . . . . . . . . . . . . . . . . . . 146

Contents ix

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2.11a Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

2.11b Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149


REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

QUESTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

APPENDIX 2A: MOLECULAR INTERPRETATION OF ENTROPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

Chapter 3 ● CONSERVATION OF MASS 172


OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

3.1 HISTORICAL CONTEXT . . . . . . . . . . . . . . . . . . . . . . . 174

3.2 MASS CONSERVATION FOR A SYSTEM . . . . . . . . . . 175

3.3 MASS CONSERVATION FOR A CONTROL VOLUME 183

3.3a Velocity Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Velocity Vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Streamlines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

3.3b Flow rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

Uniform Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

Distributed Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

Generalized Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

3.3c Average Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

3.3d General View of Mass Conservation for Control Volumes . 195

3.3e Integral Control Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . 196

Steady-State, Steady Flow . . . . . . . . . . . . . . . . . . . . . . . . . 196

Unsteady Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

3.3f Differential Control Volumes . . . . . . . . . . . . . . . . . . . . . . . 207

Steady-State, Steady Flow . . . . . . . . . . . . . . . . . . . . . . . . . 207

Unsteady Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

3.4 TURBULENCE AND TIME-AVERAGED PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

3.4a Mean and Fluctuating Quantities . . . . . . . . . . . . . . . . . . . . 213

3.4b Time-Averaged Mass Conservation . . . . . . . . . . . . . . . . . . 214

Integral Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

Differential Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

3.5 REACTING SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . 216

3.5a Atom Balances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

3.5b Stoichiometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224


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REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

QUESTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

Chapter 4 ● ENERGY AND ENERGY TRANSFER 242


OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244


4.2 SYSTEM AND CONTROL-VOLUME ENERGY . . . . . 244

4.2a Energy Associated with System or Control Volume as a Whole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

4.2b Energy Associated with Matter at a Microscopic Level . . . 247

4.3 ENERGY TRANSFER ACROSS BOUNDARIES . . . . . 247

4.3a Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

4.3b Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

4.4 SIGN CONVENTIONS AND UNITS . . . . . . . . . . . . . . . 265

4.5 RATE LAWS FOR HEAT TRANSFER . . . . . . . . . . . . . 272

4.5a Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

4.5b Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

4.5c Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294


REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

QUESTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300

Chapter 5 ● CONSERVATION OF ENERGY 308


OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310


5.2 ENERGY CONSERVATION FOR A SYSTEM . . . . . . . 311

5.2a General Integral Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . 312

For an Incremental Change . . . . . . . . . . . . . . . . . . . . . . . . 312

For a Change in State . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

At an Instant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

5.2b Reacting Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326

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Constant-Pressure Combustion . . . . . . . . . . . . . . . . . . . . . 326

Constant-Volume Combustion . . . . . . . . . . . . . . . . . . . . . . 329

5.2c Special Forms for Conduction Analysis . . . . . . . . . . . . . . . 335

Integral (Macroscopic) Systems . . . . . . . . . . . . . . . . . . . . . 335

Surfaces and Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 340

Differential (Microscopic) Systems . . . . . . . . . . . . . . . . . . . 341

Electric Circuit Analogy . . . . . . . . . . . . . . . . . . . . . . . . . . 350

5.3 ENERGY CONSERVATION FOR CONTROL VOLUMES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

5.3a Integral Control Volumes with Steady Flow . . . . . . . . . . . . 355

5.3b Road Map for Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364

5.3c Special Form for Flows with Friction . . . . . . . . . . . . . . . . . 364

5.3d Integral Control Volumes with Unsteady Flow . . . . . . . . . . 366

5.3e Differential Control Volumes with Steady Flow . . . . . . . . . 370

One-Dimensional Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 370

Two-Dimensional Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 375

5.3f Differential Control Volumes with Unsteady Flow . . . . . . . 378

SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379


REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381

NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382

QUESTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384

PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

Chapter 6 ● CONSERVATION OF MOMENTUM 406


OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408


6.2 FORCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409

6.2a Surface Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409

Pressure Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409

Viscous Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410

6.2b Body Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

6.2c Other Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414

6.3 MOMENTUM CONSERVATION FOR RIGID SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414

6.3a Fluid Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415

Manometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420

Forces on Submerged Surfaces . . . . . . . . . . . . . . . . . . . . . . 423

6.3b Buoyancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430

6.3c Rigid-Body Motion with Linear Acceleration . . . . . . . . . . . 432

6.4 MOMENTUM FLOWS . . . . . . . . . . . . . . . . . . . . . . . . . . 438

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6.5 LINEAR MOMENTUM CONSERVATION FOR CONTROL VOLUMES . . . . . . . . . . . . . . . . . . . . . . . . . . 443

6.5a Simplified General View . . . . . . . . . . . . . . . . . . . . . . . . . . 443

6.5b Integral Control Volumes with Steady Flow . . . . . . . . . . . . 444

6.5c Integral Control Volumes with Unsteady Flow . . . . . . . . . . 450

6.5d Differential Control Volumes . . . . . . . . . . . . . . . . . . . . . . . 453

Total (or Material) Derivative . . . . . . . . . . . . . . . . . . . . . . 455

Convective Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . 456

The Navier–Stokes Equation . . . . . . . . . . . . . . . . . . . . . . . 457

TUTORIAL 4—WHAT IS CFD? . . . . . . . . . . . . . . . . . . . . . . . 460

6.6 MECHANICAL ENERGY EQUATION . . . . . . . . . . . . . 471

6.7 THE BERNOULLI EQUATION . . . . . . . . . . . . . . . . . . . 475

6.8 TURBULENCE REVISITED . . . . . . . . . . . . . . . . . . . . . 477

6.8a Integral Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478

6.8b Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478

Reynolds Averaging and Turbulent Stresses . . . . . . . . . . . . 478

The Closure Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480

SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480


REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483

NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484

QUESTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486

PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487

APPENDIX 6A: LINEAR MOMENTUM CONSERVATION FOR CONTROL VOLUMES IN NONINERTIALCOORDINATE SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . 509

Chapter 7 ● SECOND LAW OF THERMODYNAMICS AND SOME OF ITS CONSEQUENCES 512


OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514


7.2 USEFULNESS OF THE SECOND LAW . . . . . . . . . . . . 515

7.3 ONE FUNDAMENTAL STATEMENT OF THE SECOND LAW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515

7.3a Reservoirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517

7.3b Heat Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518

7.3c Thermal Efficiency and Coefficients of Performance . . . . . 521

7.3d Reversibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524

7.4 CONSEQUENCES OF THE KELVIN–PLANCK STATEMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526

7.4a Kelvin’s Absolute Temperature Scale . . . . . . . . . . . . . . . . . 528

7.4b The Carnot Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529

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7.4c Some Reversible Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . 531

