www.elsolucionario.net www.elsolucionario.net hol29362_ifc 10/30/2008 18:42 www.elsolucionario.net Physical quantity Symbol Length Area Volume Velocity Density Force Mass Pressure Energy, heat Heat flow Heat flux per unit area Heat flux per unit length Heat generation per unit volume Energy per unit mass Specific heat Thermal conductivity Convection heat-transfer coefficient Dynamic Viscosity Kinematic viscosity and thermal diffusivity L A V v ρ F m p q q q/A q/L q˙ q/m c k h μ ν, α SI to English conversion English to SI conversion m = 3.2808 ft m2 = 10.7639 ft2 m3 = 35.3134 ft3 m/s = 3.2808 ft/s kg/m3 = 0.06243 lbm /ft3 N = 0.2248 lbf kg = 2.20462 lbm N/m2 = 1.45038 × 10−4 lbf /in2 kJ = 0.94783 Btu W = 3.4121 Btu/h W/m2 = 0.317 Btu/h · ft2 W/m = 1.0403 Btu/h · ft W/m3 = 0.096623 Btu/h · ft3 kJ/kg = 0.4299 Btu/lbm kJ/kg · ◦ C = 0.23884 Btu/lbm · ◦ F W/m · ◦ C = 0.5778 Btu/h · ft · ◦ F W/m2 · ◦ C = 0.1761 Btu/h · ft2 · ◦ F kg/m · s = 0.672 lbm /ft · s = 2419.2 lbm /ft · h m /s = 10.7639 ft2 /s ft = 0.3048 m ft2 = 0.092903 m2 ft3 = 0.028317 m3 ft/s = 0.3048 m/s lbm /ft3 = 16.018 kg/m3 lbf = 4.4482 N lbm = 0.45359237 kg lbf /in2 = 6894.76 N/m2 Btu = 1.05504 kJ Btu/h = 0.29307 W Btu/h · ft2 = 3.154 W/m2 Btu/h · ft = 0.9613 W/m Btu/h · ft3 = 10.35 W/m3 Btu/lbm = 2.326 kJ/kg Btu/lbm · ◦ F = 4.1869 kJ/kg · ◦ C Btu/h · ft · ◦ F = 1.7307 W/m · ◦ C Btu/h · ft2 · ◦ F = 5.6782 W/m2 · ◦ C lbm /ft · s = 1.4881 kg/m · s ft2 /s = 0.092903 m2 /s Important physical constants Avogadro’s number Universal gas constant N0 = 6.022045 × 1026 molecules/kg mol R = 1545.35 ft · lbf/lbm · mol · ◦ R = 8314.41 J/kg mol · K = 1.986 Btu/lbm · mol · ◦ R = 1.986 kcal/kg mol · K Planck’s constant h = 6.626176 × 10−34 J · sec Boltzmann’s constant k = 1.380662 × 10−23 J/molecule · K = 8.6173 × 10−5 eV/molecule · K Speed of light in vacuum c = 2.997925 × 108 m/s Standard gravitational acceleration g = 32.174 ft/s2 = 9.80665 m/s2 Electron mass me = 9.1095 × 10−31 kg Charge on the electron e = 1.602189 × 10−19 C Stefan-Boltzmann constant σ = 0.1714 × 10−8 Btu/hr · ft2 · R4 = 5.669 × 10−8 W/m2 · K4 atm = 14.69595 lbf/in2 = 760 mmHg at 32◦ F = 29.92 inHg at 32◦ F = 2116.21 lbf/ft2 = 1.01325 × 105 N/m2 # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Pg No.1 K/PMS 293 Short / Normal / Long DESIGN SERVICES OF S4CARLISLE Publishing Services www.elsolucionario.net Useful conversion factors 10/30/2008 18:42 www.elsolucionario.net Basic Heat-Transfer Relations Fourier’s law of heat conduction: ∂T qx = −kA ∂x Characteristic thermal resistance for conduction = x/kA Characteristic thermal resistance for convection = 1/hA Overall heat transfer = Toverall / Rthermal Convection heat transfer from a surface: q = hA(Tsurface − Tfree stream ) for exterior flows q = hA(Tsurface − Tfluid bulk ) for flow in channels Forced convection: Nu = f(Re, Pr) Free convection: Nu = f(Gr, Pr) ρux ρ2 gβ Tx3 Gr = μ μ2 x = characteristic dimension Re = (Chapters and 6, Tables 5-2 and 6-8) (Chapter 7, Table 7-5) Pr = cp μ k General procedure for analysis of convection problems: Section 7-14, Figure 7-15, Inside back cover Radiation heat transfer (Chapter 8) energy emitted by blackbody Blackbody emissive power, = σT area · time energy leaving surface Radiosity = area · time energy incident on surface Irradiation = area · time Radiation shape factor Fmn = fraction of energy leaving surface m and arriving at surface n Reciprocity relation: Am Fmn = An Fnm Radiation heat transfer from surface with area A1 , emissivity large enclosure at temperature T2 (K): 1, and temperature T1 (K) to q = σA1 (T14 − T24 ) LMTD method for heat exchangers (Section 10-5): q = UAF Tm where F = factor for specific heat exchanger; Tm = LMTD for counterflow double-pipe heat exchanger with same inlet and exit temperatures Effectiveness-NTU method for heat exchangers (Section 10-6, Table 10-3): Temperaure difference for fluid with minimum value of mc = Largest temperature difference in heat exchanger UA NTU = = f(NTU, Cmin /Cmax ) Cmin See List of Symbols on page xvii for definitions of terms # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Pg No.2 K/PMS 293 Short / Normal / Long DESIGN SERVICES OF S4CARLISLE Publishing Services www.elsolucionario.net hol29362_ifc 11/6/2008 15:54 www.elsolucionario.net Heat Transfer www.elsolucionario.net hol29362_fm # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Pg No.1 K/PMS 293 Short / Normal / Long DESIGN SERVICES OF S4CARLISLE Publishing Services hol29362_fm 11/6/2008 15:54 www.elsolucionario.net McGraw-Hill Series in Mechanical Engineering CONSULTING EDITORS Jack P Holman, Southern Methodist University John Lloyd, Michigan State University Anderson Modern Compressible Flow: With Historical Perspective Barber Intermediate Mechanics of Materials Baruh Analytical Dynamics Beer and Johnston Vector Mechanics for Engineers: Statics and Dynamics Beer, Johnston and DeWolf Mechanics of Materials Borman and Ragland Combustion Engineering Budynas Advanced Strength and Applied Stress Çengel and Boles Thermodynamics: An Engineering Approach Çengel and Turner Fundamentals of Thermal-Fluid Sciences Shigley and Mischke Mechanical Engineering Design Doebelin Measurement Systems: Application and Design Stoecker Design of Thermal Systems Hamrock Fundamentals of Machine Elements Mattingly Elements of Gas Turbine Propulsion Turns An Introduction to Combustion: Concepts and Applications Meirovitch Fundamentals of Vibrations Heywood Internal