Principals of heat transfer Frank Kreith, Raj M.

Conversion Factors for Commonly Used Quantities in Heat Transfer Quantity SI : English English : SI* Area 1 m2 ϭ 10.764 ft2 1 ft2 ϭ 0.0929 m2 Density ϭ 1550.0 in2 1 in2 ϭ 6.452 ϫ 10Ϫ4 m2 1 kg/m3 ϭ 0.06243 lbm/ft3 1 lbm/ft3 ϭ 16.018 kg/m3 1 slug/ft3 ϭ 515.38 kg/m3 Energy† 1 J ϭ 9.4787 ϫ 10Ϫ4 Btu 1 Btu ϭ 1055.06 J Energy per unit mass 1 J/kg ϭ 4.2995 ϫ 10Ϫ4 Btu/lbm 1 cal ϭ 4.1868 J Force 1 N ϭ 0.22481 lbf 1 lbf и ft ϭ 1.3558 J Heat flux 1 W/m2 ϭ 0.3171 Btu/(h и ft2) 1 hp и h ϭ 2.685 ϫ 106 J Heat generation 1 W/m3 ϭ 0.09665 Btu/(h и ft3) 1 Btu/lbm ϭ 2326 J/kg per unit volume 1 W/(m2 и K) ϭ 0.1761 Btu/(h и ft2 и °F) 1 lbf ϭ 4.448 N Heat transfer coefficient 1 W ϭ 3.412 Btu/h 1 Btu/(h и ft2) ϭ 3.1525 W/m2 Heat transfer rate 1 kcal/(h и m2) ϭ 1.163 W/m2 1m ϭ 3.281 ft Length ϭ 39.37 in 1 Btu/(h и ft3) ϭ 10.343 W/m3 Mass 1 kg ϭ 2.2046 lbm 1 Btu/(h и ft2 и °F) ϭ 5.678 W/(m2 и K) Mass flow rate 1 kg/s ϭ 7936.6 lbm/h 1 Btu/h ϭ 0.2931 W ϭ 2.2046 lbm/s 1 ton ϭ 12,000 Btu/h ϭ 3517.2 W Power 1 W ϭ 3.4123 Btu/h 1 ft ϭ 0.3048 m 1 in ϭ 0.0254 m Pressure and stress 1 N/m2 ϭ 0.02089 lbf/ft2 (Note: 1 Pa ϭ 1N/m2) ϭ 1.4504 ϫ 10Ϫ4 lbf/in2 1 lbm ϭ 0.4536 kg ϭ 4.015 ϫ 10Ϫ3 in water 1 slug ϭ 14.594 kg ϭ 2.953 ϫ 10Ϫ4 in Hg 1 lbm/h ϭ 0.000126 kg/s 1 lbm/s ϭ 0.4536 kg/s 1 Btu/h ϭ 0.2931 W 1 Btu/s ϭ 1055.1 W 1 lbf и ft/s ϭ 1.3558 W 1 hp ϭ 745.7 W 1 lbf/ft2 ϭ 47.88 N/m2 1 psi ϭ 1 lbf/in2 ϭ 6894.8 N/m2 1 standard atmosphere ϭ 1.0133 ϫ 105 N/m2 1 bar ϭ 1 ϫ 105 N/m2 Copyright 2011 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

