Subject Index A Absorptance, 28, 533–536 gaseous, 563–574 Adiabatic saturation temperature, 664 Air composition, 603 thermophysical properties, 714 Avogadro’s number, 601, 719 B Batteries, lead-acid, 674 Beer’s law, 567 Bernoulli equation, 282 Biot number, 23–24 for fins, 165–168 lumped capacity behavior, 23–24 Biot, J.B., 24 Black body, 28–29 emissive power, 527 Stefan-Boltzmann law, 30 Black, J., 269 Blanc’s law, 620 Blasius, H., 282 Blowing, 659 Blowing factor, 659 Boiling, 457–504 convective, 498 Forced convection boiling, 493–505 in external flows, 493–496 in tubes, 496–505 peak heat flux, see Peak heat flux pool boiling, 457–493 boiling curve, 459–462 effect of surface condition, 489–492 film boiling, 462, 486–487 gravitational influences, 492 hysteresis, 457–459 inception, 464–468 minimum heat flux, 488–489 nucleate boiling, 464–471 Rohsenow correlation, 468 slugs and columns, 460 subcooling, 492 transition boiling, 462, 489–492 small objects, 482, 487 Boiling crisis, see Peak Heat Flux Boiling number, 500 Boltzmann’s constant, 31, 719 Bond number, 482 Bonilla, C.F, 480 Boundary conditions, 70, 142–143 Boundary layers, 19, 269–330 Blasius solution, 282–286 concentration b.l., 640–645, 654–660 laminar momentum b.l. forced convection, 276–291 natural convection, 398–416 thickness, 283, 409 laminar thermal b.l. effect of Pr, 299–300, 304 forced convection, 292–311 natural convection, 398–416 thickness, 304 relation to transient conduction, 225 turbulent b.l., 313–330 thickness, 321 turbulent transition forced convection, 272–274 natural convection, 413, 416, 421 739 740 Subject Index Boussinesq, J., 322 Bubble growth, 229–231, 464–471 Buckingham pi-theorem, 151–154 applications of, 154–158 Buckingham, E., 151 Bulk enthalpy, 343 Bulk temperature, 343–346, 367–369 Bulk velocity, 343 Burnout, see Peak Heat Flux Burton, R. The Anatomy of Melancholy, 397 C Caloric, 3 Carbon oxidation, 606–608 Carburization, 634 Catalysis, 662, 675, 683 catalytic reactor, 683 Cervantes, M. de Don Quixote,49 Chilton, T.H., 480 Colburn j-factor, 312 Colburn equation, 360 Colburn, A.P., 311, 312, 480 Collision diameters, 616–617 Collision integrals, 616–617, 619, 624 Condensation dropwise condensation, 506–509 film condensation, 428–443 cone, 439 conservation equations for, 429–431 dimensional analysis, 428–429 effective gravity, 436 helical tube, 440 horizontal cylinder, 438 inclined plate, 438 latent heat correction, 434 noncondensible gases, 443, 685 rotating disk, 439 sphere, 439 tube bundles, 442 turbulent transition, 440–442 vertical plate, 429–436 forced convective condensation, 505–506 Conduction, 10–19, 49–74, 141–181, 193–251 dimensional analysis of semi-infinite region, 221–222 steady, 150–163 transient, 194–196 fins, 163–181 heat diffusion equation multidimensional, 49–56 one-dimensional, 17–19 lumped capacity, see Lumped capacity solutions multidimensional, 146–150 steady, 235–247 transient, 247–251 one-dimensional steady, 58–62, 144–145 one-dimensional transient, 203–235 cylinder, 207–208 heat removal during, 208–212 one-term solutions, 218 slab, 203–208 sphere, 207–208 temperature response charts, 208–218 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 q w , 228–229 step-change of T w , 221–225 shape factors, 241–247 table of, 245, 246 thermal resistance, see Thermal resistance volumetric heating, 54 periodic, 215–218 steady, 58–61, 144–145, 158–163 well-posed problems, 141–143 Conductivity, see Thermal conductivity Configuration factor, see View factor Conrad, J. Heart of Darkness, 597 Subject Index 741 