Fundamentals of Heat and Mass Transfer

Front Cover......Page 1
Title Page......Page 3
Copyright Page......Page 4
Preface......Page 5
CONTENTS (with direct page links)......Page 11
Symbols......Page 21
1. Introduction......Page 25
1.1 What and How?......Page 26
1.2.1 Conduction......Page 27
1.2.2 Convection......Page 30
1.2.3 Radiation......Page 32
1.3 Relationship to Thermodynamics......Page 36
1.3.1 Relationship to the First Law of Thermodynamics (Conservation of Energy)......Page 37
1.3.2 Relationship to the Second Law of Thermodynamics and the Efficiency of Heat Engines......Page 52
1.4 Units and Dimensions......Page 57
1.5 Analysis of Heat Transfer Problems: Methodology......Page 59
1.6 Relevance of Heat Transfer......Page 62
1.7 Summary......Page 66
Problems......Page 69
2. Introduction to Conduction......Page 83
2.1 The Conduction Rate Equation......Page 84
2.2 The Thermal Properties of Matter......Page 86
2.2.1 Thermal Conductivity......Page 87
2.2.2 Other Relevant Properties......Page 94
2.3 The Heat Diffusion Equation......Page 98
2.4 Boundary and Initial Conditions......Page 106
2.5 Summary......Page 110
Problems......Page 111
3. One-Dimensional, Steady-State Conduction......Page 123
3.1.1 Temperature Distribution......Page 124
3.1.2 Thermal Resistance......Page 126
3.1.3 The Composite Wall......Page 127
3.1.4 Contact Resistance......Page 129
3.1.5 Porous Media......Page 131
3.2 An Alternative Conduction Analysis......Page 145
3.3.1 The Cylinder......Page 149
3.3.2 The Sphere......Page 154
3.5 Conduction with Thermal Energy Generation......Page 155
3.5.1 The Plane Wall......Page 156
3.5.2 Radial Systems......Page 162
3.5.4 Application of Resistance Concepts......Page 163
3.6 Heat Transfer from Extended Surfaces......Page 167
3.6.1 A General Conduction Analysis......Page 169
3.6.2 Fins of Uniform Cross-Sectional Area......Page 171
3.6.3 Fin Performance Parameters......Page 177
3.6.4 Fins of Nonuniform Cross-Sectional Area......Page 180
3.6.5 Overall Surface Efficiency......Page 183
3.7.1 The Bioheat Equation......Page 187
3.7.2 Thermoelectric Power Generation......Page 191
3.7.3 Nanoscale Conduction......Page 199
3.8 Summary......Page 203
References......Page 205
Problems......Page 206
4. Two-Dimensional, Steady-State Conduction......Page 233
4.1 General Considerations and Solution Techniques......Page 234
4.2 The Method of Separation of Variables......Page 235
4.3 The Conduction Shape Factor and the Dimensionless Conduction Heat Rate......Page 239
4.4.1 The Nodal Network......Page 245
4.4.2 Finite-Difference Form of the Heat Equation: No Generation and Constant Properties......Page 246
4.4.3 Finite-Difference Form of the Heat Equation: The Energy Balance Method......Page 247
4.5.1 Formulation as a Matrix Equation......Page 254
4.5.2 Verifying the Accuracy of the Solution......Page 255
4.6 Summary......Page 260
Problems......Page 261
5. Transient Conduction......Page 277
5.1 The Lumped Capacitance Method......Page 278
5.2 Validity of the Lumped Capacitance Method......Page 281
5.3 General Lumped Capacitance Analysis......Page 285
5.3.2 Negligible Radiation......Page 286
5.3.4 Additional Considerations......Page 287
5.4 Spatial Effects......Page 296
5.5 The Plane Wall with Convection......Page 297
5.5.2 Approximate Solution......Page 298
5.5.4 Additional Considerations......Page 300
5.6.1 Exact Solutions......Page 301
5.6.3 Total Energy Transfer: Approximate Solutions......Page 302
5.6.4 Additional Considerations......Page 303
