A heat transfer textbook john lienhard IV, john lienhard v 4th edition

A Heat Transfer Textbook A Heat Transfer Textbook Fourth Edition by John H Lienhard IV and John H Lienhard V Phlogiston Press Cambridge Massachusetts Professor John H Lienhard IV Department of Mechanical Engineering University of Houston 4800 Calhoun Road Houston TX 77204-4792 U.S.A Professor John H Lienhard V Department of Mechanical Engineering Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge MA 02139-4307 U.S.A Copyright ©2012 by John H Lienhard IV and John H Lienhard V All rights reserved Please note that this material is copyrighted under U.S Copyright Law The authors grant you the right to download and print it for your personal use or for non-profit instructional use Any other use, including copying, distributing or modifying the work for commercial purposes, is subject to the restrictions of U.S Copyright Law International copyright is subject to the Berne International Copyright Convention The authors have used their best efforts to ensure the accuracy of the methods, equations, and data described in this book, but they not guarantee them for any particular purpose The authors and publisher offer no warranties or representations, nor they accept any liabilities with respect to the use of this information Please report any errata to the authors Lienhard, John H., 1930– A heat transfer textbook / John H Lienhard IV and John H Lienhard V — 4th ed — Cambridge, MA : Phlogiston Press, c2012 Includes bibliographic references and index Heat—Transmission Mass Transfer I Lienhard, John H., V, 1961– II Title TJ260.L445 2012 Published by Phlogiston Press Cambridge, Massachusetts, U.S.A This book was typeset in Lucida Bright and Lucida New Math fonts (designed by Bigelow & Holmes) using LATEX under the TEXShop System For updates and information, visit: http://ahtt.mit.edu This copy is: Version 2.02 dated June 18, 2012 Preface From the first edition of A Heat Transfer Textbook in 1981, this book was meant to serve students as they set out to understand heat transfer in its many aspects Whether the reader studies independently or in a classroom is beside the point, since learning (in either case) means formulating and surmounting one’s own questions Where the book succeeds, it will be because students encounter a series of “Oh, now I see!” moments The original edition went through several printings and was followed in 1987 by more printings of a second edition—this time with a new chapter on Mass Transfer by John H Lienhard V who had played only a minor role in John H Lienhard IV’s first edition After that, we each became involved in other pursuits and were unable to prepare the needed third edition So the book went out of print In the late 1990s, we developed a third edition which we decided to distribute free of charge on the Internet We obtained funding from the Dell Star Program, did major updating, and posted it in 2000 as a part of MIT’s then new OpenCourseWare initiative In that form, the book underwent many subsequent revisions and changes as we moved to keep up-to-date with rapidly-changing technology Indeed, the early versions of the third edition are substantially different from the last versions By 2010, these Internet versions had a quarter million downloads by people on all seven continents and in essentially every country in the world We also published a small number of paperback versions of the third edition through Phlogiston Press This fourth edition is likewise being made available by Dover Publications in an affordable hard copy In this edition, we’ve made many additional interstitial changes to the last version of the third edition (specifically, Version 31), including corrections, updates, and various text edits We are calling it a fourth edition to reflect ten years of accumulated revision of the third edition v vi With this edition we continue offering engineering juniors, seniors, and first-year graduate students their grounding in heat transfer – in conduction, convection, radiation, phase-change, and an introduction to the kindred subject of mass transfer We have designed the book in such a way as to accommodate differing levels according to the instructor’s use of it (or the student’s independent selections) Accordingly, each element of the subject begins simply and may be carried through to the more sophisticated material as the instructor (or the reader) chooses We have strived to combine clarity with unusual care to get things right and complete We take care to deal with the implications, limitations, and meaning of the many aspects of the subject We have also worked to connect the subject to the real