Carnot Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531

Stirling Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532

7.5 ALTERNATIVE STATEMENTS OF THE SECOND LAW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533

7.6 ENTROPY REVISITED . . . . . . . . . . . . . . . . . . . . . . . . . 535

7.6a Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535

7.6b Connecting Entropy to the Second Law . . . . . . . . . . . . . . . 536

7.6c Entropy Balances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541

Systems Undergoing a Change of State . . . . . . . . . . . . . . . 541

Control Volumes with a Single Inlet and Outlet . . . . . . . . . 541

7.6d Criterion for Spontaneous Change . . . . . . . . . . . . . . . . . . . 542

7.6e Isentropic Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545

7.6f Entropy Production, Head Loss, and Isentropic Efficiency . 550

7.7 THE SECOND LAW AND EQUILIBRIUM . . . . . . . . . 553

7.7a Chemical Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554

Conditions of Fixed Internal Energy and Volume . . . . . . . . 554

Conditions of Fixed Temperature and Pressure . . . . . . . . . 555

Multiple Equilibrium Reactions . . . . . . . . . . . . . . . . . . . . . 563

7.7b Phase Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563

SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565


REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567

NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568

QUESTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570

PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571

Chapter 8 ● SIMILITUDE AND DIMENSIONLESSPARAMETERS 582


OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584


8.2 THE LIMITS OF THEORY . . . . . . . . . . . . . . . . . . . . . . 585

8.3 PARAMETRIC TESTING . . . . . . . . . . . . . . . . . . . . . . . 586

8.4 SIMILITUDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588

8.5 DIMENSIONLESS PARAMETERS . . . . . . . . . . . . . . . . 591

8.5a Origins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591

8.5b Dimensionless Governing Equations . . . . . . . . . . . . . . . . . 592

Dimensional Forms of the Boundary-Layer Equations . . . . 592

Characteristic Scales or Values . . . . . . . . . . . . . . . . . . . . . 594

Making the Equations Dimensionless . . . . . . . . . . . . . . . . . 596

Reynolds, Peclet, and Prandtl Numbers . . . . . . . . . . . . . . . 597

Friction Coefficient and Nusselt Number . . . . . . . . . . . . . . 601

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8.5c Other Dimensionless Parameters . . . . . . . . . . . . . . . . . . . . 604

SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607


REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609

NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610

QUESTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611

PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611

APPENDIX 8A: THE BUCKINGHAM (VASCHY) PI THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 618

Chapter 9 ● EXTERNAL FLOWS: FRICTION, DRAG, AND HEAT TRANSFER 628


OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630


9.2 BASIC EXTERNAL FLOW PATTERNS . . . . . . . . . . . . 631

9.2a Boundary Layer Concept Revisited . . . . . . . . . . . . . . . . . . 632

9.2b Bluff Bodies, Separation, and Wakes . . . . . . . . . . . . . . . . . 633

9.3 FORCED LAMINAR FLOW—FLAT PLATE . . . . . . . . 635

9.3a Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635

9.3b Solving the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640

9.3c Exact (Similarity) Solution . . . . . . . . . . . . . . . . . . . . . . . . 640

Friction and Drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640

Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646

Reynolds Analogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 649

9.3d Uniform Surface Heat Flux . . . . . . . . . . . . . . . . . . . . . . . . 651

9.3e Calculation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652

9.4 FORCED TURBULENT FLOW—FLAT PLATE . . . . . 655

9.4a Transition Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655

9.4b Velocity Profiles and Boundary-Layer Development . . . . . 656

9.4c Friction and Drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657

9.4d Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 660

9.4e Uniform Surface Heat Flux . . . . . . . . . . . . . . . . . . . . . . . . 661

9.5 FORCED FLOW—OTHER GEOMETRIES . . . . . . . . . 665

9.5a Friction and Form Drag . . . . . . . . . . . . . . . . . . . . . . . . . . . 666

9.5b Empirical Correlations for Drag and Heat Transfer . . . . . . 668

Cylinders and Other 2-D Shapes . . . . . . . . . . . . . . . . . . . . 668

Spheres and Other 3-D Shapes . . . . . . . . . . . . . . . . . . . . . 679

9.6 FREE CONVECTION . . . . . . . . . . . . . . . . . . . . . . . . . . 683

9.6a Vertical, Flat Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684

PART two: BEYOND THE FUNDAMENTALS 627

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Physical Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684

Mathematical Description . . . . . . . . . . . . . . . . . . . . . . . . . 686

Dimensionless Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 687

Solutions and Correlations . . . . . . . . . . . . . . . . . . . . . . . . . 690

Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 690

9.6b Other Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694

SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702


REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704

NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 706

QUESTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 708

PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 709

APPENDIX 9A: BOUNDARY-LAYER EQUATIONS . . . . . . . 720

APPENDIX 9B: BOUNDARY-LAYER INTEGRAL ANALYSIS 723

Chapter 10 ● INTERNAL FLOWS: FRICTION, PRESSURE DROP, AND HEAT TRANSFER 728

LEARNING OBJECTIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 729

OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 730

10.1 HISTORICAL CONTEXT . . . . . . . . . . . . . . . . . . . . . . . . 730

10.2 THE BIG PICTURE—INTEGRAL ANALYSES . . . . . . . 731

10.2a Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731

10.2b Mass Conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 732

10.2c Momentum Conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . 733

Pressure Drop and Wall Shear Stress . . . . . . . . . . . . . . . . . . 733

Friction Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735

10.2d Mechanical Energy Conservation . . . . . . . . . . . . . . . . . . . . . 735

10.2e Energy Conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736

Nominally Isothermal Flow . . . . . . . . . . . . . . . . . . . . . . . . . 736

Nonisothermal Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 737

10.3 DETAILS—FULLY DEVELOPED LAMINAR FLOWS 746

10.3a Laminar Flow Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746

10.3b Differential Conservation Equations . . . . . . . . . . . . . . . . . . . 746

10.3c Hydrodynamic Problem Solution . . . . . . . . . . . . . . . . . . . . . 747

Velocity Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 747

Average Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 749

Wall Shear Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 749

Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 749

Head Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752

Friction Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752

10.3d Thermal Problem Solution . . . . . . . . . . . . . . . . . . . . . . . . . . 755

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Temperature Distributions . . . . . . . . . . . . . . . . . . . . . . . . . 755

Heat-Transfer Coefficient: Uniform Heat Flux . . . . . . . . . . 757

Heat-Transfer Coefficient: Fixed Wall Temperature . . . . . . 757

10.4 DETAILS—FULLY DEVELOPED TURBULENT FLOWS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 759

10.4a Velocity Distributions and Wall Friction . . . . . . . . . . . . . . . 759

A Theoretical Framework . . . . . . . . . . . . . . . . . . . . . . . . . . 759

Experimental Measurements . . . . . . . . . . . . . . . . . . . . . . . 762

Average Velocity and Friction Factor . . . . . . . . . . . . . . . . . 763

Rough Tubes and Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . 768

10.4b Heat-Transfer Relationships . . . . . . . . . . . . . . . . . . . . . . . . 772

10.5 DEVELOPING FLOWS . . . . . . . . . . . . . . . . . . . . . . . . . 782

10.5a Hydrodynamic Entry Region . . . . . . . . . . . . . . . . . . . . . . . 782