Conservation of energy, see Energy equation or Heat diffusion equation Conservation of mass general equation, 335 relation to species conservation, 628 steady incompressible flow, 276–278 Conservation of momentum, 279–282 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, 500 Conversion factors, 721–725 example of development, 14 Cooling towers, 599–600 Correlations, critically evaluating, 384–386 Counterdiffusion velocity, 637, 649 Critical heat flux (CHF), see Peak heat flux Cross flow, 374–384 cylinders flow field, 374–377 heat transfer, 377–380 tube bundles, 380–384 D Dalton’s law of partial pressures, 602 Damkohler number, 683 Darcy-Weisbach friction factor, 127, 358, 361, 363 Departure from nucleate boiling (DNB), see Peak Heat Flux Diffusion coefficient, 64, 608–623 binary gas mixtures, 614–619 dilute liquid solutions, 620–623 hydrodynamic model for liquid solutions, 620–623 kinetic theory model for gases, 610–613 multicomponent gas mixtures, 619–620 Diffusional mass flux, 604 Fick’s law for, 608–613 Diffusional mole flux, 605 Fick’s law for, 611 Diffusivity, see Thermal diffusivity Dilute gas, 610, 619 Dimensional analysis, 150–163 Dirichlet conditions, 142 Dittus-Boelter equation, 360 Dry ice, 684 Dufour effect, 613 E Earth, age of, Kelvin’s estimate, 261 Eckert number, 308 Eddy diffusivity for heat, 322 for momentum, 318 Effectiveness, see Heat exchangers or Fins Eigenvalue, 204 Einstein, A., 155, 621 Electromagnetic spectrum, 27 Emittance, 33, 527–530 diffuse and specular, 530–531 gaseous, 563–574 hemispherical, 531 monochromatic, 527 Energy equation, 292–294 analogy to momentum equation, 294–296 for boundary layers, 294 for pipe flow, 345 with mass transfer, 667 Entropy production, 9 for lumped capacity system, 24 Entry length, see Internal flow Equimolar counter-diffusion, 679 Error function, 223 Evaporation, 663–666, 672 742 Subject Index F Falling liquid films, 332, 429–431, 440–442 Fick’s law, 63, 598, 608–613 Film absorption, 681 Film boiling, see Boiling Film coefficient, see Heat transfer coefficient Film composition, 647, 660, 669 Film condensation, see Condensation Film temperature, 295, 308, 414, 669 Fins, 163–181 condition for one-dimensionality, 165–166 design considerations, 176–177 effectiveness, 176 efficiency, 176 purpose of, 163 root temperature, 174–176 thermal resistance of, 177–178 variable cross-section, 179–181 very long fins, 173 with tip heat transfer, 171–173 without tip heat transfer, 168–171 First law of thermodynamics, 7–8 Flux, see Heat flux or Mass flux Flux plot, 236–241 Forced convection, 20 boiling, see Boiling, forced convection boundary layers, see Boundary layers condensation, see Condensation cross flow, see Cross flow cylinders, 378–379 flat plates laminar, uniform q w , 309–311 laminar, uniform T w , 304–307 turbulent, 324–327 unheated starting length, 306 variable property effects, 308, 326 spheres, 684 tube bundles, 381–384 within tubes, see Internal flow Fourier number, 195 Fourier series conduction solutions, 203–207 one-term approximations, 218 Fourier’s law, 10–17, 50–51 Fourier, J.B.J., 10 The Analytical Theory of Heat,3, 10, 141 Free convection, see Natural convection Free molecule flow, 619 Friction coefficient, see Darcy-Weisbach friction factor or Skin friction coefficient Froude number, 157, 503 Fully developed flow, see Internal flow Functional replacement method, 150 G Gardon gage, 95 Gaseous radiation, 563–574 absorption, scattering, and extinction coefficients, 567 Beer’s law, 567 equation of transfer, 569 flames, 34, 574 mean beam