5.7 The Semi-Infinite Solid......Page 308
5.8.1 Constant Temperature Boundary Conditions......Page 315
5.8.2 Constant Heat Flux Boundary Conditions......Page 317
5.8.3 Approximate Solutions......Page 318
5.9 Periodic Heating......Page 325
5.10.1 Discretization of the Heat Equation: The Explicit Method......Page 328
5.10.2 Discretization of the Heat Equation: The Implicit Method......Page 335
5.11 Summary......Page 342
Problems......Page 343
6. Introduction to Convection......Page 365
6.1.1 The Velocity Boundary Layer......Page 366
6.1.2 The Thermal Boundary Layer......Page 367
6.1.3 The Concentration Boundary Layer......Page 369
6.2.1 Heat Transfer......Page 370
6.2.2 Mass Transfer......Page 371
6.3.1 Laminar and Turbulent Velocity Boundary Layers......Page 377
6.3.2 Laminar and Turbulent Thermal and Species Concentration Boundary Layers......Page 379
6.4 The Boundary Layer Equations......Page 382
6.4.1 Boundary Layer Equations for Laminar Flow......Page 383
6.5 Boundary Layer Similarity: The Normalized Boundary Layer Equations......Page 386
6.5.2 Dependent Dimensionless Parameters......Page 387
6.6 Physical Interpretation of the Dimensionless Parameters......Page 396
6.7 Boundary Layer Analogies......Page 398
6.7.1 The Heat and Mass Transfer Analogy......Page 399
6.7.2 Evaporative Cooling......Page 402
6.7.3 The Reynolds Analogy......Page 405
6.8 Summary......Page 406
References......Page 407
Problems......Page 408
7. External Flow......Page 419
7.1 The Empirical Method......Page 421
7.2 The Flat Plate in Parallel Flow......Page 422
7.2.1 Laminar Flow over an Isothermal Plate: A Similarity Solution......Page 423
7.2.2 Turbulent Flow over an Isothermal Plate......Page 429
7.2.3 Mixed Boundary Layer Conditions......Page 430
7.2.4 Unheated Starting Length......Page 431
7.2.5 Flat Plates with Constant Heat Flux Conditions......Page 432
7.3 Methodology for a Convection Calculation......Page 433
7.4.1 Flow Considerations......Page 441
7.4.2 Convection Heat and Mass Transfer......Page 443
7.5 The Sphere......Page 451
7.6 Flow Across Banks of Tubes......Page 454
7.7.1 Hydrodynamic and Geometric Considerations......Page 463
7.7.2 Convection Heat and Mass Transfer......Page 464
7.8 Packed Beds......Page 468
7.9 Summary......Page 469
Problems......Page 472
8. Internal Flow......Page 493
8.1.1 Flow Conditions......Page 494
8.1.2 The Mean Velocity......Page 495
8.1.3 Velocity Profile in the Fully Developed Region......Page 496
8.1.4 Pressure Gradient and Friction Factor in Fully Developed Flow......Page 498
8.2 Thermal Considerations......Page 499
8.2.1 The Mean Temperature......Page 500
8.2.3 Fully Developed Conditions......Page 501
8.3.1 General Considerations......Page 505
8.3.2 Constant Surface Heat Flux......Page 506
8.3.3 Constant Surface Temperature......Page 509
8.4.1 The Fully Developed Region......Page 513
8.4.2 The Entry Region......Page 518
8.5 Convection Correlations: Turbulent Flow in Circular Tubes......Page 520
8.6 Convection Correlations: Noncircular Tubes and the Concentric Tube Annulus......Page 528
8.7 Heat Transfer Enhancement......Page 531
8.8.1 Microscale Convection in Gases (0.1 µm <~ Dh <~ 100 µm)......Page 534
8.8.2 Microscale Convection in Liquids......Page 535
8.8.3 Nanoscale Convection (Dh <~ 100 nm)......Page 536
8.9 Convection Mass Transfer......Page 539
8.10 Summary......Page 541
References......Page 544
Problems......Page 545
9. Free Convection......Page 563
9.1 Physical Considerations......Page 564
9.2 The Governing Equations for Laminar Boundary Layers......Page 566