Hydrodynamic Entrance Length . . . . . . . . . . . . . . . . . . . . . 782

Increased Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . 783

10.5b Thermal Entry Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . 786

Thermal Entrance Length . . . . . . . . . . . . . . . . . . . . . . . . . 786

Local Heat-Transfer Coefficients . . . . . . . . . . . . . . . . . . . . 787

Average Heat-Transfer Coefficients . . . . . . . . . . . . . . . . . . 787

10.6 DUCTS OF NONCIRCULAR CROSS SECTION . . . . . 795

10.6a Hydraulic Diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795

10.6b Laminar Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795

10.6c Turbulent Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795

10.7 MINOR LOSSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 796

SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 798


REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 800

NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 801

QUESTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803

PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804

APPENDIX 10A: SIMPLIFYING THE GOVERNING EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 817

Chapter 11 ● THERMAL-FLUID ANALYSIS OF STEADY-FLOW DEVICES 820


OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 822

11.1 STEADY-FLOW DEVICES . . . . . . . . . . . . . . . . . . . . . . 822

11.2 NOZZLES AND DIFFUSERS . . . . . . . . . . . . . . . . . . . . . 822

11.2a General Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824

Mass Conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824

Energy Conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827

Linear Momentum Conservation . . . . . . . . . . . . . . . . . . . . 831

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11.2b Flow Separation and Diffuser Performance . . . . . . . . . . . . 832

11.2c Incompressible Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837

11.2d Compressible Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 838

A Few New Concepts and Definitions . . . . . . . . . . . . . . . . . 838

Mach Number–Based Conservation Principles and

Property Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844

Converging and Converging–Diverging Nozzles . . . . . . . . 848

Nozzle Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 857

11.3 THROTTLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 860

11.3a Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 860



Mechanical Energy Conservation . . . . . . . . . . . . . . . . . . . 861

11.3b Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 862

11.4 PUMPS, COMPRESSORS, AND FANS . . . . . . . . . . . . . 865

11.4a Classifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866

11.4b Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867

Control Volume Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . 867

Application of Conservation Principles . . . . . . . . . . . . . . . 868

Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 871

11.5 TURBINES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 881

11.5a Classifications and Applications . . . . . . . . . . . . . . . . . . . . . 881

11.5b Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884

11.6 HEAT EXCHANGERS . . . . . . . . . . . . . . . . . . . . . . . . . . 892

11.6a Classifications and Applications . . . . . . . . . . . . . . . . . . . . . 892

11.6b Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 894

Application of Conservation Principles . . . . . . . . . . . . . . . 894

Overall Heat-Transfer Coefficient . . . . . . . . . . . . . . . . . . . 901

Log-Mean Temperature Difference Method . . . . . . . . . . . . 906

Effectiveness—NTU Method . . . . . . . . . . . . . . . . . . . . . . . 917

11.7 FURNACES, BOILERS, AND COMBUSTORS . . . . . . 923

11.7a Some Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 923

11.7b Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 924

Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 925



SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 926


REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 928

NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 929

QUESTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 931

PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 932

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Chapter 12 ● SYSTEMS FOR POWER PRODUCTION,PROPULSION, AND HEATING AND COOLING 948


OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 950

12.1 FOSSIL-FUELED STEAM POWER PLANTS . . . . . . . 950

12.1a Rankine Cycle Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . 952

12.1b Rankine Cycle with Superheat and Reheat . . . . . . . . . . . . . 958

Superheat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 958

Reheat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 967

12.1c Rankine Cycle with Regeneration . . . . . . . . . . . . . . . . . . . 968



12.1d Energy Input from Combustion . . . . . . . . . . . . . . . . . . . . . 972

12.1e Overall Energy Utilization . . . . . . . . . . . . . . . . . . . . . . . . . 978

12.2 JET ENGINES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 980

12.2a Basic Operation of a Turbojet Engine . . . . . . . . . . . . . . . . 980

12.2b Integral Control Volume Analysis of a Turbojet . . . . . . . . . 981

Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 982



Momentum Conservation . . . . . . . . . . . . . . . . . . . . . . . . . . 985

12.2c Turbojet Cycle Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 986

Given Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 986

Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 986

Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 986

12.2d Propulsive Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 989

12.2e Other Performance Measures . . . . . . . . . . . . . . . . . . . . . . . 990

12.2f Combustor Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994

Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 995



12.3 GAS-TURBINE ENGINES . . . . . . . . . . . . . . . . . . . . . . . 1000

12.3a Integral Control Volume Analysis . . . . . . . . . . . . . . . . . . . . 1001

Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1001



12.3b Cycle Analysis and Performance Measures . . . . . . . . . . . . 1002

Air-Standard Brayton Cycle . . . . . . . . . . . . . . . . . . . . . . . . 1003

Air-Standard Thermal Efficiency . . . . . . . . . . . . . . . . . . . . 1003

Process Thermal Efficiency and Specific Fuel Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1005

Power and Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1005

12.4 REFRIGERATORS AND HEAT PUMPS . . . . . . . . . . . 1006

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12.4a Energy Conservation for a Reversed Cycle . . . . . . . . . . . . 1007

12.4b Performance Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1007

12.4c Vapor-Compression Refrigeration Cycle . . . . . . . . . . . . . . 1009

Cycle Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1010

Coefficients of Performance . . . . . . . . . . . . . . . . . . . . . . . . 1011

12.5 AIR CONDITIONING, HUMIDIFICATION,AND RELATED SYSTEMS . . . . . . . . . . . . . . . . . . . . . . 1017

12.5a Physical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1018

12.5b General Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1021

Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1022



12.5c Some New Concepts and Definitions . . . . . . . . . . . . . . . . . 1023

Psychrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1023

Thermodynamic Treatment of Water Vapor in Dry Air . . . . 1023

Humidity Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1024

Relative Humidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1025

Dew Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1026

12.5d Recast Conservation Equations . . . . . . . . . . . . . . . . . . . . . 1029

SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1036


REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1038

NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1039

QUESTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1041

PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1041

APPENDIX 12A: TURBOJET ENGINE ANALYSIS REVISITED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1064

APPENDIX A TIMELINE 1067

APPENDIX B THERMODYNAMIC PROPERTIES OF IDEAL GASES AND CARBON 1072

Table B.1 CO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1073

Table B.2 CO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1074

Table B.3 H2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075

Table B.4 H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1076

Table B.5 OH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1077

Table B.6 H2O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1078

Table B.7 N2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1079

Table B.8 N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1080

Table B.9 NO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1081

Table B.10 NO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1082

Table B.11 O2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1083

Table B.12 O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1084

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Table B.13 C(s) (Graphite) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1085

Table B.14 Curve-Fit Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . 1086

APPENDIX C THERMODYNAMIC AND THERMO-PHYSICAL PROPERTIES OF AIR 1087

Table C.1 Approximate Composition, Apparent Molecular Weight,and Gas Constant for Dry Air . . . . . . . . . . . . . . . . . . . . . . . . 1087

Table C.2 Thermodynamic Properties of Air at 1 atm . . . . . . . . . . 1087

Table C.3 Thermo-Physical Properties of Air . . . . . . . . . . . . . . . . 1090

APPENDIX D THERMODYNAMIC PROPERTIES OF H2O 1092

Table D.1 Saturation Properties of Water and Steam—TemperatureIncrements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1092