world that it serves, and to develop insight into the many phenomena connected with the subject In the interest of grounding students in real-world issues, we begin the book with a three-chapter introduction that takes them through the essential modes of heat transfer and gives them an understanding of the function and design of heat exchangers With that background, students find the later and more complex aspects of the subject much more meaningful Thus, the first three chapters provide background that is needed throughout the chapters that follow But only the earlier parts of subsequent chapters accumulate in this way For example, we freely use the dimensional analysis that appears early in Chapter However, while the material on fin design at the end of that chapter is an important application, much used in many industries, it is not material that one has to know to continue through subsequent chapters These goals are much the same as we’ve pursued over the past 30 years However, we’ve taken the occasion of this new edition as an opportunity to refocus and renew our purposes We owe thanks to many people These include our colleagues and students at MIT, the University of Houston, and elsewhere who have provided suggestions, advice, and corrections; and most especially the many thousands of people worldwide who have emailed us with thanks and encouragement to continue this project JHL IV, University of Houston JHL V, Massachusetts Institute of Technology December 2010 Contents I The General Problem of Heat Exchange Introduction 1.1 Heat transfer 1.2 Relation of heat transfer to thermodynamics 1.3 Modes of heat transfer 1.4 A look ahead 1.5 Problems Problems References Heat conduction concepts, thermal resistance, and the overall heat transfer coefficient 2.1 The heat diffusion equation 2.2 Solutions of the heat diffusion equation 2.3 Thermal resistance and the electrical analogy 2.4 Overall heat transfer coefficient, U 2.5 Summary Problems References Heat exchanger design 3.1 Function and configuration of heat exchangers 3.2 Evaluation of the mean temperature difference in a heat exchanger 3.3 Heat exchanger effectiveness 3.4 Heat exchanger design Problems References 3 10 35 35 37 46 49 49 56 63 78 85 86 96 99 99 103 120 126 129 137 vii viii Contents II Analysis of Heat Conduction Analysis of heat conduction and some steady one-dimensional problems 4.1 The well-posed problem 4.2 The general solution 4.3 Dimensional analysis 4.4 An illustration of dimensional analysis in a complex steady conduction problem 4.5 Fin design Problems References III Transient and multidimensional heat conduction 5.1 Introduction 5.2 Lumped-capacity solutions 5.3 Transient conduction in a one-dimensional slab 5.4 Temperature-response charts 5.5 One-term solutions 5.6 Transient heat conduction to a semi-infinite region 5.7 Steady multidimensional heat conduction 5.8 Transient multidimensional heat conduction Problems References Convective Heat Transfer 139 141 141 143 150 159 163 184 191 193 193 194 203 207 216 220 235 248 252 265 269 Laminar and turbulent boundary layers 271 6.1 Some introductory ideas 271 6.2 Laminar incompressible boundary layer on a flat surface 278 6.3 The energy equation 293 6.4 The Prandtl number and the boundary layer thicknesses 298 6.5 Heat transfer coefficient for laminar, incompressible flow over a flat surface 302 6.6 The Reynolds analogy 312 6.7 Turbulent boundary layers 315 6.8 Heat transfer in turbulent boundary layers 323 Problems 332 References 340 Contents Forced convection in a variety of configurations 343 7.1 Introduction 343 7.2 Heat transfer to and from laminar flows in pipes 344 7.3 Turbulent pipe flow 356 7.4 Heat transfer surface viewed as a heat exchanger 369 7.5 Heat transfer coefficients for noncircular ducts 371 7.6 Heat transfer during cross flow over cylinders 376 7.7 Other configurations 386 Problems 388 References 396 Natural convection in single-phase fluids and during film condensation 399 8.1 Scope 399 8.2 The nature of the problems of film condensation and of natural convection 400 Laminar natural convection on a vertical isothermal surface 403 8.4 Natural convection in other situations 416 8.5 Film condensation 429 Problems 444 References 453 8.3 ix Heat transfer in boiling and other phase-change configurations 459 9.1 Nukiyama’s experiment and the pool boiling curve 459 9.2 Nucleate boiling 466 9.3 Peak pool boiling heat flux 474 9.4 Film boiling 488 9.5 Minimum heat flux 490 9.6 Transition boiling and system influences 491 9.7 Forced convection boiling in tubes 498 9.8 Forced convective condensation heat transfer 507 9.9 Dropwise condensation 508 9.10 The heat pipe 