length, 570 Gauss’s theorem, 55, 293, 628, 667 Gnielinski equation, 361 Graetz number, 352 Grashof number, 403 for mass transfer, 646 Grashof, F., 403 Gravity effect on boiling, 492 g-jitter, 417 g eff for condensation, 436 standard acceleration of, 719 Gray body, 527–529, 534–536, 549–563 electrical analogy for heat exchange, 549–559 transfer factor, see Transfer factor Greenhouse effect, 579–581 Subject Index 743 H Hagan, G., 348 Hagan-Poiseuille flow, 348 Halocline, 674 Heat, 3 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 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, 351 parallel flow, 99, 108, 123 relationship to isothermal pipe flow, 367–369 shell-and-tube, 100, 118, 124 single-stream limit, 125–126, 368 with variable U, 114 Heat flux, defined, 10–13 Heat pipes, 509–512 merit number, 510 Heat transfer, 3 modes of, 10–34 Heat transfer coefficient, 19–20 average, 20, 306–307 effect of mass transfer, 663–669 overall, 78–85 Heisler charts, 208 Helmholtz instability, 474–477 Henry’s law, 631 Hohlraum, 28 Hot-wire anemometer, 380, 393 Hydraulic diameter, 368, 370–373 Hydrodynamic theory of CHF, see Peak Heat Flux I Ideal gas law for mixtures, 602 Ideal solution, 631 Incompressible flow, 277–278, 292, 629, 678 Indices, method of, 150 Initial condition, 142 Insulation critical radius of, 72–74 superinsulation, 14 Integral conservation equations for energy, 300–304 for momentum, 286–289 Intensity of radiation, 531–533 Interdiffusion coefficient, 639 Interfacial boundary conditions, 630–634 Internal flow bulk energy equation, 345 bulk enthalpy, 343 bulk temperature, 343–346 for uniform q w , 349 for uniform T w , 367–369 bulk velocity, 343 entry length laminar hydrodynamic, 347 laminar thermal, 351–352 turbulent, 355–356 friction factor laminar flow, 359 turbulent flow, 358–364 fully developed hydrodynamically, 343, 347–348 thermally, 343–346 hydraulic diameter, 368 laminar heat transfer developing flow, 351–354 uniform q w , fully developed, 348–351 uniform T w , fully developed, 351 laminar temperature profiles, 345–346 laminar velocity profile developing flow, 343 fully developed, 347–348 noncircular ducts, 370–374 turbulent, 355–367 744 Subject Index Internal flow (con’t) turbulent heat transfer, 357–367 Gnielinski equation, 361 liquid metals, 365–367 rough walls, 362–364 variable property effects, 361 turbulent transition, 273 Irradiance, 549 J Jakob number, 428 Jakob, M., 230, 428 Jupiter, atmosphere of, 673 K Ka ¯ lida ¯ sa Abhijña ¯ na S ¯ akuntala ¯ , 725 Kinetic theory of gases average molecular speed, 614 Chapman-Enskog theory, 615 diffusion coefficient elementary model, 610–611 exact, 615–617 limitations of, 619 mean free path, 297, 614 thermal conductivity elementary model, 297–298 gas mixtures, 625 monatomic gas, 624 viscosity elementary model, 297–298 gas mixtures, 624 monatomic gas, 624 Kirchhoff’s law, 533–536 Kirchhoff, G.R., 533 Kolmogorov scales of turbulence, 336 L L’Hospital’s rule, 112 Laplace’s equation, 235 Laplacian, 56, 235 Lardner, D. The Steam Engine Familiarly Explained and Illustrated,99 Leibnitz’s rule, 287 Lennard-Jones intermolecular potential, 615–617 Lewis number, 609 Lewis, W.K., 609, 643, 666 Liquid metal heat transfer effect of Pr, 299–300 in tube bundles, 383–384 in tubes, 365–367 laminar boundary layer, 305–307 Logarithmic mean temperature difference (LMTD), 103–120 correction factors, 114–120 defined, 111 limitations on, 113–114 Lummer, O.R., 30 Lumped capacity solutions, 22–26, 194–202 dimensional analysis of, 195–196 electrical/mechanical analogies, 