Preface ...................................................... xvii
Acknowledgments ............................................... xxi
Guide to Instructors and Students ........................... xxiii
1 Introduction and Preliminaries ................................ 1
1.1 Applications and History ................................... 1
1.1.1 Heat Transfer ....................................... 3
1.1.2 Applications ........................................ 4
1.1.3 History, Frontiers, and Integration*
1.2 Units and Normalization (Scaling) ......................... 11
1.2.1 Units .............................................. 11
1.2.2 Normalization (Scaling) ............................ 13
1.3 Thermal Systems ........................................... 13
1.3.1 Thermodynamic Properties ........................... 14
1.3.2 Thermal Nonequilibrium ............................. 14
1.3.3 Control Volume and Control Surface ................. 15
1.4 Principal Energy Carriers and Heat Flux Vector ............ 18
1.4.1 Macroscopic Heat Transfer Mechanisms ............... 18
1.4.2 Atomic-Level Heat Carriers (Heat Transfer
Physics) ........................................... 20
1.4.3 Net Heat Transfer Rate QІA ......................... 23
1.4.4 Magnitude and Representation of q .................. 25
1.5 Heat Transfer Materials and Heat Flux Tracking ............ 28
1.5.1 Three Phases of Matter: Intermolecular and
Intramolecular Forces*
1.5.2 Microscale Energies of Matter: Discrete and
Continuous Energies*
1.5.3 Multiphase Heat Transfer Medium: Composites ........ 29
1.5.4 Fluid Motion ....................................... 29
1.5.5 Intramedium and Intermedium Heat Transfer .......... 32
1.5.6 Heat Flux Vector Tracking in Various Phases ........ 32
1.6 Conservation of Energy .................................... 34
1.7 Conservation of Mass, Species, and Momentum*
1.7.1 Conservation of Mass*
1.7.2 Conservation of Species*
1.7.3 Conservation of Momentum*
1.7.4 Other Conserved Quantities*
1.8 Scope ..................................................... 45
1.9 Summary ................................................... 46
1.10 References*
1.11 Problems .................................................. 48
1.11.1 Heat Flux Vector Tracking ......................... 48
1.11.2 Integral-Volume Energy Equation ................... 57
2 Energy Equation ........................................... 66
2.1 Nonuniform Temperature Distribution: Differential
(Infinitesimal)-Volume Energy Equation .................... 68
2.1.1 Physical Interpretation of Divergence of q ......... 70
2.1.2 Relation between Volumetric Differentiation and
Surface Integration ................................ 72
2.2 Uniform Temperature in One or More Directions: Energy
Equation for Volumes with One or More Finite Lengths ...... 76
2.2.1 Integral-Volume Energy Equation .................... 76
2.2.2 Combined Integral- and Differential-Length Energy
Equation ........................................... 81
2.2.3 Discrete Temperature Nonuniformity: Finite-
Small-Volume Energy Equation*
2.2.4 Summary of Selection of Energy Equation Based on
Uniformity or Nonuniformity of Temperature ......... 85
2.3 Thermal Energy Conversion Mechanisms ...................... 86
2.3.1 Chemical- or Physical-Bond Energy Conversion ....... 87
2.3.2 Electromagnetic Energy Conversion .................. 96
2.3.3 Mechanical Energy Conversion ...................... 111
2.3.4 Summary of Thermal Energy Conversion Mechanisms ... 119
2.4 Bounding-Surface and Far-Field Thermal Conditions ........ 120
2.4.1 Continuity of Temperature across Bounding
Surface* .......................................... 121
2.4.2 Bounding-Surface Energy Equation .................. 121
2.4.3 Prescribed Bounding-Surface Thermal Conditions*
2.4.4 Far-Field Thermal Conditions*
2.5 Heat Transfer Analysis*