Combustion Engine Fundamentals Modest Radiative Heat Transfer Histand and Alciatore Introduction to Mechatronics and Measurement Systems Norton Design of Machinery Hsu MEMS and Microsystems: Design and Manufacturing Oosthuizen and Carscallen Compressible Fluid Flow Holman Experimental Methods for Engineers Oosthuizen and Naylor Introduction to Convective Heat Transfer Analysis Palm Introduction to MATLAB for Engineers Palm MATLAB for Engineering Applications Reddy Introduction to Finite Element Method Kays and Crawford Convective Heat and Mass Transfer Kelly Fundamentals of Mechanical Vibrations Kreider, Rabl and Curtiss Heating and Cooling of Buildings Ullman The Mechanical Design Process Çengel Heat Transfer: A Practical Approach Ribando Heat Transfer Tools Çengel Introduction to Thermodynamics and Heat Transfer Rizzoni Principles and Applications for Electrical Engineering Vu and Esfandiari Dynamic Systems: Modeling and Analysis Chapra and Canale Numerical Methods for Engineers Schey Introduction to Manufacturing Processes Wark Advanced Thermodynamics for Engineers Condoor Mechanical Design Modeling with ProEngineer Schlichting Boundary Layer Theory Wark and Richards Thermodynamics SDRC, Inc I-DEAS Student Edition White Fluid Mechanics SDRC, Inc I-DEAS Student Guide White Viscous Fluid Flow Shames Mechanics of Fluids Zeid CAD/CAM Theory and Practice Courtney Mechanical Behavior of Materials Dieter Engineering Design: A Materials and Processing Approach # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Pg No.2 Ugural Stresses in Plates and Shells K/PMS 293 Short / Normal / Long DESIGN SERVICES OF S4CARLISLE Publishing Services www.elsolucionario.net Anderson Computational Fluid Dynamics 11/6/2008 15:54 www.elsolucionario.net Heat Transfer Tenth Edition J P Holman www.elsolucionario.net hol29362_fm Department of Mechanical Engineering Southern Methodist University # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Pg No.3 K/PMS 293 Short / Normal / Long DESIGN SERVICES OF S4CARLISLE Publishing Services 11/6/2008 15:54 www.elsolucionario.net HEAT TRANSFER, TENTH EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020 Copyright © 2010 by The McGraw-Hill Companies, Inc All rights reserved Previous editions 2002, 1997, and 1990 No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning Some ancillaries, including electronic and print components, may not be available to customers outside the United States This book is printed on acid-free paper VNH/VNH ISBN 978–0–07–352936–3 MHID 0–07–352936–2 Global Publisher: Raghothaman Srinivasan Senior Sponsoring Editor: Bill Stenquist Director of Development: Kristine Tibbetts Developmental Editor: Lora Neyens Senior Marketing Manager: Curt Reynolds Senior Project Manager: Kay J Brimeyer Lead Production Supervisor: Sandy Ludovissy Senior Media Project Manager: Tammy Juran Associate Design Coordinator: Brenda A Rolwes Cover Designer: Studio Montage, St Louis, Missouri Cover Image: Interferometer photo of air flow across a heated cylinder, digitally enhanced by the author Compositor: S4Carlisle Publishing Services Typeface: 10.5/12 Times Roman Printer: R R Donnelley, Jefferson City, MO Library of Congress Cataloging-in-Publication Data Holman, J P (Jack Philip) Heat transfer / Jack P Holman.—10th ed p cm.—(Mcgraw-Hill series in mechanical engineering) Includes index ISBN 978–0–07–352936–3—ISBN 0–07–352936–2 (hard copy : alk paper) Heat-Transmission I Title QC320.H64 2010 621.402 2—dc22 2008033196 www.mhhe.com # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Pg No.4 K/PMS 293 Short / Normal / Long DESIGN SERVICES OF S4CARLISLE Publishing Services www.elsolucionario.net hol29362_fm 11/14/2008 11:48 www.elsolucionario.net CONTENTS Guide to Worked Examples Preface C HAPT E R ix Steady-State Conduction—Multiple Dimensions 77 xiii About the Author xvii C HAPT E R Introduction 77 Mathematical Analysis of Two-Dimensional Heat Conduction 77 3-3 Graphical Analysis 81 3-4 The Conduction Shape Factor 83 3-5 Numerical Method of Analysis 88 3-6 Numerical Formulation in Terms of Resistance Elements 98 3-7 Gauss-Seidel Iteration 99 3-8 Accuracy Considerations 102 3-9 Electrical Analogy for Two-Dimensional Conduction 118 3-10 Summary 119 Review Questions 119 List of Worked Examples 120 Problems 120 References 136 Steady-State Conduction— One Dimension 27 C HAPT E R List of Symbols 3-1 3-2 xix C HAPT E R Introduction 1-1 Conduction Heat Transfer 1-2 Thermal Conductivity 1-3 Convection Heat Transfer 10 1-4 Radiation Heat Transfer 12 1-5 Dimensions and Units 13 1-6 Summary 19 Review Questions 20 List of Worked Examples 21 Problems 21 References 25 2-1 Introduction 27 2-2 The Plane Wall 27 2-3 Insulation and R Values 28 2-4 Radial Systems 29 2-5 The Overall Heat-Transfer Coefficient 2-6 Critical Thickness of Insulation 39 2-7 Heat-Source Systems 41 2-8 Cylinder with Heat Sources 43 2-9 Conduction-Convection Systems 45 2-10 Fins 48 2-11 Thermal Contact Resistance 57 Review Questions 60 List of Worked Examples 60 Problems 61 References 75 Unsteady-State Conduction 139 www.elsolucionario.net hol29362_fm 4-1 4-2 4-3 33 Introduction 139 Lumped-Heat-Capacity System 141 Transient Heat Flow in a Semi-Infinite Solid 143 4-4 Convection Boundary Conditions 147 4-5 Multidimensional Systems 162 4-6 Transient Numerical Method 168 4-7 Thermal Resistance and Capacity Formulation 176 4-8 Summary 192 Review Questions 193 List of Worked Examples 193 Problems 194 References 