196–198 in natural convection, 411–412 second order, 199–202 with heat generation, 145 with variable ambient temperature, 198–199, 263 M Mach number, 308 Mass average velocity, 604 Mass conservation, see Conservation of mass Mass diffusion equation, 638 Mass exchangers, 683 Mass flux, 604 Mass fraction, 600 in the transferred state, 656 Mass transfer, 597–673 analogy to heat transfer, 63, 635–648 evaporation, 663–666, 672 forced convective, 640–645, 654–662 natural convective, 645–648 through a stagnant layer, 648–654 mass-based solution, 659 with simultaneous heat transfer, 663–673 Subject Index 745 Mass transfer coefficients, 640–648, 654–662 at low rates, 640–648 analogy of heat and mass transfer, 641–648 defined, 641 effect of mass transfer rate on, 658–660 variable property effects, 669 Mass transfer driving force, 655–657 at low rates, 661–662 one species transferred, 641, 657 Material derivative, 294 Mean beam length, 570 Mean free path, 297 rigid sphere molecules, 614 Melville, H. Moby Dick, 341 Microchannel heat exchanger, 351 Mixed convection, 426 Mixing-cup temperature, see Bulk temperature Mixtures binary, 609 composition of, 600–603 molecular weight of, 601 of ideal gases, 602–603 specific heat of, 627 transport properties, 614–627 gas diffusion coefficients, 614–620 liquid diffusion coefficients, 620–623 thermal conductivity of gas mixtures, 624–627 viscosity of gas mixtures, 624–627 velocities and fluxes in, 604–608 Mobility, 620 Molar concentration, 601 Mole flux, 605 Mole fraction, 601 Mole-average velocity, 605 Molecular weight, 601, 616 Momentum equation, 279–282 Momentum integral method, see Integral conservation equations Moody diagram, 359 Mothballs, 682 N Natural convection, 20, 397–427 dimensional analysis, 401–404 governing equations, 399–402 horizontal cylinders, 416–418 in enclosures, 426 in mass transfer, 645–648 inclined and horizontal plates, 420–423 spheres, 418–420 subermerged bodies, 420 turbulent, 404, 413, 421 validity of b.l. approximations, 414–416 variable-property effects, 414, 422 vertical cylinders, 418 vertical plates, 401–413 analysis compared to data, 412–413 Squire-Eckert analysis, 405–410 wide-range correlation, 412 with forced convection, 426 with uniform heat flux, 424–425 Navier-Stokes equation, 279 Nernst-Einstein equation, 620, 677 Neumann conditions, 142 Newcomen’s engine, 193 Newton’s law of cooling, 19 Newton’s law of viscous shear, 281 Newton, Isaac, 19 Nomenclature, 725–731 NTU, number of transfer units, 121 Nucleate boiling, see Boiling Nukiyama, S., 457–459 Number density, 601 Nusselt number, defined, 275 average, 307, 310 for developing internal flow, 352–353 for fully developed internal flow, 349 for mass transfer, 643 Nusselt, E.K.W., 121, 275, 403, 430, 436, 442 746 Subject Index O Ocean, salt concentration in, 674 Ohm’s law, 63 gray body radiation analogy, 549–559 thermal resistance analogy, see Thermal resistance Overall heat transfer coefficient, 78–85 typical values, 82 P Péclét number, 366 Partial density, 600 Partial pressure, 602 Peak heat flux, 462, 472–485 external flows, 494–496 general expression for, 478 horizontal plate, 478–481 internal flows, 504–505 various configurations, 481–485 very small objects, 482 Zuber-Kutateladze prediction, 480 Petukhov equation, 360 Physical constants, 719 Pi-theorem, see Buckingham pi-theorem Pipe flow, see Internal flow Planck’s constant, 31 Planck’s law, 31 Planck, M., 31 Pohlhausen, K., 286, 303 Poiseuille’s law, 348 Poiseuille, J., 348 Prandtl number, 296–299 Eucken formula, 677 relation to