2.5.1 Integration of Differential-Volume Energy Equation*
2.5.2 Single- and Multidimensional Heat Flow*
2.5.3 Time Dependence and Steady State*
2.5.4 Thermal Circuit Models*
2.5.5 Summary of Methodology for Heat Transfer
Analysis*
2.5.6 Solution Format for End-of-Chapter Problems*
2.6 Summary .................................................. 123
2.7 References*
2.8 Problems ................................................. 124
2.8.1 Finite- and Differential-Length Energy Equation ... 124
2.8.2 Energy Conversion Mechanisms (to and from
Thermal Energy) ................................... 133
2.8.3 Bounding-Surface Thermal Conditions ............... 145
2.8.4 General*
3 Conduction ............................................... 152
3.1 Microscale Heat Storage and Specific Heat Capacity cp .... 154
3.1.1 Gases: Thermal Fluctuation Motion ................. 155
3.1.2 Solids: Lattice Vibration and Phonon .............. 157
3.1.3 Liquids: Solid-Like versus Gas-Like ............... 159
3.1.4 Thermal Materials: From Zero to Infinite Heat
Capacity .......................................... 160
3.2 Microscale Conduction Heat Carriers and Thermal
Conductivity k ........................................... 163
3.2.1 Gases: Thermal Fluctuation Motion and Mean-Free
Path λƒ ........................................... 165
3.2.2 Solids: Electrons and Phonons and Their
Mean-Free Paths λe and λp ......................... 169
3.2.3 Liquids ........................................... 180
3.2.4 Composites: Local Thermal Equilibrium and
Effective Conductivity ............................ 180
3.2.5 Thermal Materials: From Ideal Insulators to Ideal
Conductors ........................................ 184
3.3 Steady-State Conduction .................................. 191
3.3.1 One-Dimensional, Intramedium Conduction:
Electrical Circuit Analogy and Thermal Resistance
Rk(°C/W) .......................................... 194
3.3.2 One-Dimensional Treatment of Composites ........... 203
3.3.3 Thermal Circuit Analysis .......................... 215
3.3.4 Conduction Thermometry*
3.3.5 Contact Resistance ................................ 221
3.3.6 Conduction and Energy Conversion .................. 225
3.3.7 Thermoelectric Coolers ............................ 230
3.3.8 Multidimensional Conduction from Buried and
Surface Objects*
3.4 Transient Conduction ..................................... 240
3.4.1 Heat Conductivity versus Capacity: Thermal
Diffusivity α ..................................... 240
3.4.2 Short and Long Elapsed-Time Behavior: Fourier
Number Fo ......................................... 242
3.4.3 Distributed versus Lumped Capacitance: Internal-
External Conduction Number Nk ..................... 243
3.5 Distributed-Capacitance (Nonuniform Temperature)
Transient: T = T(x, t) ................................... 243
3.5.1 Derivation of Temperature Distribution for Semi-
Infinite Slab: Thermal Effusivity (ρcpk)1/2 ........ 252
3.5.2 Penetration Depth δα, Penetration
Fourier Number Fos, and Penetration Speed uδ ...... 258
3.5.3 Time-Dependent Surface Temperature: Semi-
Infinite Slab*
3.5.4 Thermal Diffusivity Meter*
3.6 Lumped-Capacitance (Uniform Temperature) Transient:
Internal-External Conduction Number Nk,i < 0.1,
T = T(t) ................................................. 263
3.6.1 Single Node with Constant, Prescribed Surface
Heat Transfer Q1 .................................. 266
3.6.2 Single Node with Resistive Surface Heat Transfer
Qk, k-2(t) .......................................... 268
3.6.3 Multiple Nodes*
3.7 Discretization of Medium into Finite-Small Volumes*
3.7.1 One-Dimensional Transient Conduction*
3.7.2 Two-Dimensional Transient Conduction*
3.7.3 Nonuniform Discretization*
3.8 Conduction and Solid-Liquid Phase Change: Stefan Number
Stel*
3.9 Thermal Expansion and Thermal Stress*