Conversion Factors for Commonly Used Quantities in Heat Transfer (Continued) Quantity SI : English English : SI* Specific heat 1 J/(kg и K) ϭ 2.3886 ϫ 10Ϫ4 1 Btu/(lbm и °F) ϭ 4187 J/(kg и K) Surface tension Btu/(lbm и °F) 1 lbf/ft ϭ 14.594 N/m 1 dyne/cm ϭ 1 ϫ 10Ϫ3 N/m 1 N/m ϭ 0.06852 lbf/ft Temperature T(K) ϭ T(°C) ϩ 273.15 T(°R) ϭ 1.8T(K) ϭ T(°R)/1.8 ϭ T(°F) ϩ 459.67 ϭ [T(°F) ϩ 459.67]/1.8 T(°F) ϭ 1.8T(°C) ϩ 32 T(°C) ϭ [T(°F) Ϫ 32]/1.8 ϭ 1.8[T(K) Ϫ 273.15] ϩ 32 Temperature difference 1 K ϭ 1°C 1°R ϭ 1°F ϭ 1.8°R ϭ (5/9)K ϭ 1.8°F ϭ (5/9)°C Thermal conductivity 1 W/(m и K) ϭ 0.57782 Btu/(h и ft и °F) 1 Btu/(h и ft и °F) ϭ 1.731 W/m и K 1 kcal/(h и m и °C) ϭ 1.163 W/m и K Thermal diffusivity 1 m2/s ϭ 10.7639 ft2/s 1 ft2/s ϭ 0.0929 m2/s 1 ft2/h ϭ 2.581 ϫ 10Ϫ5 m2/s Thermal resistance 1 K/W ϭ 0.5275°F и h/Btu 1°F и h/Btu ϭ 1.896 K/W Velocity 1 m/s ϭ 3.2808 ft/s 1 ft/s ϭ 0.3048 m/s Viscosity (dynamic) 1 N и s/m2 ϭ 0.672 lbm/(ft и s) 1 lbm/(ft и s) ϭ 1.488 N и s/m2 Viscosity (kinematic) ϭ 2419.1 lbm/(ft и h) 1 lbm/(ft и h) ϭ 4.133 ϫ 10Ϫ4 N и s/m2 Volume ϭ 5.8016 ϫ 10Ϫ6 lbf и h/ft2 1 centipoise ϭ 0.001 N и s/m2 Volume flow rate 1 m2/s ϭ 10.7639 ft2/s 1 ft2/s ϭ 0.0929 m2/s 1 ft2/h ϭ 2.581 ϫ 10Ϫ5 m2/s 1m3 ϭ 35.3134 ft3 1 ft3 ϭ 0.02832 m3 1 m3/s ϭ 35.3134 ft3/s 1 in3 ϭ 1.6387 ϫ 10Ϫ5 m3 ϭ 1.2713 ϫ 105 ft3/h 1 gal (U.S. liq.) ϭ 0.003785 m3 1 ft3/h ϭ 7.8658 ϫ 10Ϫ6 m3/s 1 ft3/s ϭ 2.8317 ϫ 10Ϫ2 m3/s *Some units in this column belong to the cgs and mks metric systems. †Definitions of the units of energy which are based on thermal phenomena: 1 Btu ϭ energy required to raise 1 lbm of water 1°F at 68°F 1 cal ϭ energy required to raise 1 g of water 1°C at 20°C Copyright 2011 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

Seventh Edition Principles of HEAT TRANSFER Copyright 2011 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

Seventh Edition Principles of HEAT TRANSFER Frank Kreith Professor Emeritus, University of Colorado at Boulder, Boulder, Colorado Raj M. Manglik Professor, University of Cincinnati, Cincinnati, Ohio Mark S. Bohn Former Vice President, Engineering Rentech, Inc., Denver, Colorado Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Copyright 2011 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

This ia an electronic version of the print textbook. Due to electronic rights restrictions, some third party may be suppressed. Edition review has deemed that any suppressed content does not materially affect the over all learning experience. The publisher reserves the right to remove the contents from this title at any time if subsequent rights restrictions require it. For valuable information on pricing, previous editions, changes to current editions, and alternate format, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest. Copyright 2011 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

Principles of Heat Transfer, © 2011, 2003 Cengage Learning Seventh Edition Authors Frank Kreith, Raj M. Manglik, ALL RIGHTS RESERVED. No part of this work covered by the Mark S. Bohn copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic, electronic, or mechanical, Publisher, Global Engineering: including but not limited to photocopying, recording, scanning, Christopher M. Shortt digitizing, taping, web distribution, information networks, Senior Developmental Editor: or information storage and retrieval systems, except as permitted Hilda Gowans under Section 107 or 108 of the 1976 United States Copyright Act, Editorial Assistant: Tanya Altieri without the prior written permission of the publisher. Team Assistant: Carly Rizzo Marketing Manager: Lauren Betsos For product information and technology assistance, Media Editor: Chris Valentine contact us at Cengage Learning Customer & Director, Content and Media Sales Support, 1-800-354-9706. Production: Barbara Fuller-Jacobsen Content Project Manager: Cliff Kallemeyn For permission to use material from this text or product, Production Service: RPK Editorial submit all requests online at www.cengage.com/permissions. Services, Inc. Copyeditor: Fred Dahl Further permissions questions can be emailed to Proofreader: Martha McMaster/Erin [email protected] Wagner Indexer: Shelly Gerger-Knechtl Library of Congress Control Number: 2010922630 Compositor: Integra ISBN-13: 978-0-495-66770-4 Senior Art Director: Michelle Kunkler ISBN-10: 0-495-66770-6 Cover Designer: Andrew Adams Cover Image: Abengoa Solar; SkyTrough™ Cengage Learning © Shirley Speer/SkyFuel, Inc. 2009 200 First Stamford Place, Suite 400 Internal Designer: Jennifer Stamford, CT 06902 Lambert/jen2design USA Text and Image Permissions Researcher: Kristiina Paul Cengage Learning is a leading provider of customized learning First Print Buyer: Arethea Thomas solutions with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan. Locate your local office at: international.cengage.com/region. Cengage Learning products are represented in Canada by Nelson Education Ltd. For your course and learning solutions, visit www.cengage.com/engineering. Purchase any of our products at your local college store or at our preferred online store www.CengageBrain.com. Printed in the United States of America 1 2 3 4 5 6 7 13 12 11 10 09 Copyright 2011 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