214 v # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Pg No.5 K/PMS 293 Short / Normal / Long DESIGN SERVICES OF S4CARLISLE Publishing Services hol29362_fm 11/6/2008 15:54 www.elsolucionario.net vi Contents C HAPT E R Free Convection from Horizontal Cylinders 340 Free Convection from Horizontal Plates 342 Free Convection from Inclined Surfaces 344 Nonnewtonian Fluids 345 Simplified Equations for Air 345 Free Convection from Spheres 346 Free Convection in Enclosed Spaces 347 Combined Free and Forced Convection 358 Summary 362 Summary Procedure for all Convection Problems 362 Review Questions 363 List of Worked Examples 365 Problems 365 References 375 215 5-1 5-2 5-3 5-4 5-5 5-6 5-7 Introduction 215 Viscous Flow 215 Inviscid Flow 218 Laminar Boundary Layer on a Flat Plate 222 Energy Equation of the Boundary Layer 228 The Thermal Boundary Layer 231 The Relation Between Fluid Friction and Heat Transfer 241 5-8 Turbulent-Boundary-Layer Heat Transfer 243 5-9 Turbulent-Boundary-Layer Thickness 250 5-10 Heat Transfer in Laminar Tube Flow 253 5-11 Turbulent Flow in a Tube 257 5-12 Heat Transfer in High-Speed Flow 259 5-13 Summary 264 Review Questions 264 List of Worked Examples 266 Problems 266 References 274 C HAPT E R Radiation Heat Transfer C HAPT E R Empirical and Practical Relations for Forced-Convection Heat Transfer 277 6-1 Introduction 277 6-2 Empirical Relations for Pipe and Tube Flow 6-3 Flow Across Cylinders and Spheres 293 6-4 Flow Across Tube Banks 303 6-5 Liquid-Metal Heat Transfer 308 6-6 Summary 311 Review Questions 313 List of Worked Examples 314 Problems 314 References 324 279 C HAPT E R Natural Convection Systems 7-1 7-2 7-3 7-4 327 Introduction 327 Free-Convection Heat Transfer on a Vertical Flat Plate 327 Empirical Relations for Free Convection Free Convection from Vertical Planes and Cylinders 334 332 # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Pg No.6 379 8-1 8-2 8-3 8-4 8-5 8-6 8-7 8-8 8-9 8-10 Introduction 379 Physical Mechanism 379 Radiation Properties 381 Radiation Shape Factor 388 Relations Between Shape Factors 398 Heat Exchange Between Nonblackbodies 404 Infinite Parallel Surfaces 411 Radiation Shields 416 Gas Radiation 420 Radiation Network for an Absorbing and Transmitting Medium 421 8-11 Radiation Exchange with Specular Surfaces 426 8-12 Radiation Exchange with Transmitting, Reflecting, and Absorbing Media 430 8-13 Formulation for Numerical Solution 437 8-14 Solar Radiation 451 8-15 Radiation Properties of the Environment 458 8-16 Effect of Radiation on Temperature Measurement 459 8-17 The Radiation Heat-Transfer Coefficient 460 8-18 Summary 461 Review Questions 462 List of Worked Examples 462 Problems 463 References 485 K/PMS 293 Short / Normal / Long DESIGN SERVICES OF S4CARLISLE Publishing Services www.elsolucionario.net Principles of Convection 7-5 7-6 7-7 7-8 7-9 7-10 7-11 7-12 7-13 7-14 11/14/2008 11:54 www.elsolucionario.net 719 Index Moody, F F., 324 Moore, C J., Jr., 75 Moran, W R., 377 Morgan, V T., 306, 325, 378 Morgan, W R., 400, 485 Mueller, A E., 585 Mueller, W K., 377 Mull, W., 377 Multilayer conduction, 31–32 Multilayer cylindrical system, 31, 32–33 Multimode heat transfer, 17 Multiple dimensions, 162–168 See also Steady-state conduction—multiple dimensions Multiple-radiation-shield problems, 418–420 Multiplier factors, SI units, 16 Murakami, K., 377 Myers, G E., 214 Myers, R F., 136 N Nagle, W M., 585 Nakai, S., 299, 325 Natural convection systems, 11, 327–378 See also Convection heat transfer across gap space, estimates, 610, 621–623 body forces, 327 boundary-layer thickness estimates, 610, 617–618 character dimensions, 333 combined free-forced convection, 358–362 constant-heat-flux surfaces, 336–340, 342–343 empirical relations, 332–334 enclosed spaces, 347–358 evacuated (low-density) spaces, 354–358 examples See Worked examples—convection heat transfer Grashof number, 331–332 heat-transfer coefficients, 11 horizontal cylinders, 340–342 # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e horizontal plates, 342–344 inclined surfaces, 344–345 irregular solids, 343 isothermal surfaces, 334–335, 342 modified Grashof number, 336 nonnewtonian fluids, 345 problem solving, 608–623 radiation R-value for gap, 351 Rayleigh number, 333 simplified equations for air, 345–346 spheres, 346–347 summary (heat transfer relations), 362 vertical flat plate, 327–332 vertical planes/cylinders, 334–340 Nelson, K E., 486 Net viscous-shear force, 224 Newell, M E., 376 Newton, 16 Newton’s law of cooling, 10, 231 Newton’s second law of motion, 14, 16, 222 Nickell, R E., 214 Nicolson, P., 136 Nine-node problem, 93–95, 689–691, 694–697 Nix, G H., 503, 518 Nodal equations, for x = y, specific formulations, 101–102, 173–175 Nodal equations, general formulation steady state, 98 transient, 172–175 Nodal formulas for finite-difference calculations, 92–93 Nodal spreadsheet formulas, display of in Excel, 679–681 Noncircular cylinders, 299–300 Nonmetals, properties, 653–655 Nonnewtonian fluids, 345 Nordenson, T J., 603 NTU, 542 NTU relations for heat exchangers, 546 Nucleate boiling, 496–497, 505 Nucleate boiling heat-transfer coefficients, 512 Number of transfer units (NTU), 542 Numbers See Dimensionless groups Pg No.719 K/PMS 293 Short / Normal / Long Numerical-analysis procedure (heat exchangers), 559 Numerical formulation/heat generation, 104–106 Numerical formulation/resistance elements, 98–99 Numerical method of analysis, 88–97 Numerical solution