3.10 Summary .................................................. 273
3.11 References*
3.12 Problems ................................................. 275
3.12.1 Microscales of Specific Heat Capacity and
Thermal Conductivity .............................. 275
3.12.2 Thermal Conduction Resistance and Thermal
Circuit Analysis .................................. 281
3.12.3 Conduction Contact Resistance ..................... 290
3.12.4 Conduction and Energy Conversion and
Thermoelectric Cooling ............................ 294
3.12.5 Multidimensional Conduction ....................... 302
3.12.6 Distributed-Capacitance Transient Conduction and
Penetration Depth ................................. 307
3.12.7 Lumped-Capacitance Transient Conduction ........... 315
3.12.8 Multinode Systems and Finite-Small-Volume
Analysis*
3.12.9 Solid-Liquid Phase Change ......................... 323
3.12.10 Thermal Expansion and Thermal Stress*
3.12.11 General*
4 Radiation ................................................ 324
4.1 Microscale Radiation Heat Carrier: Photon and Surface
Thermal Radiation Emission ............................... 326
4.1.1 Thermal Radiation ................................. 326
4.1.2 Ideal Photon Emission: Emissive Power Eb,λ Еb ...... 326
4.1.3 Band Fraction F0-λT ................................ 330
4.1.4 Deviation from Ideal Emission: Emissivity ϵr ...... 334
4.2 Interaction of Irradiation and Surface ................... 337
4.2.1 Surface-Radiation Properties: Absorptivity αr,
Reflectivity ρr, and Transmissivity τr ............ 339
4.2.2 Opaque Surface τr = 0 ............................. 342
4.2.3 Relation among Absorptivity, Emissivity, and
Reflectivity for Opaque Surfaces .................. 344
4.3 Thermal Radiometry*
4.3.1 Pyranometer*
4.3.2 Infrared Surface-Temperature Sensor*
4.4 Enclosure Surface-Radiation Heat Transfer Qr,i among
Gray, Diffuse, and Opaque Surfaces ....................... 347
4.4.1 Surface-Grayness Resistance Rr,ϵ(1/m2) ............. 348
4.4.2 View-Factor Resistance Rr,F(1/m2) .................. 350
4.4.3 Thermal Circuit Analysis of Enclosures ............ 356
4.4.4 Two-Surface Enclosures ............................ 360
4.4.5 Radiation Insulators (Shields) .................... 362
4.4.6 Three-Surface Enclosures .......................... 366
4.4.7 Three-Surface Enclosures with One Surface Having
S - Q = 0 ......................................... 371
4.5 Prescribed Irradiation and Nongray Surfaces*
4.5.1 Laser Irradiation (qr,i)l*
4.5.2 Solar Irradiation (qr,i)s*
4.5.3 Flame Irradiation (qr,i)ƒ*
4.5.4 Nongray Surfaces*
4.6 Inclusion of Substrate ................................... 375
4.6.1 Steady-State, Series Conduction-Surface
Radiation, Conduction-Radiation Number Nr ......... 375
4.6.2 Transient Heat Transfer: Lumped Capacitance for
Nr < 0.1 .......................................... 384
4.7 Summary .................................................. 388
4.8 References*
4.9 Problems .................................................. 389
4.9.1 Volumetric and Surface-Radiation Fundamentals ..... 389
4.9.2 View Factor ....................................... 393
4.9.3 Two-Surface, Opaque, Diffuse Gray Enclosures ...... 394
4.9.4 Three-Surface, Opaque, Diffuse Gray Enclosures .... 402
4.9.5 Nongray Surfaces and Prescribed Irradiation ....... 405
4.9.6 Inclusion of Substrate ............................ 410
4.9.7 General*
5 Convection: Unbounded Fluid Streams*
5.1 One-Dimensional Conduction-Convection Energy Equation*
5.2 Parallel Conduction-Convection Resistance Rr,u(°C/W)
and Conduction-Convection Number Nu = PeL*
5.3 Evaporation Cooling of Gaseous Streams*
5.3.1 Cooling of Gaseous Streams*
5.3.2 Cooling of Liquid and Gaseous Streams by Wall
Seepage and Surface Evaporation*
5.4 Combustion Heating of Gaseous Streams*
5.4.1 Conservation Equations, Adiabatic Flame