To our students all over the world Copyright 2011 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

PREFACE When a textbook that has been used by more than a million students all over the world reaches its seventh edition, it is natural to ask, “What has prompted the authors to revise the book?” The basic outline of how to teach the subject of heat transfer, which was pioneered by the senior author in its first edition, published 60 years ago, has now been universally accepted by virtually all subsequent authors of heat transfer texts. Thus, the organization of this book has essentially remained the same over the years, but newer experimental data and, in particular the advent of computer technology, have necessitated reorganization, additions, and integration of numerical and computer methods of solution into the text. The need for a new edition was prompted primarily by the following factors: 1) When a student begins to read a chapter in a textbook covering material that is new to him or her, it is useful to outline the kind of issues that will be important. We have, therefore, introduced at the beginning of each chapter a summary of the key issues to be covered so that the student can recognize those issues when they come up in the chapter. We hope that this pedagogic technique will help the students in their learning of an intricate topic such as heat transfer. 2) An important aspect of learning engineering science is to connect with practical applications, and the appro- priate modeling of associated systems or devices. Newer applications, illustrative modeling examples, and more current state-of-the art predictive correlations have, therefore, been added in several chapters in this edition. 3) The sixth edition used MathCAD as the computer method for solving real engineering problems. During the ten years since the sixth edition was published, the teaching and utilization of MathCAD has been supplanted by the use of MATLAB. Therefore, the MathCAD approach has been replaced by MATLAB in the chapter on numerical analysis as well as for the illustrative problems in the real world applications of heat transfer in other chapters. 4) Again, from a pedagogic perspective of assessing student learning performance, it was deemed important to prepare general problems that test the stu- dents’ ability to absorb the main concepts in a chapter. We have, therefore, provided a set of Concept Review Questions that ask a student to demonstrate his or her abil- ity to understand the new concepts related to a specific area of heat transfer. These review questions are available on the book website in the Student Companion Site at www.cengage.com/engineering. Solutions to the Concepts Review Questions are available for Instructors on the same website. 5) Furthermore, even though the sixth edition had many homework problems for the students, we have introduced some additional problems that deal directly with topics of current interest such as the space program and renewable energy. The book is designed for a one-semester course in heat transfer at the junior or senior level. However, we have provided some flexibility. Sections marked with vii Copyright 2011 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

viii Preface asterisks can be omitted without breaking the continuity of the presentation. If all the sections marked with an asterisk are omitted, the material in the book can be covered in a single quarter. For a full semester course, the instructor can select five or six of these sections and thus emphasize his or her own areas of interest and expertise. The senior author would also like to express his appreciation to Professor Raj M. Manglik, who assisted in the task of updating and refreshing the sixth edition to bring it up to speed for students in the twenty-first century. In turn, Raj Manglik is profoundly grateful for the opportunity to join in the authorship of this revised edition, which should continue to provide students worldwide an engaging learning experience in heat transfer. Although Dr. Mark Bohn decided not to participate in the seventh edition, we wish to express our appreciation for his previous contribu- tion. In addition, the authors would like to acknowledge the contributions by the reviewers of the sixth edition who have provided input and suggestions for the update leading to the new edition of the book: B. Rabi Baliga, McGill University; F.C. Lai, University of Oklahoma; S. Mostafa Ghiaasiaan, Georgia Tech; Michael Pate, Iowa State University; and Forman A. Williams, University of California, San Diego. The authors would also like to thank Hilda Gowans, the Senior Developmental Editor for Engineering at Cengage Learning, who has provided sup- port and encouragement throughout the preparation of the new edition. On a more personal level, Frank Kreith would like to express his appreciation to his assistant, Bev Weiler, who has supported his work in many tangible and intangible ways, and to his wife, Marion Kreith, whose forbearance with the time taken in writing books has been of invaluable help. Raj Manglik would like to thank his graduate students Prashant Patel, Rohit Gupta, and Deepak S. Kalaikadal for the computational solu- tions and algorithms in the book. Also, he would like to express his fond gratitude to his wife, Vandana Manglik, for her patient encouragement during the long hours needed in this endeavor, and to his children, Aditi and Animaesh, for their affection and willingness to forego some of our shared time. Copyright 2011 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