for variable conductivity, 190–192 Numerical solutions (radiation), 437–451 Nusselt, Wilhelm, 235, 282, 324, 489, 517 Nusselt number, 235–236, 609, 610, 611, 613–616 O www.elsolucionario.net hol29362_Index Off-center temperatures, 674–675 Oil flow over heated flat plate, 240 Okazaki, T., 299, 325 One-dimensional heat-conduction equation, One-dimensional systems, 27 See also Steady-state conduction—one dimension Open cylindrical shield in large room, 418–420 Open hemisphere in large room, 413 Oppenheim, A K., 405, 486 Order-of-magnitude analysis, 277, 278, 360 Orthogonal functions, 81 Orvis, W J., 137, 712 Ostrach, S., 376 O’Toole, J., 377 Overall heat-transfer coefficient, 33–39, 521–527 Overall heat-transfer coefficient for tube, 39 Ozisik, M N., 119, 136, 214 Ozoe, H., 237, 275 P Palm, W., 137 Parallel-flow heat-exchanger, 532, 540, 541, 543, 545 Particulate scattering, 457 Patankar, S V., 137, 214 Peclet number, 284, 310 DESIGN SERVICES OF S4CARLISLE Publishing Services hol29362_Index 11/14/2008 11:54 www.elsolucionario.net Index Pera, L., 344, 376, 377 Perry, J H., 585, 603 Peterson, G P., 519 Petukhov, B S., 282, 325 Pioro, I L., 519 Piret, E L., 518 Pitts, C C., 518 Planck blackbody radiation spectrum, 624 Planck’s constant, 379 Plane wall, 25–26 Plane wall with heat sources, 41–42 Plate with unheated starting length, 239–240 Pletcher, R H., 137, 214 Pohlhausen, E., 669 Pool boiling, 496 Powe, R E., 350, 378 Prandtl, Ludwig, 234 Prandtl mixing length, 245 Prandtl number, 230, 234–235, 280 Present, R D., 603 Prigogine, L., 587, 603 Principles of convection, 215–275 See also Convection heat transfer Bernoulli equation, 218–219 bulk temperature, 255–257 constant heat flux, 236–237, 249 eddy viscosity, 243, 244–247 energy equation of boundary layer, 228–231 equations, 265 examples See Worked examples—convection heat transfer fluid friction/heat transfer, 241–242 general calculation procedure, 264 high-speed heat transfer calculations, 259–264 introduction, 215 inviscid flow, 218–221 laminar boundary layer on flat plate, 222–228 laminar tube flow, heat transfer, 253–257 Nusselt number, 235–236 Prandt number, 234–235 Reynolds analogy for tube flow, 258 Reynolds number, 216–218 thermal boundary layer, 231–241 turbulent-boundary-layer thickness, 250–253 turbulent-bound-layer heat transfer, 243–250 turbulent flow in tube, 257–259 universal velocity profile, 246, 247 viscous flow, 215–218 Problem-solving principles, 605 conduction problems, 606–607 convection heat-transfer relations, 608–623 heat exchangers, 628–645 introduction, 605 radiation heat transfer, 623–628 Properties air, 658 gases, 659–660 low-melting point metals, 661 metals, 650–652, 661 nonmetals, 653–655 radiation, 381–388 saturated liquids, 656–657 water, 662 Pulsed energy at surface of semi-infinite solid, 146–147 Q Quartz-fiber anemometers, 332 R Radial systems, 29–33 Radiant electric stove for boiling water, 644–645 Radiant heater, 642–643 coolant for, 644 Radiation boundary condition, 111–113 in Excel, 683–684 in numerical methods, 101–102 Radiation formulas, 461 Radiation from hole with variable radiosity, 443–446 Radiation functions, 386–387 # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Pg No.720 Radiation heating and cooling, 186–188 Radiation heat transfer, 12–13, 379–486 apparent emissivity, 413–415, 433–434 Beer’s law, 420 blackbody, 12–13, 380, 624, 625 convex object in large enclosure, 411–412 examples See Worked examples—radiation heat transfer formulas, 461 gas radiation, 420 gray body, 625 infinite parallel surfaces, 411–416 insolation, 456–459 insulated surfaces, 407–408, 440 Kirchhoff’s identity, 382–383 nonblackbodies, 404–411 numerical solutions, 437–451 physical mechanism, 379–381 problem solving, 623–628 propagation of thermal radiation, 379 radiation heat-transfer coefficient, 461–462 radiation network for analyzing transmitting absorbing systems, 421–426 radiation properties, 381–388 radiation properties of environment, 456–459 radiation R-value for gap, 351 radiation shape factor, 388–398 radiation shields, 416–420 reciprocity relations, 389, 398, 400, 422 relations between shape factors, 398–404 solar radiation, 451–456 specular surfaces, 426–430 Stefan-Boltzmann law, 380 surface roughness, 382 surfaces with large areas, 407–408, 440 temperature measurement, 459–460 three-body problem, 406, 407 K/PMS 293 Short / Normal / Long DESIGN SERVICES OF S4CARLISLE Publishing Services www.elsolucionario.net 720 11/14/2008 11:54 www.elsolucionario.net Index transmitting/reflecting absorbing media, 430–437 Wien’s displacement law, 383 Radiation, blackbody, 12–13 Planck spectrum, 624 Radiation heat-transfer coefficient, 460–461 Radiation properties, 381–388 Radiation shape factor, 388–398 Radiation shape factor relations, 393–396 Radiation shields, 416–420 Radiosity, 404 Raithby, G D., 378 Rayleigh number, 333, 347 Real surfaces, 393–394 Reciprocity relations, 389, 398, 400, 422 Recovery factor, 260 Rectangular fin, 49, 50 Reduction of convection in air gap, 353–354 Reference-enthalpy method, 261 Reflectivity, 381 Refrigerator storage in desert climate, 638–639 Reid, R C., 603 Reid, R L., 25 Reiher, H., 377 Relative humidity of air stream, 597 Resistance-capacity formulation, 176–192 Reynolds analogy for mass transfer, 595–596 Reynolds analogy for tube flow, 258 Reynolds-Colburn analogy, 242, 247 Reynolds number, 216–218, 280–281, 491, 492, 609 Richardson, P D., 214 Richtmeyer, R D., 136 Rod