Table D.2 Saturation Properties of Water and Steam—Pressure Increments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1094

Table D.3 Superheated Vapor (Steam) . . . . . . . . . . . . . . . . . . . . . . 1097

Table D.4 Compressed Liquid (Water) . . . . . . . . . . . . . . . . . . . . . 1109

Table D.5 Vapor Properties: Saturated Solid (Ice)–Vapor . . . . . . . . 1112

APPENDIX E VARIOUS THERMODYNAMIC DATA 1113

Table E.1 Critical Constants and Specific Heats for Selected Gases 1113

Table E.2 Van der Waals Constants for Selected Gases . . . . . . . . . 1113

APPENDIX F THERMO-PHYSICAL PROPERTIES OF SELECTED GASES AT 1 ATM 1114

Table F.1 Thermo-Physical Properties of Selected Gases (1 atm) 1114

APPENDIX G THERMO-PHYSICAL PROPERTIES OF SELECTED LIQUIDS 1120

Table G.1 Thermo-Physical Properties of Saturated Water . . . . . . . 1121

Table G.2A Thermo-Physical Properties of Various Saturated Liquids 1124

APPENDIX H THERMO-PHYSICAL PROPERTIES OF HYDROCARBON FUELS 1126

Table H.1 Selected Properties of Hydrocarbon Fuels . . . . . . . . . . . 1127

Table H.2 Curve-Fit Coefficients for Fuel Specific Heat and Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1128

Table H.3 Curve-Fit Coefficients for Fuel Vapor Thermal Conductivity, Viscosity, and Specific Heat . . . . . . . . . . . . . . 1129

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APPENDIX I THERMO-PHYSICAL PROPERTIES OF SELECTED SOLIDS 1130

Table I.1 Thermo-Physical Properties of Selected Metallic Solids 1131

Table I.2 Thermo-Physical Properties of Selected Nonmetallic Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1136

Table I.3 Thermo-Physical Properties of Common Materials . . . . . 1138

Table I.4 Thermo-Physical Properties of Structural Building Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1140

Table I.5 Thermo-Physical Properties of Industrial Insulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1142

APPENDIX J RADIATION PROPERTIES OF SELECTED MATERIALS AND SUBSTANCES 1144

Table J.1 Total, Normal (n), or Hemispherical (h) Emissivity of Selected Surfaces: Metallic Solids and Their Oxides . . . . . . 1144

Table J.2 Total, Normal (n), or Hemispherical (h) Emissivity of Selected Surfaces: Nonmetallic Substances . . . . . . . . . . . . . 1145

APPENDIX K MACH NUMBER RELATIONSHIPS FOR COMPRESSIBLE FLOW 1146

Table K.1 One-Dimensional, Isentropic, Variable-Area Flow of Air with Constant Properties (� � 1.4) . . . . . . . . . . . . . . 1146

Table K.2 One-Dimensional Normal-Shock Functions for Air with Constant Properties (� � 1.4) . . . . . . . . . . . . . . . . . . . . 1147

ANSWERS TO SELECTED PROBLEMS 1149

ILLUSTRATION CREDITS 1157

INDEX 1159

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Sample Syllabus—One-Semester Survey Course*

Period, Topic(s) followed by Textbook Reference

1 Preliminaries & course introduction ➤ 1.1

Introductory Topics & Groundwork

2 Thermal-science applications, systems & control volumes ➤ 1.2–1.3

3 General conservation principles & key concepts ➤ 1.4

4 Properties, states, processes, cycles, & equilibrium concepts ➤ 1.5

5 Real flows, dimensions & units, problem-solving method ➤ 1.6–1.8

Thermodynamic Properties & Equations of State

6 Common properties related to 1st law & equation of state ➤ 2.1–2.2a

7 State principle, ideal-gas equation of state, P–v–T space ➤ 2.3, 2.4a–2.4c

8 Multiphase substances: phase boundaries, x, tables, & NIST software ➤ 2.6

9 Multiphase substances (continued) ➤ 2.6

Conservation of Mass

10 Conservation of mass: systems & control volumes, flow rates ➤ 3.1–3.3c

11 Conservation of mass: control volumes, steady state, steady flow ➤ 3.3d–3.3e

Calorific Properties & Calorific Equations of State

12 Internal energy, enthalpy, & specific heats ➤ 2.3b

13 Calorific equation of state: ideal gases ➤ 2.4d

Groundwork for Energy Conservation

14 Energy: macroscopic & microscopic ➤ 4.1–4.2

15 Identifying heat & work interactions ➤ 4.3–4.4

Sample Syllabi

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16 Identifying heat & work interactions (continued) ➤ 4.3–4.4

A Closer Look at Heat Transfer

17 Heat transfer modes: conduction & convection ➤ 4.5a–4.5b

18 Heat transfer modes: radiation ➤ 4.5c

Energy Conservation—Thermodynamic Systems

19 Energy conservation for a system & applications ➤ 5.1a–5.2a

20 Energy conservation for a system & applications (continued) ➤ 5.2a

Application of Energy Conservation to Conduction Heat Transfer

21 Conduction analysis: integral (lumped) formulations ➤ 5.2c

22 1-D conduction (planar) & electrical analog ➤ 5.2c

23 1-D conduction (cylindrical) & electrical analog ➤ 5.2c

Energy Conservation—Control Volumes

24 Energy conservation for a control volume ➤ 5.3a–5.3b

25 Steady-flow processes & devices ➤ 5.3a–5.3b, 11.1

Second Law of Thermodynamics & Related Topics

26 2nd law: statement, consequences, & prerequisite concepts ➤ 7.1–7.4a

27 Carnot efficiency, reversibility, & entropy ➤ 7.4b–7.6b

28 2nd-law property relationships ➤ 2.2c, 2.3d, 2.4e–2.4h

29 Isentropic efficiency ➤ 7.6e

Conservation of Momentum & Fluid Statics

30 Conservation of linear momentum—forces ➤ 6.1–6.2

31 Conservation of linear momentum—fluid statics ➤ 6.3a

32 Fluid statics: manometry & forces on submerged surfaces ➤ 6.3a

Momentum Conservation—Control Volumes

33 Momentum flows & conservation of linear momentum: integral CVs ➤ 6.4

34 Momentum flows & conservation of linear momentum: integral CVs ➤ 6.5a–6.5b

35 Mechanical energy equation, Bernoulli equation ➤ 6.6–6.7

Similitude & Dimensionless Parameters

36 Similitude & dimensionless parameters ➤ 8.1–8.5

Conservation Principles Applied to Internal & External Flows

37 External flows: friction and heat transfer; basic flow patterns & physics ➤ 9.1–9.2

38 Forced flows—flat plate ➤ 9.3–9.4

39 Forced flows—other geometries ➤ 9.5

40 Internal flows: friction & heat transfer; integral analyses ➤ 10.2a–10.2d

41 Internal flows: friction & heat transfer; integral analyses (continued) ➤ 10.2e

42 Fully developed laminar flows ➤ 10.3

43 Fully developed turbulent flows ➤ 10.4

xxiv Sample Syllabi

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Sample Syllabus—Thermal-Fluid Sciences I*