511 Problems 515 References 519 x Contents IV Thermal Radiation Heat Transfer 10 Radiative heat transfer 10.1 The problem of radiative exchange 10.2 Kirchhoff’s law 10.3 Radiant heat exchange between two finite black bodies 10.4 Heat transfer among gray bodies 10.5 Gaseous radiation 10.6 Solar energy Problems References V Mass Transfer 525 527 527 535 538 551 565 576 586 594 597 11 An introduction to mass transfer 599 11.1 Introduction 599 11.2 Mixture compositions and species fluxes 602 11.3 Diffusion fluxes and Fick’s law 610 11.4 Transport properties of mixtures 615 11.5 The equation of species conservation 629 11.6 Mass transfer at low rates 637 11.7 Steady mass transfer with counterdiffusion 651 11.8 Mass transfer coefficients at high rates of mass transfer 657 11.9 Simultaneous heat and mass transfer 665 Problems 675 References 689 VI Appendices 693 A Some thermophysical properties of selected materials 695 References 698 B Units and conversion factors 725 References 729 C Nomenclature 731 Citation Index 739 Subject Index 745 742 Citation Index Mehendale, Jacobi, and Shah (2000), 353, 396 Meyer, McClintock, Silvestri, and Spencer (1993), 696–698 Millat, Dymond, and Nieto de Castro (1996), 621, 627, 689 Mills (1998), 669, 691 Mills (1999), 206, 265 Mills (2001), 47, 671, 675, 691 Modest (1993), 538, 555, 565, 594 Mohr and Taylor (2005), 698, 701 Morse and Feshbach (1953), 245, 266 Müller-Steinhagen (1999), 84, 97 N Nakai and Okazaki (1975), 381, 398 Norris, Buckland, Fitzroy, Roecker, and Kaminski (1977), 696, 699 Nukiyama (1934), 459, 519 Nusselt (1915), 405, 453 Nusselt (1916), 432, 456 O Okado and Watanabe (1988), 468, 519 Oppenheim (1956), 551, 595 R Raithby and Hollands (1998), 421, 423, 424, 427, 428, 454 Ramilison and Lienhard (1987), 493, 521 Ramilison, Sadasivan, and Lienhard (1992), 494, 522 Ravigururajan and Bergles (1996), 365, 397 Rayleigh (1915), 151, 192 Reed (1987), 368, 397 Reid, Prausnitz, and Poling (1987), 614, 621, 622, 625–627, 689 Restrepo and Glicksman (1974), 424, 455 Reynolds (1874), 313, 340 Reynolds (1974), 600, 689 Rich (1953), 422, 455 Rohsenow and Hartnett (1973), 65, 96 Rohsenow, Hartnett, and Cho (1998), 47, 386, 398 Rohsenow (1952), 471–473, 520 Rohsenow (1956), 433, 456 Rose, Uehara, Koyama, and Fujii (1999), 443, 444, 457 Rose, Utaka, and Tanasawa (1999), 510, 524 Rüdenberg (1925), 246, 247, 266 P S Pera and Gebhart (1973), 422, 455 Perkins, Friend, Roder, and Nieto de Castro (1991), 697, 701 Perry, Green, and Maloney (1997), 129, 137 Petukhov (1970), 325, 340, 362, 363, 396 Pioro (1999), 471, 520 Pitschmann and Grigull (1970), 489, 521 Plesset and Zwick (1954), 231, 266 Poirier and Geiger (1994), 47, 614, 642, 689 Pope (2000), 332, 341 Prausnitz, Lichtenthaler, and de Azevedo (1986), 633, 690 Sadasivan and Lienhard (1987), 435, 456, 488, 521 Sanders and Holman (1972), 405, 453 Schetz (1984), 323, 340 Schlichting and Gersten (2000), 46 Schlichting (1968), 281, 288, 305, 327, 340 Schneider (1955), 182, 192 Schneider (1963), 215, 266 Schrock and Grossman (1962), 503, 523 Scriven (1959), 231, 266 Seban and Shimazaki (1951), 368, 397 Sellars, Tribus, and Klein (1956), 354, 396 Sernas (1969), 475, 520 Shah and Bhatti (1987), 353, 354, 396 Citation Index Shah and London (1978), 353, 375, 376, 396 Shah and Sekulic (1998), 83, 96, 129, 137 Shah and Sekulic (2003), 129, 137 Shah (1982), 503, 523 Shamsundar (1982), 117, 137 Sharan and Lienhard (1985), 497, 522 Shekriladze and Gomelauri (1966), 508, 524 Sieder and Tate (1936), 360, 396 Siegel and Howell (2001), 46, 544, 565, 576, 580, 594 Skartveit, Olseth, Czeplak, and Rommel (1996), 578, 579, 595 Span and Wagner (1996), 696–699 Sparrow and Cess (1978), 530, 594 Sparrow and Gregg (1959), 434, 435, 440, 456, 457 Sparrow and Gregg (1961), 415, 454 Sparrow and Lin (1963), 444, 457 Steiner and Taborek (1992), 501, 505, 522 Stewart, Jacobsen, and Wagner (1991), 696–699 Stott, Tett, Jones, Allen, Mitchell, and Jenkins (2000), 583, 596 Streeter and Wylie (1979), 150, 155, 191 Sun and Lienhard (1970), 486, 521 Sutherland (1905), 622, 690 Svehla (1962), 617, 689 T Taborek (1979), 128, 137 Taitel and Dukler (1976), 506, 523 Taylor (1970), 363, 397 Taylor (1995), 725, 729 Team, Pachauri, and Reisinger (2007), 583, 596 Tegeler, Span, and Wagner (1999), 697, 701 Tien and Lienhard (1978), 300, 340, 616, 626, 689 Tillner-Roth and Baehr (1994), 696, 697, 699 743 Tillner-Roth, Harms-Watzenberg, and Baehr (1993), 697–699 Touloukian (1970 to 1975), 696–698 Tubular Exchanger Manufacturer’s Association (1959 and 1978), 83, 96, 100, 117, 128, 137 Tufeu, Ivanov, Garrabos, and Neindre (1984), 697–699 U U.S Department of Commerce (1977), 584, 