b.l. thickness, 299–300, 304 turbulent Prandtl number, 322 Prandtl, L., 270, 271, 282, 315 Pringsheim, E., 30 Properties of substances, see Thermophysical property data Property reference state, see Film temperature or Film composition Psychrometer, sling, 663 Pumping power, 126 Q Quenching, 485 R Radiation, see Thermal radiation Radiation heat transfer coefficient, 74 Radiation shield, 34, 539, 553 Radiosity, 549 Raoult’s law, 631 Rayleigh number, 403 for mass transfer, 646 for uniform wall heat flux, 424 Rayleigh, Lord (J.W. Strutt), 151 Reactions heterogeneous, 606, 627, 673–675, 683 homogeneous, 627, 673 Reflectance, 28 diffuse and specular, 530–531 Relativity, theory of, 156 Resistance, see Thermal resistance Resistance thermometer, 457 Reversibility and heat transfer, 8 Reynolds number, 271 Reynolds, O., 272, 311 Reynolds-Colburn analogy for laminar flow, 311–313 for mass transfer, 666 for turbulent flow, 322–325 Richardson, L.F., 313 Roughness, see Surface roughness effects S S.I. System, 14, 721–725 Samurai sword, 220–221 Savery’s engine, 193 Scattering, 564 Schmidt number, 609 Schmidt, E., 275, 609 Second law of thermodynamics, 8–10 Self-diffusion, 610, 614 Separation of variables solutions, 146–150 Shakespeare, Wm. Macbeth, 457 Venus and Adonis, 525 Sherwood number, 643 Subject Index 747 Sherwood, T.K., 643 Sieder-Tate equation, 360 Similarity transformations, 224, 282–284 Simultaneous heat and mass transfer, 663–673 energy balances for, 670–673 Skin drag, see Skin friction coefficient Skin friction coefficient, 287 for laminar flow, 290 for turbulent flow, 322, 325 for turbulent pipe flow, 358–364 versus profile drag, 312 Solar energy, 574–582 solar collectors, 582 wavelength distribution, 529 Solubility, 631 Soret effect, 612, 675 Species conservation, 627–648 boundary conditions for, 630–634 equation of, 627–629 for stationary media, 635–639 for steady state, 635–638 for unsteady diffusion, 638–639 Species-average velocity, 604 Specific heat capacity, 18, 292 for mixtures, 627 Specific heat ratio, 624 Speed of light in vacuum, 31, 719 Stagnant film model, 658–659, 681 Stanton number, 312 Stefan tube, 648 Stefan, J., 648 Stefan-Boltzmann constant, 30, 719 Stefan-Boltzmann law, 30 Stefan-Maxwell equation, 676 Stegosaurus, 163 Steradian, defined, 531 Stokes’ law, 621 Stokes, G.G., 621 Stokes-Einstein equation, 621 Stream function, 276–278 Streamlines, 276 String rule, 586 Strouhal number, 376 Sublimation, 633, 643, 666, 682, 684 Suction, 659 Surface roughness effects on friction factor, 358, 362–364 on nucleation, 467–468 on pool boiling, 489–492 on turbulent forced convection, 362–364 on turbulent transition, 327 Surface tension, 465–467 Sutherland, W., 621 Sweat cooling, 672 T Taylor instability, 472–474 Taylor, G.I., 472 Temperature gradient, defined, 50 Temperature response charts, 208–218 Thermal conductivity, 10–16, 51 equations for gases, 624–627 Eucken correction, 624 simple kinetic theory model, 297–298 temperature dependence, 50–51 Thermal diffusion, 612 Thermal diffusivity, 18 Thermal expansion, coefficient of, 401 for an ideal gas, 403 Thermal radiation, 27–34, 525–583 black body, 28–31 black body exchange, 536–548 diffuse and specular, 530–531 enclosures gray, algebraic solutions, 559–563 nonisothermal, nongray, or nondiffuse, 563 gaseous, see Gaseous radiation gray body, 527 gray body exchange, 534–536 electrical analogy, 549–559 with a specified wall flux, 556 with an adiabatic surface, 556 infrared radiation, 27–28 intensity, 531–533 Kirchhoff’s law, 533–536 monochromatic emissive