CONTENTS Chapter 1 Basic Modes of Heat Transfer 2 1.1 The Relation of Heat Transfer to Thermodynamics 3 1.2 Dimensions and Units 7 1.3 Heat Conduction 9 1.4 Convection 17 1.5 Radiation 21 1.6 Combined Heat Transfer Systems 23 1.7 Thermal Insulation 45 1.8 Heat Transfer and the Law of Energy Conservation 51 References 58 Problems 58 Design Problems 68 Chapter 2 Heat Conduction 70 2.1 Introduction 71 78 2.2 The Conduction Equation 71 2.3 Steady Heat Conduction in Simple Geometries 2.4 Extended Surfaces 95 2.5* Multidimensional Steady Conduction 105 2.6 Unsteady or Transient Heat Conduction 116 2.7* Charts for Transient Heat Conduction 134 2.8 Closing Remarks 150 References 150 Problems 151 Design Problems 163 Chapter 3 Numerical Analysis of Heat Conduction 166 3.1 Introduction 167 3.2 One-Dimensional Steady Conduction 168 3.3 One-Dimensional Unsteady Conduction 180 ix Copyright 2011 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

x Contents 3.4* Two-Dimensional Steady and Unsteady Conduction 195 3.5* Cylindrical Coordinates 215 3.6* Irregular Boundaries 217 3.7 Closing Remarks 221 References 221 Problems 222 Design Problems 228 Chapter 4 Analysis of Convection Heat Transfer 230 4.1 Introduction 231 4.2 Convection Heat Transfer 231 4.3 Boundary Layer Fundamentals 233 4.4 Conservation Equations of Mass, Momentum, and Energy for Laminar Flow Over a Flat Plate 235 4.5 Dimensionless Boundary Layer Equations and Similarity Parameters 239 4.6 Evaluation of Convection Heat Transfer Coefficients 243 4.7 Dimensional Analysis 245 4.8* Analytic Solution for Laminar Boundary Layer Flow Over a Flat Plate 252 4.9* Approximate Integral Boundary Layer Analysis 261 4.10* Analogy Between Momentum and Heat Transfer in Turbulent Flow Over a Flat Surface 267 4.11 Reynolds Analogy for Turbulent Flow Over Plane Surfaces 273 4.12 Mixed Boundary Layer 274 4.13* Special Boundary Conditions and High-Speed Flow 277 4.14 Closing Remarks 282 References 283 Problems 284 Design Problems 294 Chapter 5 Natural Convection 296 5.1 Introduction 297 5.2 Similarity Parameters for Natural Convection 299 5.3 Empirical Correlation for Various Shapes 308 5.4* Rotating Cylinders, Disks, and Spheres 322 5.5 Combined Forced and Natural Convection 325 5.6* Finned Surfaces 328 Copyright 2011 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