596 V van de Hulst (1981), 566, 595 Vargaftik, Vinogradov, and Yargin (1996), 697, 700 Vargaftik (1975), 697, 698, 700 Vesovic, Wakeham, Olchowy, Sengers, Watson, and Millat (1990), 696–698 Viswanath and Natarajan (1989), 697, 700 Vliet (1969), 422, 455 W Weast (1976), 636, 690 Webb (1987), 365, 397 Westwater and Breen (1962), 489, 521 Whalley (1987), 507, 524 Wheeler (1959), 65, 96 Whitaker (1972), 328, 341 White (1969), 323, 340 White (1974), 325, 340, 349, 396 White (1991), 46, 276, 323, 340 Wilke and Lee (1955), 617, 689 Wilke (1950), 626, 690 Wilkinson (2000), 47, 636, 690 Witte and Lienhard (1982), 493, 521 Witte (1968), 498, 522 Witte (1999), 498, 522 Woodruff and Westwater (1979), 510, 524 Y Yamagata, Hirano, Nishiwaka, and Matsuoka (1955), 470, 520 744 Citation Index Yang, Taniguchi, and Kudo (1995), 565, 576, 595 Yang (1987), 428, 456 Younglove and Hanley (1986), 697, 701 Younglove (1982), 698, 701 Yovanovich (1986), 65, 96 Yovanovich (1998), 247, 267 Yuge (1960), 421, 454 Z Zuber (1959), 230, 266, 480, 481, 490, 520 Ž Žukauskas and Ambrazyavichyus (1961), 327, 341 Žukauskas and Šlanciauskas (1987), 327, 341 Žukauskas (1972), 382, 384, 385, 398 Žukauskas (1987), 382, 398 Subject Index A Absorptance, 28, 535–538 gaseous, 565–576 Adiabatic saturation temperature, 666 Air composition, 605 thermophysical properties, 718 Avogadro’s number, 603, 723 B Batteries, lead-acid, 676 Beer’s law, 569 Bernoulli equation, 283 Bikram yoga, 688 Biot number, 23–24 for fins, 165–167 for lumped capacity behavior, 23–24 Biot, J.B., 24 Black body, 28–29 emissive power, 529 Stefan-Boltzmann law, 30 Black, J., 271 Blanc’s law, 622 Blasius, H., 284 Blowing, 662 Blowing factor, 662 Boiling, 459–506 convective, 500 Forced convection boiling, 495–507 in external flows, 495–498 in tubes, 498–507 peak heat flux, see Peak heat flux pool boiling, 459–495 boiling curve, 461–464 effect of surface condition, 491–494 film boiling, 464, 488–489 gravitational influences, 494 hysteresis, 459–461 inception, 466–470 minimum heat flux, 490–491 nucleate boiling, 466–473 Rohsenow correlation, 471 slugs and columns, 462 subcooling, 494 transition boiling, 464, 491–494 small objects, 484, 489 Boiling crisis, see Peak Heat Flux Boiling number, 502 Boltzmann’s constant, 31, 723 Bond number, 484 Bonilla, C.F, 482 Boundary conditions, 69, 142–143 Boundary layers, 19, 271–332 Blasius solution, 284–288 concentration b.l., 642–647, 657–662 laminar momentum b.l forced convection, 278–293 natural convection, 400–416 thickness, 286, 411 laminar thermal b.l effect of Pr, 301–302, 305 forced convection, 293–312 natural convection, 400–416 thickness, 305 relation to transient conduction, 225 turbulent b.l., 315–332 thickness, 323 turbulent transition forced convection, 274–276 natural convection, 414, 418, 422 Boussinesq, J., 324 Bubble growth, 230–231, 466–473 745 746 Subject Index Buckingham pi-theorem, 151–154 applications of, 154–158 Buckingham, E., 151 Bulk enthalpy, 345 Bulk temperature, 345–348, 369–371 Bulk velocity, 345 Burnout, see Peak Heat Flux Burton, R The Anatomy of Melancholy, 399 C Caloric, Carbon oxidation, 608–610 Carburization, 636 Catalysis, 664, 677, 685 catalytic reactor, 685 Cervantes, M de Don Quixote, 49 Chilton, T.H., 482 Colburn j-factor, 314 Colburn equation, 360 Colburn, A.P., 313, 314, 482 Collision diameters, 617–619 Collision integrals, 617–619, 621, 625 Condensation dropwise condensation, 508–510 film condensation, 429–444 cone, 440 conservation equations for, 431–433 dimensional analysis, 429–430 effective gravity, 437 helical tube, 441 horizontal cylinder, 439 inclined plate, 439 latent heat correction, 436 noncondensible gases, 444, 687 rotating disk, 440 sphere, 440 tube bundles, 443 turbulent transition, 441–443 vertical plate, 431–437 forced convective condensation, 507–508 Conduction, 10–19, 49–73, 141–182, 193–252 dimensional analysis of semi-infinite region, 221–222 steady, 150–163 transient, 194–196 fins, 163–182 heat diffusion equation multidimensional, 49–56 one-dimensional, 17–19 lumped capacity, see Lumped capacity solutions multidimensional, 146–150 steady, 235–248 transient, 248–252 one-dimensional steady, 56–62, 144–146 one-dimensional transient, 203–235 cylinder, 207–208 heat removal during, 212 one-term solutions, 216–220 slab, 203–208 sphere, 207–208 temperature response charts, 207–216 semi-infinite region, 220–235 contact of two, 231–233 convection at surface, 225–228 heat flux to, 228 oscillating surface temperature, 233–235 step-change of qw , 228–229 step-change of Tw , 221–225 shape factors, 240–248 table of, 245, 246 thermal resistance, see Thermal resistance volumetric heating, 54 periodic, 