with heat sources, 56–57 Rogers, D F., 136 Rohsenow, W M., 136, 490, 493, 501, 504, 518, 519 Rohsenow equation, 501, 626 Rose, J W., 518 Ross, D C., 377 Rotern, Z., 376 Rouse, M W., 310, 325 Rowe, R E., 377 # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Ruch, M A., 519 Rudenberg, R., 136 R-value, 28–29 R-value, for enclosed space, 348 S Sabersky, R H., 324, 325 Salman, Y K., 378 Sammakia, B., 331, 332, 375 Sanders, C J., 376 Santangelo, J G., 498, 519 Sarofim, A F., 486 Saturated boiling, 496–497 Saturated liquids, properties, 656–657 Sauer, E T., 519 Saunders, O A., 377 Scanlan, J A., 375, 377 Scattering, 457 Schenck, H., 214 Schlanciauskas, A., 325 Schlichting, H., 224, 247, 274, 279, 324 Schlunder, E W., 585 Schmidt, E., 377, 485, 486, 489, 518 Schmidt, F W., 376 Schmidt number, 595 Schneider, G E., 137, 214 Schneider, P J., 75, 119, 136, 148, 151, 214 Schultz-Grunow, F., 247, 275 Schurig, W., 518 Scorah, E L., 496, 518 Sears, F W., 485 Seban, R A., 310, 324 Sellars, J R., 256, 274, 287 Sellschop, W., 518 Semi-infinite cylinder suddenly exposed to convection, 165–166 Semi-infinite solid, 143–147 Separation constant, 79 Separation-of-variables method, 78, 139–141, 162 Separation point, 295 Shah, R K., 285, 287, 325 Shape-factor algebra for cylindrical reflector, 403–404 Shape-factor algebra for open ends of cylinders, 401–402 Pg No.721 K/PMS 293 Short / Normal / Long 721 Shape-factor algebra for truncated cone, 402–403 Shell-and-tube exchanger as air heater, 552 Shell-and-tube heat exchanger, 528–530, 537–539 Sheriff, N., 325 Sherwood, T K., 603 Sherwood number, 595 Shimazaki, T T., 310, 324 Shires, G L., 585 Shum, Y M., 214 Sieder, E N., 282, 283, 324 Sieder-Tate relation, 283 Siegal, R., 521, 584 Siegel, R., 50, 75, 486 Silver, Silveston, P L., 377 Similarity variable, 667 Simonds, R R., 377 Simplified equations for air, 345–346 Sine-function boundary condition, 79 Singh, S N., 378 Single-lump heat-capacity, 141 SI system, 15, 16 SI units, 15, 16, 666 Skin-friction coefficient, 247 Skupinshi, E., 310, 324 Sleicher, C A., 310, 325 Slug-flow model, 308–309 Small cylinder, cooling of, 676–677 Smith, J W., 325 Smith, T F., 486 Soehngen, E E., 331, 375, 377 Software packages, 96–97, 118 See also Excel Solar constant, 451 Solar radiation, 451–456 Solids, thermal conductivities of, Somerscales, E F C., 349, 375, 585 Space resistance for radiation, 405 Sparrow, E M., 137, 214, 376, 377, 378, 404, 486, 521, 585 Specular reflection, 381 Specular surfaces, 426–430 Speed of light, 379 Spheres forced convection, 300 free convection, 346–347 Heisler charts, 673–675 www.elsolucionario.net hol29362_Index DESIGN SERVICES OF S4CARLISLE Publishing Services hol29362_Index 11/14/2008 11:54 www.elsolucionario.net Index Spheres—Cont steady-state conduction, 31 Spherical coordinates, Stability criteria, Biot and Fourier numbers, 172–173 Stability criteria, in Excel, 682–683 Stability criteria, most restrictive for x = y, 172–173 Stanton number, 241, 261 Steady-flow energy equation for adiabatic process, 259 Steady state as limiting case of transient solution, 178 Steady-state conduction—multiple dimensions, 77–137 accuracy considerations, 102–118 conduction shape factor, 83–88 electrical analogy for two-dimensional conduction, 118–119 examples See Worked examples—steady-state conduction Gauss-Seidel iteration, 99–102 general calculation procedure, 119, 606–607 graphical analysis, 81–83 Laplace equation, 77 mathematical analysis of two-dimensional problem, 77–81 numerical formulation/resistance elements, 98–99 numerical method of analysis, 88–97 problem solving, 606–607 separation-of-variables method, 78 software packages, 96–97, 118 two-dimensional, Steady-state conduction—one dimension, 27–75 conduction-convection systems, 44–48 convection boundary conditions, 33 critical insulation thickness, 39–41 cylinder with heat sources, 43–45 cylinders, 29–31 examples See Worked examples—steady-state conduction fins, 48–57 See also Fins general approach to problems, 606–607 heat flow, heat-source systems, 5, 41–42 insulation/R values, 28–29 overall heat-transfer coefficient, 33–39 plane wall, 25–26 plane wall with heat sources, 41–42 problem solving, 606–607 radial systems, 29–33 spheres, 31 thermal contact resistance, 57–60 Steel ball cooling in air, 143 Steel-pipe dimensions, 665 Stefan-Boltzmann constant, 13, 380 Stefan-Boltzmann law, 13, 380 Stefan’s law, 593 Stefany, N E., 349, 375 Stegun, I., 214 Stein, R., 324 Stewart, W E., 593, 603 Straight aluminum fin, 55 Stretton, A J., 378 Subcooled boiling, 496 Sudden cooling of rod, 178–179 Summary, 605–645 Summary tables, list of, 20 Sun, K H., 506, 519 Sunderland, J E., 75, 136 Superinsulations, Surface area, 20 Surface in radiant balance, 410–411 Surface resistance for radiation, 404–405 Surface roughness, 382 Surfaces with large areas, 407–408, 440 Swanee, P K., 325 Symbols, list of, xvii–xx Système International d’Unités, 15, 16 T Tables, 20 air, properties at atmospheric pressure, 658 # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Pg No.722 conversion factors, 666 diffusion coefficients (gases/vapors), 661 emissivity, 663–664 error function, 649 gases, properties at atmospheric pressure, 659–660 low-melting-point metals, physical properties, 661 metals, properties, 650–652 nonmetals, properties, 653–655 saturated liquids, properties, 656–657 SI units, 666 steel-pipe dimensions, 665 water, properties, 662 Tanaka, H., 377 Tanger, G E., 