Contents xi 5.7 Closing Remarks 333 References 338 Problems 340 Design Problems 348 Chapter 6 Forced Convection Inside Tubes and Ducts 350 6.1 Introduction 351 382 6.2* Analysis of Laminar Forced Convection in a Long Tube 360 6.3 Correlations for Laminar Forced Convection 370 6.4* Analogy Between Heat and Momentum Transfer in Turbulent Flow 6.5 Empirical Correlations for Turbulent Forced Convection 386 6.6 Heat Transfer Enhancement and Electronic-Device Cooling 395 6.7 Closing Remarks 406 References 408 Problems 411 Design Problems 418 Chapter 7 Forced Convection Over Exterior Surfaces 420 7.1 Flow Over Bluff Bodies 421 422 7.2 Cylinders, Spheres, and Other Bluff Shapes 7.3* Packed Beds 440 7.4 Tube Bundles in Cross-Flow 444 7.5* Finned Tube Bundles in Cross-Flow 458 7.6* Free Jets 461 7.7 Closing Remarks 471 References 473 Problems 475 Design Problems 482 Chapter 8 Heat Exchangers 484 8.1 Introduction 485 8.2 Basic Types of Heat Exchangers 485 8.3 Overall Heat Transfer Coefficient 494 8.4 Log Mean Temperature Difference 498 8.5 Heat Exchanger Effectiveness 506 8.6* Heat Transfer Enhancement 516 8.7* Microscale Heat Exchangers 524 Copyright 2011 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

xii Contents 8.8 Closing Remarks 525 References 527 Problems 529 Design Problems 539 Chapter 9 Heat Transfer by Radiation 540 9.1 Thermal Radiation 541 610 9.2 Blackbody Radiation 543 9.3 Radiation Properties 555 9.4 The Radiation Shape Factor 571 9.5 Enclosures with Black Surfaces 581 9.6 Enclosures with Gray Surfaces 585 9.7* Matrix Inversion 591 9.8* Radiation Properties of Gases and Vapors 602 9.9 Radiation Combined with Convection and Conduction 9.10 Closing Remarks 614 References 615 Problems 616 Design Problems 623 Chapter 10 Heat Transfer with Phase Change 624 10.1 Introduction to Boiling 625 10.2 Pool Boiling 625 10.3 Boiling in Forced Convection 647 10.4 Condensation 660 10.5* Condenser Design 670 10.6* Heat Pipes 672 10.7* Freezing and Melting 683 References 688 Problems 691 Design Problems 696 Appendix 1 The International System of Units A3 Appendix 2 Data Tables A6 Properties of Solids A7 A14 Thermodynamic Properties of Liquids Heat Transfer Fluids A23 Copyright 2011 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

Contents xiii Liquid Metals A24 Thermodynamic Properties of Gases A26 Miscellaneous Properties and Error Function A37 Correlation Equations for Physical Properties A45 Appendix 3 Tridiagonal Matrix Computer Programs A50 Solution of a Tridiagonal System of Equations A50 Appendix 4 Computer Codes for Heat Transfer A56 Appendix 5 The Heat Transfer Literature A57 Index I1 Copyright 2011 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

NOMENCLATURE Symbol Quantity International English System System of of Units Units a velocity of sound m/s ft/s ft/s2 a acceleration m/s2 ft2 A area; Ac cross-sectional area; Ap, m2 ft Btu/lbm °F projected area of a body normal to the Btu/°F direction of flow; Aq, area through Btu/h °F which rate of heat flow is q; As, surface area; Ao, outside surface area; Ai, inside ft surface area Btu/lbm b breadth or width m Btu Btu/h ft2 c specific heat; cp, specific heat at J/kg K (Continued) constant pressure; c␯, specific heat at xv constant volume C constant C thermal capacity J/K C hourly heat capacity rate in Chapter 8; W/K Cc, hourly heat capacity rate of colder fluid in a heat exchanger; Ch, hourly heat capacity rate of warmer fluid in a heat exchanger CD total drag coefficient Cf skin fdriicsttiaonncecoxeffrfoicmienleta; dCifnx,gloedcagle;vaCqlfu,e of Cf at average value of Cf defined by Eq. (4.31) d, D diameter; DH, hydraulic diameter; Do, m outside diameter; Di, inside diameter e base of natural or Napierian logarithm e internal energy per unit mass J/kg E internal energy J E emissive power of a radiating body; Eb, W/m2 emissive power of blackbody Copyright 2011 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