215–216 steady, 58–61, 144–146, 158–163 well-posed problems, 141–143 Conductivity, see Thermal conductivity Configuration factor, see View factor Conrad, J Heart of Darkness, 599 Conservation of energy, see Energy equation or Heat diffusion equation Conservation of mass general equation, 337 Subject Index relation to species conservation, 631 steady incompressible flow, 278–280 Conservation of momentum, 280–284 Conservation of species, see Species conservation Contact resistance, see Thermal resistance Continuity equation, see Conservation of mass Convection, 19–22 topics, see Boiling, Boundary layers, Condensation, Forced convection, Heat transfer coefficient, or Natural convection Convection number, 502 Conversion factors, 725–729 example of development, 14 Cooling towers, 601–602 Correlations, critically evaluating, 386–388 Counterdiffusion velocity, 640, 652 Critical heat flux (CHF), see Peak heat flux Cross flow, 376–385 cylinders flow field, 376–378 heat transfer, 378–382 tube bundles, 382–385 D Dalton’s law of partial pressures, 604 Damkohler number, 685 Darcy-Weisbach friction factor, 127, 359, 362, 365 Departure from nucleate boiling (DNB), see Peak Heat Flux Diffusion coefficient, 64, 610–625 binary gas mixtures, 616–621 dilute liquid solutions, 622–625 hydrodynamic model for liquid solutions, 622–625 kinetic theory model for gases, 611–615 multicomponent gas mixtures, 621–622 747 Diffusional mass flux, 606 Fick’s law for, 610–615 Diffusional mole flux, 607 Fick’s law for, 613 Diffusivity, see Thermal diffusivity Dilute gas, 612, 621 Dimensional analysis, 150–163 Dirichlet conditions, 142 Dittus-Boelter equation, 360 Dry ice, 686 Dufour effect, 615 E Earth, age of, Kelvin’s estimate, 262 Eckert number, 310 Eddy diffusivity for heat, 324 for momentum, 319 Effectiveness, see Heat exchangers or Fins Eigenvalue, 204 Einstein, A., 156, 623 Electromagnetic spectrum, 27 Emittance, 33, 529–532 diffuse and specular, 532–533 gaseous, 565–576 hemispherical, 533 monochromatic, 529 Energy equation, 293–296 analogy to momentum equation, 296–298 for boundary layers, 296 for pipe flow, 347 with mass transfer, 669 Entropy production, for lumped capacity system, 24 Entry length, see Internal flow Equimolar counter-diffusion, 681 Error function, 223 Evaporation, 665–668, 673 F Falling liquid films, 334, 431–432, 441–443 Fick’s law, 63, 600, 610–615 Film absorption, 683 Film boiling, see Boiling 748 Subject Index Film coefficient, see Heat transfer coefficient Film composition, 649, 662, 671 Film condensation, see Condensation Film temperature, 297, 310, 415, 671 Fins, 163–182 arrays, 178 condition for one-dimensionality, 165–166 design considerations, 176–177 effectiveness, 176 efficiency, 176 purpose of, 163 root temperature, 174 thermal resistance of, 177–178 variable cross-section, 180–182 very long fins, 173 with tip heat transfer, 171–172 without tip heat transfer, 168–171 First law of thermodynamics, 7–8 Flux, see Heat flux or Mass flux Flux plot, 236–240 Forced convection, 20 boiling, see Boiling, forced convection boundary layers, see Boundary layers condensation, see Condensation cross flow, see Cross flow cylinders, 379–381 flat plates laminar, uniform qw , 311–312 laminar, uniform Tw , 306–309 turbulent, 326–329 unheated starting length, 308 variable property effects, 310, 328 spheres, 686 tube bundles, 382–386 within tubes, see Internal flow Fourier number, 195 Fourier series conduction solutions, 203–207 one-term approximations, 216–220 Fourier’s law, 10–17, 51–54 Fourier, J.B.J., 12 The Analytical Theory of Heat, 3, 10, 141 Free convection, see Natural convection Free molecule flow, 621 Friction coefficient, see Darcy-Weisbach friction factor or Skin friction coefficient Froude number, 157, 506 Fully developed flow, see Internal flow Functional replacement method, 150 G Gardon gage, 95 Gaseous radiation, 565–576 absorption, scattering, and extinction coefficients, 569 Beer’s law, 569 equation of transfer, 571 flames, 34, 576 mean beam length, 572 Gauss’s theorem, 55, 295, 630, 669 Gnielinski equation, 362 Graetz number, 354 Grashof number, 405 for mass transfer, 648 Grashof, F., 405 Gravity effect on boiling, 494 g-jitter, 418 geff for condensation, 437 standard acceleration of, 723 Gray body, 529–531, 536–538, 551–565 electrical analogy for heat exchange, 551–561 transfer factor, see Transfer factor Greenhouse effect, 581–583 H Hagan, G., 350 Hagan-Poiseuille flow, 350 Subject Index Halocline, 676 Heat, Heat capacity, see Specific heat capacity Heat conduction, see Conduction Heat convection, see Convection Heat diffusion equation multidimensional, 49–56 one-dimensional, 17–19 Heat exchangers, 