503, 518 Tate, C E., 282, 283, 324 Temperature conversions, 15 Temperature for property evaluation for convection with ideal gases, 632–634 Temperature measurement, 459–460 Temperature, off-center, 674–675 Template, Excel composite interface, 680 for steady-state conduction, 680 Thermal boundary layer, 231–241 Thermal capacity, lumped, 142 Thermal conductivity, 2, 5–9 Thermal conductivity/fin temperature profiles, 53–55 Thermal contact resistance, 57–60 Thermal diffusion, 587 Thermal diffusivity, Thermal-energy storage system, 560–563 Thermal impedance, 98 Thermal radiation, 12, 379 See also Radiation heat transfer Thermal resistance/capacity formulation, 176–192 Thermodynamics, Thermometer error, due to radiation, 459–460 Three-body problem, 406, 407 Three-dimensional heat-conduction equation, K/PMS 293 Short / Normal / Long DESIGN SERVICES OF S4CARLISLE Publishing Services www.elsolucionario.net 722 11/14/2008 11:54 www.elsolucionario.net 723 Index Three-dimensional numerical formulation, 115–118 Three-dimensional systems, 162–168 See also Steady-state conduction—multiple dimensions Threlkeld, J L., 486 Tien, C L., 347, 378, 519 Time constant, 142 TK Solver, 96 T4 law, 382 Tong, L S., 501, 505, 506, 518 Torborg, R H., 486 Torrance, K E., 486 Tortel, J., 310, 324 Townes, H W., 325 Transient conduction with heat generation, 188–190 Transient heat-transfer See Unsteady-state conduction Transient numerical method, 168–175 Triangular fin, 49, 50 Tribus, M., 256, 274, 287, 519 Turbulent-boundary-layer thickness, 250–253 Turbulent-bound-layer heat transfer, 243–250 Turbulent flow in tube, 257–259 Turbulent heat transfer from isothermal flatplate, 249–250 Turbulent heat transfer in short tube, 292 Turbulent heat transfer in tube, 287–288 Turbulent shear stress and mixing length, 243–244 Turton, R., 214 Two-dimensional systems, 162–168 See also Steady-state conduction—multiple dimensions U Units, 13–16 Universal velocity profile, 246, 247 Unny, T E., 378 Unsteady-state conduction, 139–214 # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e backward-difference technique, 172–175 Biot number, 151, 153 convection boundary conditions, 147–162 examples See Worked examples—unsteady-state conduction explicit formulation, 172 forward-difference technique, 172–175 Fourier number, 151, 153 general approach to problems, 192–193, 606–607 Heisler charts, 148, 151, 153 implicit formulation, 174–175 introduction, 139–141 lumped-heat-capacity system, 141–143 multidimensional systems, 162–168 problem solving, 606–607 semi-infinite solid, 143–147 separation-of-variables method, 139–141 steady-state as limiting case of transient solution, 178 thermal resistance/capacity formulation, 176–192 transient numerical method, 168–175 V Vachon, R I., 503, 518 Van der Held, E F M., 377 Variable-conductance heat pipe, 510 Variable conductivity, numerical solution, 190–192 Variable mesh size, 113–115 Vautrey, L., 310, 324 Velocity, 10 flow-velocity estimates, 610, 619–620 Vernon, H C., 519 Vertical flat plate, 327–332 Vertical planes/cylinders, 334–340 Viscosity, 10–11 View factor, 389 Viscous flow, 215–218 Pg No.723 K/PMS 293 Short / Normal / Long Viscous-shear stress, 218 Vliet, G C., 300, 324, 344, 376, 377 Volume of resistance elements, 100 von Kármán, T., 224, 274 W Wallis, G B., 501, 505, 518 Warner, C Y., 335, 376 Warrington, R O., 350, 378 Water, properties, 662 Water evaporation rate, 599–600 Water flow in diffuser, 220–221 Webb, R L., 547, 585, 596, 603 Weber, N., 377 Weil, L., 519 Westwater, J W., 498, 499, 500, 518, 519 Wet-bulb temperature, 596–597 Whitaker, S., 249, 275, 299, 300, 325 White, F M., 274 Whiting, G H., 519 Wiebelt, J A., 486 Wien’s displacement law, 383 Wilson, E L., 214 Winterton, R H S., 325 Wire-mesh chart, 682, 685, 690, 691, 693 Witt, C L., 376 Witte, L C., 310, 325 Worked examples See also worked examples for specific subject matters conduction through copper plate, 16–17 convection calculation, 17 heat source and convection, 17–18 multimode heat transfer, 17 radiation heat transfer, 18 total heat loss by convection/radiation, 18–19 Worked examples—convection heat transfer airflow across isothermal cylinder, 300–301 combined free and forced convection, 360–361 constant heat flux from vertical plate, 338–339 cube cooling in air, 343–344 www.elsolucionario.net hol29362_Index DESIGN SERVICES OF S4CARLISLE Publishing Services hol29362_Index 11/14/2008 11:54 www.elsolucionario.net Index Worked examples—convection heat transfer—Cont drag force on flat plate, 242 flat plate with constant heat flux, 238–239 heated horizontal pipe in air, 341–342 heating of air in laminar tube flow, 289–290 heating of air with in-line tube bank, 306–307 heating of air with isothermal tube wall, 290–291 heating of liquid bismuth in tube, 311 heating of water in laminar tube flow, 288–289 heat transfer across evacuated space, 357–358 heat transfer across horizontal air gap, 352 heat transfer across vertical air gap, 351–352 heat transfer across water layer, 353 heat transfer from electrically heated wire, 301–302 heat transfer from fine wire in air, 341 heat transfer from horizontal tube in water, 340–341 heat transfer from isothermal vertical plate, 339–340 heat transfer from sphere, 302–303 heat transfer in rough tube, 291 high-speed heat transfer for flat plate, 261–264 isentropic expansion of air, 221 isothermal flat plate heated over entire length, 237–238 mass flow/boundary-layer thickness, 227–228 