1 Preliminaries & course introduction ➤ 1.1–1.2


2 Physical frameworks & introduction to conservation principles ➤ 1.3–1.4

3 Key concepts & definitions ➤ 1.5

4 Key concepts & definitions (continued) ➤ 1.5


Thermodynamic Properties

6 Motivation for study of properties, common thermodynamic properties ➤ 2.1–2.2

7 Properties related to first & second laws of thermodynamics ➤ 2.1–2.2

8 State principle, state relationships, ideal-gas state relationships ➤ 2.3, 2.4a–2.4c

9 Calorific equation of state; P–v, T–v, u–T, h–T plots for ideal gases ➤ 2.4d, 2.4g

10 Nonideal gases: van der Waals equation of state & generalized compressibility ➤ 2.5

11 Multiphase substances: phase boundaries, quality, T–v diagrams ➤ 2.6a

12 Multiphase substances: tabular data, NIST database, log P–log v diagrams ➤ 2.6b

13 Compressed liquids & solids ➤ 2.7–2.8


14 Conservation of mass: systems ➤ 3.1–3.2

15 Conservation of mass: flow rates & average velocities ➤ 3.3a–3.3c

16 Conservation of mass for integral control volumes: steady state & steady flow ➤ 3.3e

17 Conservation of mass for integral control volumes: unsteady flow ➤ 3.3e


18 Energy storage, heat & work interactions at boundaries ➤ 4.1–4.3

19 Identifying heat & work interactions ➤ 4.3–4.4

A Closer Look at Heat Transfer

20 Rate laws for heat transfer: conduction & convection ➤ 4.5a–4.5b

21 Rate laws for heat transfer: radiation ➤ 4.5c


22 Energy conservation for a system: finite processes ➤ 5.1a–5.2a

23 Energy conservation for a system: at an instant ➤ 5.2a

24 Energy conservation for a system: examples & applications ➤ 5.2a

Application of Energy Conservation to Conduction Heat transfer

25 Conduction heat transfer: Integral (lumped) analysis ➤ 5.2c

Sample Syllabi xxv

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26 Conduction heat transfer: 1-D differential analysis & solutions ➤ 5.2c

27 Electric circuit analogy for conduction heat transfer ➤ 5.2c

Energy Conservation—Control Volumes

28 Energy conservation for an integral control volume: Introduction ➤ 5.3a–5.3b

29 Steady-flow processes ➤ 5.3c, 11.1

30 Steady-flow devices: nozzles, diffusers, & throttles ➤ 11.2c, 11.3

31 Steady-flow devices: pumps, compressors, fans, & turbines ➤ 11.4, 11.5

32 Steady-flow devices: heat exchangers ➤ 11.6 (early portions)

33 Steam power plants revisited ➤ 1.2a, 12.1a

Second Law of Thermodynamics

34 2nd law of thermodynamics: overview, Kelvin–Planck statement,consequences ➤ 7.1–7.3

35 Carnot cycle & Carnot efficiency, other 2nd-law statements ➤ 7.4–7.5

36 Definition of entropy, entropy-based statement of 2nd law, & entropy balances ➤ 7.6a–7.6c

Second-Law Properties, Property Relationships, & Efficiencies

37 2nd-law property relationships ➤ 2.2c, 2.3d, 2.4e

38 T–s relationships for ideal gases, air tables, isentropic relationships ➤ 2.4e–2.4f

39 Isentropic & polytropic processes, T–s & P–v diagrams ➤ 2.4g–2.4h

40 Isentropic efficiencies ➤ 7.6e

Steam Power Plant—Application of the 1st & 2nd Laws

41 Steam power plant: Rankine cycle ➤ 12.1a

42 Steam power plant: superheat & reheat ➤ 12.1b

43 Steam power plant: regeneration ➤ 12.1c

Sample Syllabus—Thermal-Fluid Sciences II*


1 Preliminaries & course introduction

Review of Mass & Energy Conservation

2 Flow rates & mass conservation for control volumes ➤ 3.1–3.3e

3 Conservation of energy for systems & control volumes ➤ 5.1a–5.2a, 5.3a–5.3c

Reacting Systems & Flows—Combustion Basics

4 Mass conservation: atom balances & stoichiometry ➤ 3.5a

5 Mass conservation: atom balances & stoichiometry (continued) ➤ 3.5b

6 Ideal-gas mixture properties: specifying composition ➤ 2.9a–2.9b

xxvi Sample Syllabi

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7 Ideal-gas mixture properties: standardized properties ➤ 2.9c–2.9e

8 Enthalpy of combustion & heating values ➤ 2.10

Reacting Systems & Flows—Conservation of Energy

9 Constant-pressure combustion: systems & control volumes ➤ 5.2b, 11.7

10 Constant-pressure combustion: systems & control volumes (continued) ➤ 5.2b, 11.7

11 Constant-volume combustion ➤ 5.2b

Chemical Equilibrium

12 Introduction & relationship to entropy ➤ 7.6d, 7.7a

13 Conditions of fixed temperature & pressure, Gibbs function, & equilibrium constants ➤ 7.7a

14 Multiple equilibrium reactions ➤ 7.7a

Refrigerators & Heat Pumps

15 Reversed cycles & coefficients of performance ➤ 12.4

16 Vapor-compression refrigeration cycle ➤ 12.4

17 Heat pumps ➤ 12.4

Air Conditioning, Humidification, & Related Systems

18 Physical systems & general analysis ➤ 12.5a–12.5b

19 Air–water vapor mixtures, dew point, & measures of humidity ➤ 12.5c

20 Applications ➤ 12.5d

21 Applications (continued) ➤ 12.5d

Groundwork for Momentum Conservation

22 Forces in fluids, fluid statics, & buoyancy ➤ 6.1– 6.3

23 Manometry ➤ 6.3

24 Forces on submerged surfaces ➤ 6.3

25 Rigid-body motion ➤ 6.3

26 Momentum flows ➤ 6.4

Linear Momentum Conservation—Integral Control Volumes

27 Simplified general view; steady-flow formulations ➤ 6.5a–6.5b

28 Examples & applications ➤ 6.5b, 11.2a

Linear Momentum Conservation—Differential Control Volumes

29 Application of mass & momentum conservation to differential control volumes ➤ 3.3f, 6.5d

30 Total derivative & convective acceleration ➤ 6.5d

31 The Navier–Stokes equation ➤ 6.5d

Mechanical Energy & Bernoulli Equations

32 Mechanical energy & Bernoulli equations: origins ➤ 6.6–6.7

33 Mechanical energy & Bernoulli equations: applications ➤ 6.6–6.7

Sample Syllabi xxvi i

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Nozzles & Diffusers—Application of Conservation Principles & Property Relations