power, 30 Monte Carlo method, 563, 574 Planck’s law, 31 radiant exchange described, 31–34 748 Subject Index Thermal Radiation (con’t) radiation heat transfer coefficient, 74 radiation shield, 34, 539, 553 small object in large environment, 33, 552 solar, 574–583 Stefan-Boltzmann law, 30 transfer factor, see Transfer factor view factor, see View factor wavelength distribution, 27–31, 527–530 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, 74–78 fouling resistance, 83–85 in parallel, 75–78, 80–81 in series, 72, 73, 78, 79 Ohm’s law analogy, 62–63 Thermophysical property data, 691 accuracy of, 691–694 critical point temperature, 465–467, 710–711 density, 698–718 diffusion coefficient, 613 air-water, 612 dynamic viscosity, 714–718 emittance gases, 564–574 surfaces, 528 gases at 1 atm pressure, 714–718 kinematic viscosity, 704–718 latent heat of vaporization, 710–711 liquid metals, 704–709 metallic solids, 698–700 mixtures, see Mixtures molecular weights, 616 nonmetallic solids, 700–703 Prandtl number, 704–718 saturated liquids, 704–709 saturated vapors, 711–713 specific heat capacity, 698–718 surface tension, 465–467 thermal conductivity, 15, 52, 53, 698–718 thermal diffusivity, 698–718 thermal expansion coefficient, 704–713 triple point temperature, 710–711 vapor pressure, 711–713 CCl 4 (l), 680 CO 2 (s), 684 ethanol, 685 H 2 O(s), 634 napthalene, 643, 682 paradichlorobenzene, 682 Time constant, 22, 196, 200 Transfer factor, 33, 527 parallel plates, 551 two diffuse gray bodies, 552 two specular gray bodies, 553 Transmittance, 29 Transpiration cooling, 670–671 Transport laws, 8 Tube bundles, 380–384 Tube flow, see Internal flow Turbulence, 313–330 eddy diffusivities, 317–323 friction velocity, 319 internal flow, 355–367 lengthscales of, 315–316, 336 log law, 321 mixing length, 315–321 Reynolds-Colburn analogy, 322–325 transition to, 272–274 viscous sublayer, 320 Two-phase flow heat transfer boiling, 496–505 condensing, 505–506 regimes for horizontal tubes, 503–504 without gravity force, 498–499 U Units, 721–725 Universal gas constant, 602, 719 [...]... Verne, J Around the World in 80 Days, 5 View factor, 32 , 536 –548 between small and large objects, 546 examples of view factor algebra, 537 –548 general integral for, 540–542 reciprocity relation, 539 some three-dimensional configurations, 544, 545 some two-dimensional configurations, 5 43 summation rule, 537 View factors string rule, 586 Viscosity correction for temperature dependence of, 32 6, 36 1 dynamic,... dependence of, 32 6, 36 1 dynamic, 270 gas mixtures, 624 kinematic, 271 monatomic gas, 624 Newton’s law of viscous shear, 281 simple kinetic theory model, 297–298 Sutherland formula for gases, 33 5 von Kármán constant, 32 0 von Kármán, T., 286 Vortex shedding, 37 4 37 7 W Watt, James, 1 93 Weber number, 495 Wet-bulb temperature, 6 63 666 Wetting agent, 507 Wien’s law, 30 Y Yamagata equation, 468 749 . Index Thermal Radiation (con’t) radiation heat transfer coefficient, 74 radiation shield, 34 , 539 , 5 53 small object in large environment, 33 , 552 solar, 574–5 83 Stefan-Boltzmann law, 30 transfer factor,. 549–559 transfer factor, see Transfer factor Greenhouse effect, 579–581 Subject Index 7 43 H Hagan, G., 34 8 Hagan-Poiseuille flow, 34 8 Halocline, 674 Heat, 3 Heat capacity, see Specific heat capacity Heat conduction,. velocity, 34 3 entry length laminar hydrodynamic, 34 7 laminar thermal, 35 1 35 2 turbulent, 35 5 35 6 friction factor laminar flow, 35 9 turbulent flow, 35 8 36 4 fully developed hydrodynamically, 34 3, 34 7 34 8 thermally,