oil flow over heated flat plate, 240 plate with unheated starting length, 239–240 reduction of convection in air gap, 353–354 simplified relations, 346 turbulent-boundary-layer thickness, 251–253 turbulent heat transfer from isothermal flat plate, 249–250 turbulent heat transfer in short tube, 292 turbulent heat transfer in tube, 287–288 water flow in diffuser, 220–221 Worked examples—Excel cooling of finned aluminum solid, 699–702 nine-node problem, 93–95, 689–691, 694–697 plate with boundary heat source and convection, 693–694 solid with composite materials, 707–711 symmetric formulations, 704–707 temperature distribution in two-dimensional plate, 686–688 temperature distribution in two-dimensional straight fin, 688–689 transient analysis of nine-node problem carried to steady state, 93–95, 694–697 transient heating of electronic box in enclosure, 702–704 Worked examples—heat exchangers ammonia condenser, 553 calculation of size from known temperature, 536–537 cold draft in a warm room, 639–640 coolant for a radiant heater, 644 cooling of a finned block, 630–631 cooling of an aluminum cube, 628–629 cross-flow exchanger, 539 cross-flow exchanger as energy conservation device, 553–555 cross-flow exchanger with both fluids unmixed, 548–550 double-pipe heat exchanger, 635–638 evacuated insulation design, 640–642 fouling factor, 527–528 heat-transfer coefficient in compact exchanger, 558 # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Pg No.724 insulating window, design analysis, 634–635 off-design calculation using effectiveness-NTU method, 547 overall heat-transfer coefficient for pipe exposed to steam, 525–527 overall heat-transfer coefficient for pipe in air, 523–525 radiant electric stove for boiling water, 644–645 radiant heater, 642–643 refrigerator storage in desert climate, 638–639 shell-and-tube exchanger, 537–539 shell-and-tube exchanger as air heater, 552 single-/two-exchanger options, compared, 550–552 temperature for property evaluation for convection with ideal gases, 632–634 transient response of thermal-energy storage system, 560–563 variable-properties analysis of duct heater, 563–565 Worked examples—mass transfer diffusion coefficient for CO2 , 589–590 diffusion of water in tube, 593 relative humidity of air stream, 597 water evaporation rate, 599–600 web-bulb temperature, 596–597 Worked examples—radiation heat transfer cavity with transparent cover, 434–435 effective emissivity of finned surface, 415–416 flat-plate solar collector, 455–456 heater with constant heat flux/surrounding shields, 446–449 heat transfer between black surfaces, 397 heat transfer reduction with parallel-plate shield, 418 K/PMS 293 Short / Normal / Long DESIGN SERVICES OF S4CARLISLE Publishing Services www.elsolucionario.net 724 11/14/2008 11:54 www.elsolucionario.net 725 Index hot plates enclosed in room, 408–409 influence of convection on solar equilibrium temperatures, 454 network for gas radiation between parallel plates, 425–426 numerical solution for combined convection-radiation, 449–451 numerical solution for enclosure, 441 numerical solutions for parallel plates, 441–443 open cylindrical shield in large room, 418–420 open hemisphere in large room, 413 radiation from hole with variable radiosity, 443–446 shape-factor algebra for cylindrical reflectors, 403–404 shape-factor algebra for open ends of cylinders, 401–402 shape-factor algebra for truncated cone, 402–403 solar-environment equilibrium temperatures, 453–454 surface in radiant balance, 410–411 temperature measurement error caused by radiation, 460 transmission/absorption in glass plate, 388 transmitting/reflecting system for furnace opening, 435–437 Worked examples—steady-state conduction buried disk, 87–88 buried parallel disks, 88 buried pipe, 87 # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e circumferential aluminum fin, 55–56 composite material with nonuniform nodal elements, 108–110 contact conductance/heat transfer, 59, 60 critical insulation thickness, 40–41 cubical furnace, 87 Gauss-Seidel calculation, 103 heat generation with nonuniform nodal elements, 106–108 heat source with convection, 44–45 heat transfer through composite wall, 36–37 multilayer conduction, 31–32 multilayer cylindrical system, 31, 32–33 nine-node problem, 93–95, 689–691, 694–697 numerical formulation/heat generation, 104–106 overall heat-transfer coefficient for tube, 39 radiation boundary condition, 111–113 rod with heat sources, 56–57 straight aluminum fin, 55 thermal conductivity/fin temperature profiles, 53–55 three-dimensional numerical formulation, 115–118 variable mesh size, 113–115 Worked examples—unsteady state conduction aluminum plate suddenly exposed to convection, 160–161 cooling of ceramic, 181–182 cooling of steel rod, 182–186 Pg No.725 K/PMS 293 Short / Normal / Long finite-length cylinder suddenly exposed to convection, 166–167 heat loss for finite-length cylinder, 167–168 heat removal from semi-infinite solid, 147 implicit formulation, 179–181 long cylinder suddenly exposed to convection, 161–162 numerical solution for variable conductivity, 190–192 pulsed energy at surface of semi-infinite solid, 146–147 radiation heating and cooling, 186–188 semi-infinite cylinder suddenly exposed to convection, 165–166 semi-infinite solid with sudden change in surface conditions, 146 steel ball cooling in air, 143 sudden cooling of rod, 178–179 sudden exposure of semi-infinite slab to convections, 159–160 transient conduction