99–129 balanced counterflow, 112, 126 counterflow, 99, 108, 123 cross-flow, 100, 118, 124 design of, 126–129 effectiveness-NTU method, 120–126 function and configuration, 99–103 logarithmic mean temperature difference, see Logarithmic mean temperature difference mean temperature difference in, 103–113 microchannel, 353 parallel flow, 99, 108, 123 relationship to isothermal pipe flow, 369–370 shell-and-tube, 100, 118, 124 single-stream limit, 125–126, 370 with variable U , 114–116 Heat flux, defined, 10–13 Heat pipes, 511–513 merit number, 512 Heat sink, 178 Heat transfer, modes of, 10–34 Heat transfer coefficient, 19–20 average, 20, 308–309 effect of mass transfer, 665–671 overall, 78–85 Heisler charts, 208 Helmholtz instability, 476–479 Henry’s law, 633 Hohlraum, 28 Hot-wire anemometer, 382, 395 Hydraulic diameter, 370–375 749 Hydrodynamic theory of CHF, see Peak Heat Flux I Ideal gas law for mixtures, 604 Ideal solution, 634 Incompressible flow, 279–280, 294, 631, 680 Indices, method of, 150 Initial condition, 142 Insulation critical radius of, 72–73 superinsulation, 14 Integral conservation equations for energy, 302–306 for momentum, 288–290 Intensity of radiation, 533–535 Interdiffusion coefficient, 642 Interfacial boundary conditions, 632–637 Internal flow bulk energy equation, 347 bulk enthalpy, 345 bulk temperature, 345–348 for uniform qw , 351 for uniform Tw , 369–370 bulk velocity, 345 entry length laminar hydrodynamic, 349 laminar thermal, 353–354 turbulent, 356–358 friction factor laminar flow, 361 turbulent flow, 359–366 fully developed hydrodynamically, 345, 349–350 thermally, 345–348 hydraulic diameter, 370 laminar heat transfer developing flow, 353–356 uniform qw , fully developed, 350–352 uniform Tw , fully developed, 353 750 Subject Index laminar temperature profiles, 347–348 laminar velocity profile developing flow, 345 fully developed, 349–350 noncircular ducts, 371–376 turbulent, 356–369 turbulent heat transfer, 358–369 Gnielinski equation, 362 liquid metals, 366–369 rough walls, 364–366 variable property effects, 363 turbulent transition, 275 Irradiance, 551 J Jakob number, 430 Jakob, M., 230, 430 Jupiter, atmosphere of, 675 K Kalidasa ¯ Abhijña ¯ na Sakuntala, 731 ¯ of ¯ gases ¯ Kinetic theory average molecular speed, 616 Chapman-Enskog theory, 616 diffusion coefficient elementary model, 611–613 exact, 616–619 limitations of, 621 mean free path, 299, 616 thermal conductivity elementary model, 299–300 gas mixtures, 627 monatomic gas, 625 viscosity elementary model, 299–300 gas mixtures, 627 monatomic gas, 625 Kirchhoff’s law, 535–538 Kirchhoff, G.R., 535 Kolmogorov scales of turbulence, 338 L L’Hospital’s rule, 113 Laplace’s equation, 235 Laplacian, 56, 235 Lardner, D The Steam Engine Familiarly Explained and Illustrated, 99 Leibnitz’s rule, 289 Lennard-Jones intermolecular potential, 617–619 Lewis number, 611 Lewis, W.K., 611, 645, 668 Liquid metal heat transfer effect of Pr, 301–302 in tube bundles, 385–386 in tubes, 366–369 laminar boundary layer, 307–309 Logarithmic mean temperature difference (LMTD), 103–120 correction factors, 116–120 defined, 111 limitations on, 114–116 Lucretius de Rerum Natura, 695 Lummer, O.R., 30 Lumped capacity solutions, 22–26, 194–202 dimensional analysis of, 195–196 electrical/mechanical analogies, 196–198 in natural convection, 413 second order, 200–202 with heat generation, 145–146 with variable ambient temperature, 198–199, 264 M Mach number, 309 Mass average velocity, 606 Mass conservation, see Conservation of mass Mass diffusion equation, 640 Mass exchangers, 685 Mass flux, 606 Mass fraction, 602 in the transferred state, 658 Mass transfer, 599–675 analogy to heat transfer, 63, 637–650 evaporation, 665–668, 673 Subject Index forced convective, 642–647, 657–664 natural convective, 648–650 through a stagnant layer, 651–656 mass-based solution, 661 with simultaneous heat transfer, 665–675 Mass transfer coefficients, 642–650, 657–664 at low rates, 642–650 analogy of heat and mass transfer, 644–650 defined, 643 effect of mass transfer rate on, 660–662 variable property effects, 671 Mass transfer driving force, 657–660 at low rates, 663–664 one species transferred, 643, 659 Material derivative, 296 Mean beam length, 572 Mean free path, 299 rigid sphere molecules, 616 Melville, H Moby Dick, 343 Microchannel heat exchanger, 353 Mixed convection, 429 Mixing-cup temperature, see Bulk temperature Mixtures binary, 611 composition of, 602–605 molecular weight of, 603 of ideal gases, 604–605 specific heat of, 629 transport properties, 615–629 gas diffusion coefficients, 616–622 liquid diffusion coefficients, 622–625 thermal conductivity of gas mixtures, 