Temperature, and Far-Field Thermal Conditions*
5.4.2 Preheat and Reaction Regions*
5.4.3 Adiabatic Flame Speed uƒ,1 and Thickness δ*
5.4.4 Nonadiabatic Flame Speed: Lateral Heat Losses*
5.4.5 Effect of Thermal Conductivity: Effective
Thermal Conductivity*
5.4.6 Volumetric Radiation Heat Transfer: Radiant
(Photon) Conductivity (kr)*
5.4.7 Effect of Free-Stream Turbulence: Turbulence
Intensity Tu*
5.5 Joule Heating of Gaseous Streams*
5.5.1 Thermal Plasma Generators*
5.5.2 Thermal Plasma Classification*
5.5.3 Integral-Length Analysis*
5.6 Gas-Stream Volumetric Radiation*
5.7 Summary*
5.8 References*
5.9 Problems*
6 Convection: Semi-Bounded Fluid Streams ................... 426
6.1 Flow and Surface Characteristics ......................... 427
6.2 Semi-Infinite Plate as a Simple Geometry ................. 430
6.2.1 Local Surface-Convection Resistance Rku(°C/W) ..... 430
6.2.2 Viscous versus Thermal Boundary Layer: Prandtl
Number Pr ......................................... 431
6.2.3 Boundary-Layer Flow with Zero Prandtl Number:
Axial-Lateral Peclet Number PeL ................... 432
6.2.4 Dimensionless Surface-Convection Conductance:
Nusselt Number NuL = Nku,ƒ and Heat Transfer
Coefficient h ..................................... 439
6.2.5 Nonzero Prandtl Number: Reynolds Number ReL ....... 444
6.2.6 Average Nusselt Number (Nu)L and Average
Surface-Convection Resistance (Rku)L .............. 450
6.3 Parallel Turbulent Flow: Transition Reynolds Number
ReL ...................................................... 454
6.3.1 Turbulent Convection Heat Flux*
6.3.2 Microscale Turbulent Convection: Turbulent
Conductivity kt and Turbulent Mixing Length λt* ... 457
6.3.3 Variation of Turbulent Mixing Length Near Solid
Surface*
6.3.4 Averaged, Laminar-Turbulent Nusselt Number ........ 457
6.4 Perpendicular Flows: Impinging Jets ...................... 461
6.5 Thermobuoyant Flows ...................................... 466
6.5.1 Laminar Flow Adjacent to Vertical Plates:
Grashof and Rayleigh Numbers GrL, RaL ............. 469
6.5.2 Turbulent Thermobuoyant Flow over Vertical Plate .. 475
6.5.3 Combined Thermobuoyant-Forced Parallel Flows ...... 476
6.6 Liquid-Gas Phase Change .................................. 478
6.6.1 Theoretical Maximum Heat Flux for Evaporation
and Condensation qmax (Kinetic Limit)*
6.6.2 Bubble and Film Evaporation: Pool Boiling
Regimes ........................................... 481
6.6.3 Dropwise and Film Condensation*
6.6.4 Impinging-Droplets Surface Convection with
Evaporation*
6.7 Summary of Nusselt Number Correlations ................... 490
6.7.1 Sphere: Forced-Flow Regimes and Correlations ...... 490
6.7.2 Tabular Presentation of Correlations for Some
Flows and Geometries .............................. 493
6.8 Inclusion of Substrate ................................... 505
6.8.1 Steady-State, Series Conduction-Surface
Convection: Conduction-Convection or Biot Number
Nku,s = BiL ........................................ 506
6.8.2 Steady-State Simultaneous Conduction-Surface
Convection: Extended Surface and Fin Efficiency
ηƒ ................................................ 514
6.8.3 Transient: Lumped Capacitance for BiL < 0.1 ....... 523
6.8.4 Hot-Wire Anemometry*
6.9 Surface-Convection Evaporation Cooling*
6.10 Summary .................................................. 533
6.11 References*
6.12 Problems ................................................. 534
6.12.1 Laminar Parallel-Flow Surface Convection .......... 534
6.12.2 Turbulent Parallel-Flow Surface Convection ........ 537
6.12.3 Impinging-Jet Surface Convection .................. 538
6.12.4 Thermobuoyant-Flow Surface Convection ............. 541
6.12.5 Boiling and Condensation Surface Convection ....... 545
6.12.6 Impinging-Droplets Surface Convection ............. 547
6.12.7 Surface Convection with Other Flows and