34 General analysis ➤ 11.2a–11.2c

35 Compressible flow introduction ➤ 11.2d

36 Choked flow; converging–diverging nozzles ➤ 11.2d

37 Choked flow; converging–diverging nozzles (continued) ➤ 11.2d

Turbojet Engines—Application of Fundamentals to a Complex System

38 Turbojet components & integral control volume analysis ➤ 12.2a–12.2b

39 Integral mass, energy, & momentum analyses (continued) ➤ 12.2a–12.2b

40 Air-standard turbojet cycle analysis & performance measures ➤ 12.2c–12.2d

41 Air-standard turbojet cycle analysis & performance measures (continued) ➤ 12.2c– 12.2d

42 Combustor analysis ➤ 12.2f

43 Combustor analysis (continued) ➤ 12.2f

Sample Syllabus—Thermal-Fluid Sciences III*


1 Preliminaries & course introduction

Differential Forms of the Conservation Principles

2 Mass & energy conservation: differential forms ➤ 3.3f, 5.3e

3 Momentum conservation: differential form ➤ 6.4d

Turbulence Review

4 Tubulent flows & Reynolds decomposition ➤ 1.6, 3.4a

5 Time-averaged integral & differential mass & momentum equations ➤ 3.4b, 6.8

Application of Dimensional Analysis to Thermal-Fluids Sciences

6 Parametric testing & similitude ➤ 8.1–8.4

7 Dimensionless parameters: origins & applications ➤ 8.5

8 Dimensionless parameters (continued) ➤ 8.5

Introduction to External Flows

9 Basic flow patterns & concept of boundary layers ➤ 9.1–9.2

Forced Laminar Flow over Flat Plates

10 Velocity & temperature profiles in boundary layers ➤ 9.3a–9.3b

11 Friction & drag solutions ➤ 9.3c

12 Friction & drag solutions (continued) ➤ 9.3c

13 Heat transfer solutions ➤ 9.3c–9.3e

14 Heat transfer solutions (continued) ➤ 9.3c–9.3e

xxvi i i Sample Syllabi

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Forced Turbulent Flow over Flat Plates

15 Laminar–turbulent transition & boundary-layer growth ➤ 9.4a–9.4b

16 Friction & drag ➤ 9.4c

17 Heat transfer ➤ 9.4d–9.4e

Forced Flow over Cylinders, Spheres, & Other Geometries

18 Friction & form drag ➤ 9.5a

19 Empirical correlations for drag & heat transfer ➤ 9.5b

20 Applications & examples ➤ 9.1–9.5

Free Convection

21 Vertical flat plate—physical & mathematical description ➤ 9.6a

22 Vertical flat plate—dimensionless parameters, solutions, & correlations ➤ 9.6a

23 Other geometries, applications, & examples ➤ 9.6b

Introduction to Internal Flows—Integral Analyses

24 Mass, momentum, & mechanical energy conservation ➤ 10.1–10.2c

25 Mass, momentum, & mechanical energy conservation (continued) ➤ 10.2d

26 Energy conservation: isothermal & nonisothermal flows with uniform heat flux ➤ 10.2e

27 Energy conservation: nonisothermal flows with uniform wall temperature ➤ 10.2e

Fully Developed Laminar Flows

28 Laminar flow criterion, differential conservation equations, & solutions ➤ 10.3a–10.3b

29 Laminar velocity distribution: average velocity, wall shear stress, pressure drop ➤ 10.3c

30 Laminar velocity distribution: head loss & friction factor ➤ 10.3c

31 Temperature distributions: heat-transfer coefficients ➤ 10.3d

32 Applications & examples ➤ 10.1–10.3

Fully Developed Turbulent Flows

33 Velocity distributions & wall friction: theory & experiment ➤ 10.4a

34 Average velocity, friction factor, rough tubes, & pipes ➤ 10.4a

35 Heat-transfer relationships ➤ 10.4b

Internal Flows—Additional Considerations

36 Developing flows, ducts of noncircular cross section, & minor losses ➤ 10.5–10.7

37 Developing flows, ducts of noncircular cross section, & minor losses (continued) ➤ 10.5–10.7

Applications to Heat Exchangers

38 Heat exchanger classifications & applications; integral analysis ➤ 11.6

39 Overall heat-transfer coefficient ➤ 11.6

40 Log-mean temperature difference method for heat exchanger design ➤ 11.6

41 NTU–effectiveness method for heat exchanger design & analysis ➤ 11.6

42 NTU–effectiveness method for heat exchanger design & analysis (continued) ➤ 11.6

43 Review and synthesis

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Sample Syllabus—Traditional One-SemesterThermodynamics Course*


1 Preliminaries & course introduction ➤ 1.1–1.2


2 Physical frameworks & introduction to conservation principles ➤ 1.3–1.4

3 Key concepts & definitions ➤ 1.5

4 Key concepts & definitions (continued) ➤ 1.5


Thermodynamic Properties & State Relationships

6 Motivation for study of properties, common thermodynamic properties ➤ 2.1–2.2

7 Properties related to first & second laws of thermodynamics ➤ 2.2

8 State principle, state relationships, ideal-gas state relationships ➤ 2.3–2.4

9 Calorific equation of state; P–v, T–v, u–T, h–T plots for ideal gases ➤ 2.4

10 Nonideal gases: van der Waals equation of state & generalized compressibility ➤ 2.5

11 Multiphase substances: phase boundaries, quality, T–v diagrams ➤ 2.6

12 Multiphase substances: tabular data, NIST database, log P–log v diagrams ➤ 2.6

13 Compressed liquids & solids ➤ 2.7–2.8


14 Conservation of mass: systems; flow rates ➤ 3.1–3.3b

15 Conservation of mass: control volumes ➤ 3.3d–3.3e


16 Energy storage, heat & work interactions at boundaries ➤ 4.1–4.3

17 Identifying heat & work interactions ➤ 4.3


18 Energy conservation for a system: finite processes ➤ 5.1–5.2a

19 Energy conservation for a system: at an instant ➤ 5.2a

20 Energy conservation for a system: examples & applications ➤ 5.2a

Energy Conservation—Control Volumes & Some Applications

21 Energy conservation for a control volume: introduction ➤ 5.3a–5.3b

22 Steady-flow processes & devices ➤ 5.3a, 11.1–11.2a

23 Steady-flow devices: nozzles, diffusers, & throttles ➤ 11.2c, 11.3

24 Steady-flow devices: pumps, compressors, fans, & turbines ➤ 11.4–11.5

25 Steady-flow devices: heat exchangers ➤ 11.6

26 Steam power plants & jet engines revisited ➤ 1.2a, 1.2d, 12.1a, 12.2a

xxx Sample Syllabi

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Second Law of Thermodynamics

27 2nd law of thermodynamics: overview, Kelvin–Planck statement,consequences ➤ 7.1–7.4a