625–629 viscosity of gas mixtures, 625–629 velocities and fluxes in, 606–610 Mobility, 622 Molar concentration, 603 Mole flux, 607 751 Mole fraction, 603 Mole-average velocity, 607 Molecular weight, 603, 618 Momentum equation, 280–284 Momentum integral method, see Integral conservation equations Moody diagram, 361 Mothballs, 684 N Natural convection, 20, 399–428 dimensional analysis, 403–406 governing equations, 401–403 horizontal cylinders, 416–419 in enclosures, 428 in mass transfer, 648–650 inclined and horizontal plates, 422–425 spheres, 420–422 submerged bodies, 421 turbulent, 406, 414, 422 validity of b.l approximations, 416 variable-property effects, 415, 424 vertical cylinders, 419–420 vertical plates, 403–415 analysis compared to data, 414–415 Squire-Eckert analysis, 406–411 wide-range correlation, 414 with forced convection, 428 with uniform heat flux, 425–427 Navier-Stokes equation, 280 Nernst-Einstein equation, 623, 679 Neumann conditions, 142 Newcomen’s engine, 193 Newton’s law of cooling, 20 Newton’s law of viscous shear, 283 Newton, Isaac, 19 Nomenclature, 731–737 NTU, number of transfer units, 122 Nucleate boiling, see Boiling Nukiyama, S., 459–461 Number density, 603 Nusselt number, defined, 277 average, 309, 312 752 Subject Index for developing internal flow, 354–355 for fully developed internal flow, 351 for mass transfer, 645 Nusselt, E.K.W., 122, 277, 405, 432, 437, 443 O Ocean, salt concentration in, 676 Ohm’s law, 63 gray body radiation analogy, 551–561 thermal resistance analogy, see Thermal resistance Overall heat transfer coefficient, 78–85 typical values, 82 P Péclét number, 367 Partial density, 602 Partial pressure, 604 Peak heat flux, 464, 474–487 external flows, 496–498 general expression for, 480 horizontal plate, 480–483 internal flows, 506 various configurations, 483–487 very small objects, 484 Zuber-Kutateladze prediction, 481 Petukhov equation, 362 Physical constants, 723 Pi-theorem, see Buckingham pi-theorem Pipe flow, see Internal flow Planck’s constant, 31 Planck’s law, 31 Planck, M., 30 Pohlhausen, K., 288, 305 Poiseuille’s law, 350 Poiseuille, J., 350 Prandtl number, 298–301 Eucken formula, 679 relation to b.l thickness, 301–302, 305 turbulent Prandtl number, 324 Prandtl, L., 272, 273, 284, 317 Pringsheim, E., 30 Properties of substances, see Thermophysical property data Property reference state, see Film temperature or Film composition Psychrometer, sling, 665 Pumping power, 127 Q Quenching, 487 R Radiation, see Thermal radiation Radiation heat transfer coefficient, 74 Radiation shield, 34, 541, 555 Radiosity, 551 Raoult’s law, 633 Rayleigh number, 405 for mass transfer, 648 for uniform wall heat flux, 426 Rayleigh, Lord (J.W Strutt), 151 Reactions heterogeneous, 608, 629, 675–677, 685 homogeneous, 629, 675 Reflectance, 28 diffuse and specular, 532–533 Relativity, theory of, 156 Resistance, see Thermal resistance Resistance thermometer, 459 Reversibility and heat transfer, Reynolds number, 273 Reynolds, O., 274, 313 Reynolds-Colburn analogy for laminar flow, 312–315 for mass transfer, 668 for turbulent flow, 324–327 Richardson, L.F., 315 Roughness, see Surface roughness effects S S.I System, 14, 725–729 Subject Index Samurai sword, 220–221 Savery’s engine, 193 Scattering, 566 Schmidt number, 611 Schmidt, E., 277, 611 Second law of thermodynamics, 8–10 Self-diffusion, 612, 616 Separation of variables solutions, 146–150 Shakespeare, Wm Macbeth, 459 Venus and Adonis, 527 Sherwood number, 645 Sherwood, T.K., 645 Sieder-Tate equation, 362 Similarity transformations, 224, 284–287 Simultaneous heat and mass transfer, 665–675 energy balances for, 672–675 Skin drag, see Skin friction coefficient Skin friction coefficient, 289 for laminar flow, 292 for turbulent flow, 323, 327 for turbulent pipe flow, 359–366 versus profile drag, 313 Smith, W A Dictionary of Greek and Roman Antiquities, 725 Solar energy, 576–585 solar collectors, 584–585 wavelength distribution, 531 Solubility, 632 Soret effect, 615, 677 Species conservation, 629–650 boundary conditions for, 632–637 equation of, 629–632 for stationary media, 637–642 for steady state, 637–640 for unsteady diffusion, 640–642 Species-average velocity, 606 Specific heat capacity, 18, 294 for mixtures, 629 Specific heat ratio, 626 Speed of light in vacuum, 31, 723 Stagnant film model, 661, 683 Stanton number, 313 Stefan tube, 651 753 Stefan, J., 651 Stefan-Boltzmann constant, 30, 723 Stefan-Boltzmann law, 30 Stefan-Maxwell equation, 678 Stegosaurus, 163 Steradian, defined, 533 Stokes’ law, 623 Stokes, G.G., 623 Stokes-Einstein equation, 623 Stream function, 278–280 Streamlines, 278 String rule, 588 Strouhal number, 376 Subliming, 