Geometries ........................................ 549
6.12.8 Inclusion of Substrate ............................ 555
6.12.9 Surface-Convection Evaporation Cooling*
6.12.10 General*
7 Convection: Bounded Fluid Streams ........................ 570
7.1 Flow and Surface Characteristics ......................... 570
7.2 Tube Flow and Heat Transfer .............................. 574
7.2.1 Velocity-Area Averaged Fluid Temperature .......... 575
7.2.2 Tube-Surface Temperature Ts: Uniform or Varying ... 576
7.2.3 Local and Average Surface-Convection Resistance:
Nusselt Number NuD, (Nu)D ......................... 576
7.2.4 Negligible Axial Conduction: Large Peclet Number .. 578
7.2.5 Axial Variation of Fluid Temperature for Uniform
Ts: Effectiveness ϵhe and Number of Transfer
Units NTU ......................................... 578
7.2.6 Average Convection Resistance (Ru)L(°C/W) ......... 583
7.2.7 Prescribed Uniform Surface Heat Flux qs ........... 584
7.3 Laminar and Turbulent Flows, Entrance Effect,
Thermobuoyant Flows, and Phase Change .................... 588
7.3.1 Laminar versus Turbulent Flow: Transition
Reynolds Number ReDt .............................. 588
7.3.2 Developing versus Fully Developed Region,
Entrance Length Lδ: Laminar Flow .................. 589
7.3.3 Entrance Length Lδ: Turbulent Flow ................ 590
7.3.4 Thermobuoyant Flows ............................... 590
7.3.5 Liquid-Gas Phase Change ........................... 591
7.4 Summary of Nusselt Number Correlations ................... 593
7.4.1 Laminar Flow: Tube Cross-Sectional Geometry
Dependence ........................................ 593
7.4.2 Turbulent Flow: Geometric Universality of Using
Hydraulic Diameter Dh ............................. 595
7.4.3 Discontinuous Solid Surfaces and Large Specific
Surface Areas: Geometric Universality of
Particle Diameter Dp .............................. 596
7.4.4 Extended Surfaces: Overall Surface Efficiency ..... 599
7.4.5 Tabular Presentation of Correlation for Some
Geometries ........................................ 599
7.5 Inclusion of Bounding Solid .............................. 609
7.6 Heat Exchange between Two Bounded Streams ................ 614
7.6.1 Exit Temperatures in Coaxial Heat Exchangers ...... 615
7.6.2 Heat Exchanger Effectiveness ϵhe and Number of
Transfer Units NTU ................................ 618
7.6.3 ϵhe-NTU Relation for Other Heat Exchangers ......... 620
7.6.4 Heat Exchanger Analysis ........................... 622
7.6.5 Overall Thermal Resistance in Heat Exchangers RΣ .. 627
7.6.6 Dielectric and Inert Heat-Transfer Fluids*
7.7 Summary .................................................. 628
7.8 References*
7.9 Problems ................................................. 629
7.9.1 Average Convection Resistance and ϵhe-NTU .......... 629
7.9.2 Tubes and Ducts: Hydraulic Diameter ............... 632
7.9.3 High Specific Surface Area: Particle Diameter ..... 637
7.9.4 Inclusion of Bounding Solid and Other Flows ....... 643
7.9.5 Heat Exchangers ................................... 648
7.9.6 Overall Thermal Resistance in Heat Exchangers RΣ .. 654
7.9.7 General*
8 Heat Transfer in Thermal Systems*
8.1 Primary Thermal Functions*
8.1.1 Primary Functions of Heat Transfer Media*
8.1.2 Primary Thermal Functions of Bounding Surfaces*
8.1.3 Heat Transfer Material*
8.2 Thermal Engineering Analysis*
8.2.1 Simplifications, Approximations, and
Assumptions: Modeling*
8.2.2 Nodal Energy Equation*
8.2.3 Simultaneous Inclusion of Various Heat Transfer
Mechanisms*
8.2.4 Optimization*
8.3 Examples*
8.4 Summary*
8.5 References*
8.6 Problems*
Nomenclature*
Glossary*
Answers to Problems ........................................... 665
* - This section is found on the Web at
www.cambridge.org/kaviany
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