with heat generation, 188–190 Wright, L T., Jr., 485 Y Yamada, Y., 377 Ybarrondo, L J., 75 Yuge, T., 346, 375 www.elsolucionario.net hol29362_Index Z Zehnder-Mach interferometer, 332 Zienkiewicz, O C., 214 Zuber, N., 518, 519 Zukauskas, A A., 305, 325 DESIGN SERVICES OF S4CARLISLE Publishing Services 11/14/2008 11:54 www.elsolucionario.net www.elsolucionario.net hol29362_Index # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Pg No.726 K/PMS 293 Short / Normal / Long DESIGN SERVICES OF S4CARLISLE Publishing Services 11/14/2008 11:54 www.elsolucionario.net www.elsolucionario.net hol29362_Index # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Pg No.727 K/PMS 293 Short / Normal / Long DESIGN SERVICES OF S4CARLISLE Publishing Services 11/14/2008 11:54 www.elsolucionario.net www.elsolucionario.net hol29362_Index # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Pg No.728 K/PMS 293 Short / Normal / Long DESIGN SERVICES OF S4CARLISLE Publishing Services 11/14/2008 11:54 www.elsolucionario.net www.elsolucionario.net hol29362_Index # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Pg No.729 K/PMS 293 Short / Normal / Long DESIGN SERVICES OF S4CARLISLE Publishing Services 11/14/2008 11:54 www.elsolucionario.net www.elsolucionario.net hol29362_Index # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Pg No.730 K/PMS 293 Short / Normal / Long DESIGN SERVICES OF S4CARLISLE Publishing Services 10/30/2008 16:50 www.elsolucionario.net www.elsolucionario.net hol29362_ibc # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Pg No.1 K/PMS 293 Short / Normal / Long DESIGN SERVICES OF S4CARLISLE Publishing Services # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Forced or free Convection? Pg No.2 K/PMS 293 Short / Normal / Long S4CARLISLE Publishing Services DESIGN SERVICES OF Modify temperature property determination as needed Select correlation for convection heat-transfer coefficient Use Table 5-2 for flat plates, Table 6-8 for other forced convection, Table 7-5 for free convection www.elsolucionario.net Summary of Convection Calculation Procedure Determine Gr Pr for free convection to determine flow regime Be careful to select correct characteristic dimension for both free and forced convection Evaluate Reynolds number for forced convection to determine flow regime Specify geometry, exterior or interior flow, etc q = hAsurface(Tsurface ¯ Tbulk) for internal flow q = hAsurface(Tsurface ¯ Tfree stream) for exterior flows Calculate heat transfer with Calculate heat-transfer coefficient 10/30/2008 Determine temperature for fluid property determinations: usually film temperature for exterior flows and average bulk temperature for interior flows Specify Fluid Be careful to employ the correct value for Asurface, which is the surface area in contact with the fluid for which h is calculated For forced convection inside a tube, Asurface is π diL (not the flow cross-sectional area π di2/4), while for cross flow or free convection on the outside of a tube Asurface = π doL The surface area for complicated fin arrangements like those illustrated in Figure 2-14 would be the total fin(s) surface area in contact with the surrounding fluid (presumably air) hol29362_ibc 16:50 www.elsolucionario.net # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Forced or free Convection? Pg No.2 K/PMS 293 Short / Normal / Long S4CARLISLE Publishing Services DESIGN SERVICES OF Modify temperature property determination as needed Select correlation for convection heat-transfer coefficient Use Table 5-2 for flat plates, Table 6-8 for other forced convection, Table 7-5 for free convection www.elsolucionario.net Summary of Convection Calculation Procedure Determine Gr Pr for free convection to determine flow regime Be careful to select correct characteristic dimension for both free and forced convection Evaluate Reynolds number for forced convection to determine flow regime Specify geometry, exterior or interior flow, etc q = hAsurface(Tsurface ¯ Tbulk) for internal flow q = hAsurface(Tsurface ¯ Tfree stream) for exterior flows Calculate heat transfer with Calculate heat-transfer coefficient 10/30/2008 Determine temperature for fluid property determinations: usually film temperature for exterior flows and average bulk temperature for interior flows Specify Fluid Be careful to employ the correct value for Asurface, which is the surface area in contact with the fluid for which h is calculated For forced convection inside a tube, Asurface is π diL (not the flow cross-sectional area π di2/4), while for cross flow or free convection on the outside of a tube Asurface = π doL The surface area for complicated fin arrangements like those illustrated in Figure 2-14 would be the total fin(s) surface area in contact with the surrounding fluid (presumably air) hol29362_ibc 16:50 www.elsolucionario.net ... Mechanical Design Process Çengel Heat Transfer: A Practical Approach Ribando Heat Transfer Tools Çengel Introduction to Thermodynamics and Heat Transfer Rizzoni Principles and Applications for Electrical... Function 649 Property Values for Metals 650 Properties of Nonmetals 654 Properties of Saturated Liquids 656 Properties of Air at Atmospheric Pressure 658 A-6 Properties of Gases at Atmospheric Pressure... Donnelley, Jefferson City, MO Library of Congress Cataloging-in-Publication Data Holman, J P (Jack Philip) Heat transfer / Jack P Holman. —10th ed p cm.—(Mcgraw-Hill series in mechanical engineering) Includes