635, 645, 668, 684, 686, 687 Suction, 662 Surface roughness effects on friction factor, 360, 364–366 on nucleation, 469–470 on pool boiling, 491–494 on turbulent forced convection, 364–366 on turbulent transition, 329 Surface tension, 467–469 Sutherland, W., 623 Sweat cooling, 673 T Taylor instability, 474–476 Taylor, G.I., 474 Temperature gradient, defined, 50 Temperature response charts, 207–216 Thermal conductivity, 10–16, 51–54 equations for gases, 625–629 Eucken correction, 626 simple kinetic theory model, 299–300 temperature dependence, 51–54 Thermal diffusion, 615 Thermal diffusivity, 19 Thermal expansion, coefficient of, 403 for an ideal gas, 404 Thermal radiation, 27–34, 527–586 black body, 28–31 black body exchange, 538–550 diffuse and specular, 532–533 enclosures 754 Subject Index gray, algebraic solutions, 561–565 nonisothermal, nongray, or nondiffuse, 565 gaseous, see Gaseous radiation gray body, 529 gray body exchange, 536–538 electrical analogy, 551–561 with a specified wall flux, 558 with an adiabatic surface, 558 infrared radiation, 27–28 intensity, 533–535 Kirchhoff’s law, 535–538 monochromatic emissive power, 30 Monte Carlo method, 565, 576 Planck’s law, 31 radiant exchange described, 31–34 radiation heat transfer coefficient, 74 radiation shield, 34, 541, 555 small object in large environment, 33, 554 solar, 576–586 Stefan-Boltzmann law, 30 transfer factor, see Transfer factor view factor, see View factor wavelength distribution, 27–31, 529–532 Wien’s law, 30 Thermal resistance, 62–66 contact resistance, 64–66 defined, 62 for a cylinder, 69 for a fin, 177–178 for a slab, 62 for convection, 72 for thermal radiation, 73–77 fouling resistance, 83–85 in parallel, 75–77, 80–81 in series, 72, 78, 79 Ohm’s law analogy, 62–63 Thermophysical property data, 695 accuracy of, 695–698 critical point temperature, 467–469, 714–715 density, 702–722 diffusion coefficient, 614 air-water, 615 dynamic viscosity, 718–722 emittance gases, 566–576 surfaces, 530 gases at atm pressure, 718–722 kinematic viscosity, 708–722 latent heat of vaporization, 714–715 liquid metals, 708–713 metallic solids, 702–704 mixtures, see Mixtures molecular weights, 618 nonmetallic solids, 704–707 Prandtl number, 708–722 saturated liquids, 708–713 saturated vapors, 715–717 specific heat capacity, 702–722 surface tension, 467–469 thermal conductivity, 15, 52, 53, 702–722 thermal diffusivity, 702–722 thermal expansion coefficient, 708–717 triple point temperature, 714–715 vapor pressure, 715–717 CCl4 (l), 682 CO2 (s), 686 ethanol, 687 H2 O(s), 636 napthalene, 646, 684 paradichlorobenzene, 684 Time constant, 22, 196, 200 Transfer factor, 33, 529 parallel plates, 553 two diffuse gray bodies, 554 two specular gray bodies, 555 Transmittance, 29 Transpiration cooling, 672–673 Transport laws, Tube bundles, 382–385 Tube flow, see Internal flow Turbulence, 315–332 eddy diffusivities, 319–324 friction velocity, 321 internal flow, 356–369 lengthscales of, 317–318, 338 log law, 322 Subject Index mixing length, 317–322 Reynolds-Colburn analogy, 324–327 transition to, 274–276 viscous sublayer, 322 Two-phase flow heat transfer boiling, 498–507 condensing, 507–508 regimes for horizontal tubes, 505–506 without gravity force, 500–501 U Units, 725–729 Universal gas constant, 604, 723 V Verne, J Around the World in 80 Days, View factor, 32, 538–550 between small and large objects, 548 examples of view factor algebra, 539–550 general integral for, 542–544 reciprocity relation, 541 some three-dimensional configurations, 546, 547 some two-dimensional configurations, 545 summation rule, 539 View factors string rule, 588 Viscosity correction for temperature dependence of, 328, 363 dynamic, 272 gas mixtures, 627 kinematic, 273 monatomic gas, 625 Newton’s law of viscous shear, 283 simple kinetic theory model, 299–300 Sutherland formula for gases, 337 von Kármán constant, 321 755 von Kármán, T., 288 Vortex shedding, 376–378 W Watt, James, 193 Weber number, 496 Wet-bulb temperature, 665–668 Wetting agent, 508 Wien’s law, 30 Y Yamagata equation, 470 Yoga, see Bikram yoga ... A Heat Transfer Textbook Fourth Edition by John H Lienhard IV and John H Lienhard V Phlogiston Press Cambridge Massachusetts Professor John H Lienhard IV Department of Mechanical Engineering... report any errata to the authors Lienhard, John H., 1930– A heat transfer textbook / John H Lienhard IV and John H Lienhard V — 4th ed — Cambridge, MA : Phlogiston Press, c2012 Includes bibliographic... surface is insulated Assume one-dimensional heat transfer and calculate the rate of heat transfer in watts from top to bottom To this, note that the heat transfer, Q, must be the same at every