xvi Nomenclature Symbol Quantity International English System E␭ System of of Units Ᏹ monochromatic emissive power per Units f micron at wavelength ␭ Btu/h ft2 micron W/m2 ␮m f heat exchanger effectiveness defined by Eq. (8.22) lbf N F Darcy friction factor for flow through a ft/s2 FT pipe or a duct, defined by Eq. (6.13) m/s2 32.2 ft lbm/lbf s2 F1–2 1.0 kg m/N s2 lbm/h ft2 Ᏺ1–2 friction coefficient for flow over banks kg/m2 s Btu/h ft2 g of tubes defined by Eq. (7.37) W/m2 Btu/lbm gc J/kg Btu/h ft2°F G force W/m2 K Btu/h ft2°F W/m2 K G temperature factor defined by Eq. (9.119) Btu/lbm J/kg deg h geometric shape factor for radiation rad amp hc from one blackbody to another amp Btu/h sr hq W/sr Btu/h sr micron geometric shape and emissivity factor for W/sr ␮m Btu/h ft2 hfg radiation from one graybody to another W/m2 i acceleration due to gravity i I dimensional conversion factor I␭ J mass flow rate per unit area (G ϭ ␳Uϱ) irradiation incident on unit surface in unit time enthalpy per unit mass local convection heat transfer coefficient combined heat transfer coefficient qh = qhc + qhr; hb, heat transfer coefficient of a boiling liquid, defined by Eq. (10.1); qhc, average coefficient; convection heat transfer hqr, average heat transfer coefficient for radiation latent heat of condensation or evaporation angle between sun direction and surface normal electric current intensity of radiation intensity per unit wavelength radiosity Copyright 2011 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

Nomenclature xvii Symbol Quantity International English System k System of of Units thermal conductivity; ks, thermal Units K conductivity of a solid; kf, thermal Btu/h ft °F conductivity of a fluid W/m K l Btu/h °F L thermal conductance; Kk, thermal W/K Lf conductance for conduction heat ft or in. m# transfer; Kc, thermal conductance for m ft or in. M convection heat transfer; Kr, thermal m Btu/lbm m conductance for radiation heat transfer J/kg lbm/s or lbm/h N kg/s lbm p length, general kg lbm/lb-mole P gm/gm-mole q length along a heat flow path or psi, lbf/ft2, or atm characteristic length of a body N/m2 ft q# G m Btu/h qЉ latent heat of solidification W Q Btu/h ft3 # mass flow rate W/m3 Btu/h ft2 Q W/m2 Btu r mass J ft3/h R m3/s ft or in. molecular weight m h °F/Btu Re K/W number in general; number of tubes, etc. ohm ohm (Continued) static pressure; pc, critical pressure; pA, partial pressure of component A wetted perimeter rate of heat flow; qk, rate of heat flow by conduction; qr, rate of heat flow by radiation; qc, rate of heat flow by convection; qb, rate of heat flow by nucleate boiling rate of heat generation per unit volume heat flux quantity of heat volumetric rate of fluid flow radius; rH, hydraulic radius; ri, inner radius; ro, outer radius thermal resistance; Rc, thermal resistance to convection heat transfer; Rk, thermal resistance to conduction heat transfer; Rr, thermal resistance to radiation heat transfer electrical resistance Copyright 2011 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

xviii Nomenclature Symbol Quantity International English System r System of of Units S perfect gas constant Units S 1545 ft lbf/lb-mole °F SL shape factor for conduction heat flow 8.314 J/K kg-mole ST ft t spacing m T ft distance between centerlines of tubes m u in adjacent longitudinal rows ft u m ft distance between centerlines of tubes m R or °F U in adjacent transverse rows K or °C Uϱ ␷ thickness J/kg Btu/lbm ␷ temperature; Tb, temperature of bulk m/s ft/s or ft/h V of fluid; Tf, mean film temperature; W/m2 K Btu/h ft2 °F w Ts, surface temperature; Tϱ, temperature m/s ft/s of fluid far removed from heat source m3/kg ft3/lbm w or sink; Tm, mean bulk temperature m/s ft/s or ft/h # of fluid flowing in a duct; Tsv, temperature W of saturated vapor; Tsl, temperature of a m3 ft3 x saturated liquid; Tfr, freezing temperature; m/s ft/s Tl, liquid temperature; Tas, adiabatic wall temperature m ft or in. W Btu/h internal energy per unit mass m ft time average velocity in x direction; uЈ, instantaneous fluctuating x component of velocity; qu, average velocity overall heat transfer coefficient free-stream velocity specific volume time average velocity in y direction; ␷Ј, instantaneous fluctuating y component of velocity volume time average velocity in z direction; wЈ, instantaneous fluctuating z component of velocity width rate of work output distance from the leading edge; xc, distance from the leading edge where flow becomes turbulent Copyright 2011 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.