28 Carnot cycle & Carnot efficiency, definition of entropy ➤ 7.4b–7.6a

29 Entropy-based statement of 2nd law, entropy balances, other 2nd-law statements ➤ 7.6b–7.6c

Second-Law Properties, Property Relationships, & Efficiencies

30 2nd-law property relationships ➤ 2.2c, 2.3d, 2.4e–2.4h

31 T–s relationships for ideal gases, air tables, isentropic relationships ➤ 2.4e–2.4h

32 Isentropic & polytropic processes, T–s & P–v diagrams ➤ 2.4e–2.4h

33 Isentropic efficiencies ➤ 7.6e, 11.4b, 11.5b

Steam Power Plant—Application of the 1st & 2nd Laws

34 Steam power plant: Rankine cycle ➤ 12.1a

35 Steam power plant: superheat & reheat ➤ 12.1b

36 Steam power plant: regeneration ➤ 12.1c

37 Steam power plant (continued) ➤ 12.1

Turbojet Engine—Application of the 1st & 2nd Laws

38 Jet engines: overall integral control volume analysis ➤ 12.2a–12.2b

39 Turbojet engine cycle analysis ➤ 12.2c

40 Turbojet engine cycle analysis (continued) ➤ 12.2d–12.2e

Other Applications of Thermodynamics & Conservation Principles

41 Selected topics ➤ Chapter 12

42 Selected topics ➤ Chapter 12

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THIS BOOK WAS CONCEIVED to address the needs of instructors desiringan integrated approach to teaching the thermal-fluid sciences. Traditionally,the thermal-fluid sciences are taught in a sequence of three or more separatecourses treating individually the disciplines of thermodynamics, fluidmechanics, and heat transfer. Although this traditional grouping makesconsiderable sense, many engineering educators believe that a more effectiveand efficient treatment of these subjects can be achieved by integratingtopics. The author hopes that this book will appeal to these educators.

The following organizational principles undergird this book:

● The fundamental conservation principles of mass, energy, and momentumare used as the primary integrating device.

● Related topics are grouped together hierarchically.● Many examples revisit a few particular practical devices or applications.

As an understanding of these principles is important to the use of this book,some elaboration is helpful.

The use of the fundamental conservation principles (mass, energy, andmomentum) is a natural choice as an integrating device for the thermal-fluidsciences and should be a comfortable choice for many engineering educators.The conservation principles are introduced in Chapter 1 in two general forms:a form associated with a process occurring over a finite time interval and aform expressing the conservation principle at an instant. These generalformulations are then elaborated for mass conservation in Chapter 3, forenergy conservation in Chapter 5, and momentum conservation in Chapter 6.Entropy balances introduced in Chapter 7 also follow the same generalformulation, although entropy is not conserved in the same sense as are mass,energy, and momentum. Showing that all conserved quantities obey a singlesimple accounting (in minus out plus generated equals stored) provides aneven higher level of integration. Also, stressing that the many ways theseconservation principles are expressed within various subject domains all havetheir origins in just three basic statements should help engineering studentsstructure their knowledge in useful ways. In a sense, this helps to establish theconservation principles as bedrock in the hierarchy of engineering science.

The second organizing principle, the hierarchical arrangement of subjectmatter, is perhaps best illustrated in Chapter 2. In this chapter, essentially all

page xxxiii

Preface

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material related to thermodynamic and thermophysical properties is groupedtogether. In this way, we are able to show clearly the hierarchy ofthermodynamic state relationships starting with the basic equation of stateinvolving P, v, and T; adding first-law-based calorific equations of stateinvolving u, h, P, T, and v; and ending with the second-law-based state relation-ships involving s, T, P, and v, for example. Such arrangement requires thatChapter 2 be revisited at appropriate places in the study of later chapters. Inthis sense, Chapter 2 is a resource that is to be returned to many times.Chapter 5 is another example of a hierarchical arrangement. Here theconservation of energy principle is applied to simple systems and thenextended to the most complicated forms typically presented in undergraduatefluid mechanics and heat-transfer textbooks. For example, both simpleconduction heat transfer and combustion are integrated within the context ofconservation of energy. Therefore, Chapter 5, like Chapter 2, can be revisitedand does not have to be studied from beginning to end.

What purpose is served by such an arrangement? First, it provides animportant structure for a beginning learner. Experts who have mastered andwork within a discipline organize material this way in their minds, whereasnovices tend to treat concepts in an undifferentiated way as a collection ofseemingly unrelated topics.1 It is hoped that providing a useful hierarchy fromthe start may speed learning and aid in retention. A second reason for ahierarchical arrangement is flexibility. In general, the book has been designedto permit an instructor to select topics from within a chapter and combinethem with material from other chapters in a relatively seamless manner. Thisflexibility allows the book to be used in many ways depending on theeducational goals of a particular course or a sequence of courses. The severalsyllabi that follow the table of contents suggest some arrangements.

The third device used to promote the integration of the thermal-fluidsciences is the selection of several topics that are revisited in variousexamples used throughout the book. Motivation for the particular topicschosen is elaborated in Chapter 1.

With this philosophical understanding behind us, we now examine thespecific structure of the book. The book is divided into two parts: Chapters1–8 comprise the part designated as Fundamentals; Chapters 9–12 aredenoted Beyond the Fundamentals. This division is a natural one in that all ofthe fundamental concepts are developed in Chapters 1–8, that is, propertyrelationships in Chapter 2; the three conservation principles in Chapters 3, 5,and 6; the second law of thermodynamics in Chapter 7; and dimensionalanalysis in Chapter 8. Chapters 9–12 then see the application of thesefundamentals to a variety of mechanical engineering topics. Chapter 9 treatsexternal flows, combining the problems of friction and drag and heat transfer,topics usually treated separately in traditional fluid mechanics and heat-transfer courses. In a similar way, internal flows are examined in Chapter 10.Both chapters emphasize conservation principles in both integral anddifferential form. Chapter 11 focuses on steady-flow devices. Portions of thischapter can and should be used earlier than their placement in a later chaptersuggests. For example, entry points into Chapter 11 are indicated in Chapters5, 6, and 7. Coverage of thermal-fluids systems is grouped in Chapter 12.Topics from this chapter can be selected to integrate many of the fundamentalconcepts developed in earlier chapters. For example, the section on jet

xxxiv Preface

1Larkin, J., McDermott, J., Simon, D. P., and Simon, H. A., “Expert and Novice Performance inSolving Physics Problems,” Science, 208: 1335–1342 (1980).

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engines combines all three conservation principles. This section also utilizesadvanced ways of dealing with properties and the first and second laws ofthermodynamics when the air-standard cycle is modified to include aconstant-pressure combustion process.

In addition to structure, many other pedagogical devices are employed inthis book. These include the following:

● An abundance of color photographs and images illustrate importantconcepts and emphasize practical applications;

● Each chapter begins with a list of learning objectives, a chapter overview,and a brief historical perspective, where appropriate, and concludes with abrief summary;

● Each chapter contains many examples that follow a standard problem-solving format;

● Self tests follow most examples;● Key equations are denoted by colored backgrounds;● Each chapter concludes with a checklist of key concepts and definitions

linked to specific end-of-chapter questions and problems;● The National Institute of Science and Technology (NIST) database for

thermodynamic and transport properties (included in the NIST12 v.5.2software provided with the book) is used extensively.

All of these features are intended to enhance student motivation and learningand to make teaching easier for the instructor. For example, the many colorphotographs make connections to real-world devices, a strong motivator forundergraduate students. Also, the learning objectives and checklists areparticularly useful. For the instructor, they aid in the selection of homeworkproblems and the creation of quizzes and exams, or other instructional tools.For students, they can be used as self tests of comprehension and can monitorprogress. The checklists also cite topic-specific questions and problems. Inhis use of the book, the author utilizes the learning objectives to guide reviewsof the material prior to examinations. Having well-defined learning objectivesis also useful in meeting engineering accreditation requirements. Manyquestions and problems are included at the end of each chapter. The purposeof the questions is to reinforce conceptual understanding of the material andto provide an outlet for students to articulate such understanding. Throughoutthe book, students are encouraged to use the National Institute of Science andTechnology (NIST) databases to obtain thermodynamic and transportproperties. The online NIST property database is easily accessible and is apowerful resource. It is a tool that will always be up to date. The NIST12 v.5.2software included with this book has features not available online. This user-friendly software provides extensive property data for eighteen fluids and hasan easy-to-use plotting capability. This invaluable resource makes dealingwith properties easy and can be used to enhance student understanding.

TO THE INSTRUCTOR

Two specific uses of this book are envisioned: 1. as the primary textbook fora multisemester sequence of thermal-fluid science courses for mechanicalengineering majors and 2. as a textbook for a one-semester survey course forengineering students in disciplines outside of mechanical engineering. (Asimilar one-semester survey course for mechanical engineering majors mayalso be useful in a modern curriculum.) Because of the inherent flexibility in

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the organization of the materials, this book can meet the needs of a coursesequence, or a survey course, in a variety of ways. To assist in selecting topics,the text distinguishes three levels: level 1 (basic) material is unmarked, level 2(intermediate) material appears with a blue background and a blue edge stripe,and level 3 (advanced) material is denoted with a light red background and ared edge stripe. Instructors can therefore choose from the numerous topicspresented to create courses that meet their specific educational objectives. Toshow how this might be done, sample syllabi preceding this preface illustratea three-semester sequence of courses and a one-semester survey course. Bothof these examples emphasize topics traditionally included in thermodynamicscourses, reflecting the author’s view on teaching the thermal-fluid sciences. Athree-semester sequence was chosen to be compatible with the present trend inmechanical engineering curricula to limit the core thermal-fluid sciences tothree 3-credit courses, or their equivalent. In fact, the repackaging of thethermal-fluids core from typically 12 to 9 credits was a strong motivator forthe creation of this book.

Also presented in the preceding is a syllabus showing how this book canbe used for a traditional single-semester first course in thermodynamics. Thissyllabus is presented for two reasons: to illustrate the flexibility of the bookin creating courses to meet specific needs and to provide an option for thoseinstructors who might want to use the book in a traditional way before tryinga more integrated approach.

Feedback from instructors who use this book is most welcome.

xxxvi Preface

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Stephen R. Turns received degrees in mechanical engineering from ThePennsylvania State University (B.S.), Wayne State University (M.S.), and theUniversity of Wisconsin-Madison (Ph.D.). From 1970 to 1975, he worked asa research engineer at General Motors Research Laboratories; for the pasttwenty-six years, he has been a member of the mechanical engineeringfaculty at The Pennsylvania State University. Turns teaches a wide range ofcourses in the thermal-fluids sciences and also conducts research in the areaof combustion. At Penn State, Turns has received numerous teaching awards,including the University’s prestigious Milton S. Eisenhower Award forDistinguished Teaching. Turns is a member of The Combustion Institute, theAmerican Society of Engineering Education, the American Society ofMechanical Engineers, and the Society of Automotive Engineers. He is alsoa program evaluator for the Accreditation Board for Engineering andTechnology (ABET), serving in this capacity since 1994. Turns is the authorof An Introduction to Combustion: Concepts & Applications, a textbookwidely used in the United States and around the world.

page xxxvii

About the Author

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THIS BOOK HAS BEEN A LONG TIME COMING and many people havecontributed along the way. First I would like to thank the many reviewers andstudents, too many to name here, all of whom contributed both mightily, andsubtly. Without their candid comments and careful reading this project wouldnot have been possible.

I am indebted to Peter Gordon at Cambridge University Press for his visionof a richly illustrated and colorful book and the managers at the Press forsupporting our shared vision. To this end, I am happy to acknowledge RickMedvitz and Jared Ahern of the Applied Research Laboratory at Penn State fortheir creation of the many exciting computational fluid dynamics illustrationssprinkled throughout the text. Thanks also are owed to Joel Peltier and EricPaterson at ARL for their support of the CFD effort. Regina Brooks and AnneWells at Serendipity Literary Agency worked hard to find photographs, and thecooperation of AGE fotostock is gratefully acknowledged. Jessica Cepalak andMichelle Lin at Cambridge were indispensable in many ways throughout theproject. The stunning book design was the effort of José Fonfrias. Thank you,José.

Special thanks go to Chris Mordaunt for his creation of the self tests andhis meticulous reading of the manuscript and insightful comments. Thanksalso go to the members of the solutions manual team: Jacob Stenzler andDave Kraige, leaders of the effort, and Justin Sabourin, Yoni Malchi, andShankar Narayanan. For nearly a decade, Mary Newby deciphered my pencilscrawls to create a word-processed manuscript. I thank Mary for herinvaluable efforts.

I would like to acknowledge the production team at Cambridge—AlanGold (Senior Production Controller) and Pauline Ireland (Director,Production and New Media Development)—who broke a great number of oldrules to make a very new book. I especially want to thank Anoop Chaturvediand his production team at TechBooks for their careful attention to detail. Ialso thank fellow textbook authors Dwight Look, Jr., and Harry Sauer, Jr.;Glen Myers; Alan Chapman; David Pnueli and Chaim Gutfinger; andGertrude Shepherd, wife of deceased author Dennis Shepherd, for theirpermission to use selected problems from their works. Thanks also are owedto Eric Lemmon at NIST for assembling the software provided with this bookand to Joan Sauerwein for making the agreement.

Acknowledgments

page xxxix

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For the hospitality shown during a sabbatical year spent writing, I thankAllan Kirkpatrick and Charles Mitchell at Colorado State University andTaewoo Lee and Don Evans at Arizona State University. I would also like tothank good friends Kathy and Dan Wendland for opening their home to us foran extended stay in Fort Collins. Thanks also are extended to Nancy and DavePearson, more good friends, for their help and companionship in Tempe.

The sales and marketing team at Cambridge are a joy to work with. Thanksgo to Liza Murphy, Kerry Cahill, Liz Scarpelli, Robin Silverman, TedGuerney, Catherine Friedl, and Valerie Yaw, along with their counterparts inthe UK, Rohan Seery, Ben Ashcroft, Gurdeep Pannu, and Cherrill Richardson.I would also like to thank Jae Hong for his contributions to this project.

Moral support has come from many fronts, especially from the crowd atSaints Cafe and from Bob Santoro. Three people, however, deserve myheartfelt thanks. The first is Peter Gordon at Cambridge. Peter came to therescue in trying times and breathed new life into this project. Second is DickBenson, friend and confidant. Without Dick’s enthusiastic support, this bookwould not have been possible. Third, but hardly last, is Joan, my wife. Icannot thank her enough for her help, patience, and support. Thank you, Joan.

xl Acknowledgments

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