9.3 Similarity Considerations......Page 568
9.4 Laminar Free Convection on a Vertical Surface......Page 569
9.5 The Effects of Turbulence......Page 572
9.6 Empirical Correlations: External Free Convection Flows......Page 574
9.6.1 The Vertical Plate......Page 575
9.6.2 Inclined and Horizontal Plates......Page 578
9.6.3 The Long Horizontal Cylinder......Page 583
9.6.4 Spheres......Page 587
9.7 Free Convection Within Parallel Plate Channels......Page 588
9.7.1 Vertical Channels......Page 589
9.8.1 Rectangular Cavities......Page 591
9.8.2 Concentric Cylinders......Page 594
9.8.3 Concentric Spheres......Page 595
9.9 Combined Free and Forced Convection......Page 597
9.10 Convection Mass Transfer......Page 598
9.11 Summary......Page 599
References......Page 600
Problems......Page 601
10. Boiling and Condensation......Page 619
10.1 Dimensionless Parameters in Boiling and Condensation......Page 620
10.2 Boiling Modes......Page 621
10.3.1 The Boiling Curve......Page 622
10.3.2 Modes of Pool Boiling......Page 623
10.4.1 Nucleate Pool Boiling......Page 626
10.4.2 Critical Heat Flux for Nucleate Pool Boiling......Page 628
10.4.4 Film Pool Boiling......Page 629
10.4.5 Parametric Effects on Pool Boiling......Page 630
10.5 Forced Convection Boiling......Page 635
10.5.2 Two-Phase Flow......Page 636
10.6 Condensation: Physical Mechanisms......Page 639
10.7 Laminar Film Condensation on a Vertical Plate......Page 641
10.8 Turbulent Film Condensation......Page 645
10.9 Film Condensation on Radial Systems......Page 650
10.10 Condensation in Horizontal Tubes......Page 655
10.11 Dropwise Condensation......Page 656
References......Page 657
Problems......Page 659
11. Heat Exchangers......Page 669
11.1 Heat Exchanger Types......Page 670
11.2 The Overall Heat Transfer Coefficient......Page 672
11.3 Heat Exchanger Analysis: Use of the Log Mean Temperature Difference......Page 675
11.3.1 The Parallel-Flow Heat Exchanger......Page 676
11.3.2 The Counterflow Heat Exchanger......Page 678
11.3.3 Special Operating Conditions......Page 679
11.4.1 Definitions......Page 686
11.4.2 Effectiveness–NTU Relations......Page 687
11.5 Heat Exchanger Design and Performance Calculations......Page 694
11.6 Additional Considerations......Page 703
11.7 Summary......Page 711
Problems......Page 712
12. Radiation: Processes and Properties......Page 725
12.1 Fundamental Concepts......Page 726
12.2 Radiation Heat Fluxes......Page 729
12.3.1 Mathematical Definitions......Page 731
12.3.2 Radiation Intensity and Its Relation to Emission......Page 732
12.3.3 Relation to Irradiation......Page 737
12.3.4 Relation to Radiosity for an Opaque Surface......Page 739
12.4 Blackbody Radiation......Page 740
12.4.1 The Planck Distribution......Page 741
12.4.3 The Stefan–Boltzmann Law......Page 742
12.4.4 Band Emission......Page 743
12.5 Emission from Real Surfaces......Page 750
12.6 Absorption, Reflection, and Transmission by Real Surfaces......Page 759
12.6.1 Absorptivity......Page 760
12.6.2 Reflectivity......Page 761
12.6.4 Special Considerations......Page 763
12.7 Kirchhoff’s Law......Page 768
12.8 The Gray Surface......Page 770
12.9 Environmental Radiation......Page 776
12.9.1 Solar Radiation......Page 777
12.9.2 The Atmospheric Radiation Balance......Page 779
12.9.3 Terrestrial Solar Irradiation......Page 781
12.10 Summary......Page 784
Problems......Page 788
13. Radiation Exchange Between Surfaces......Page 809
13.1.1 The View Factor Integral......Page 810
13.1.2 View Factor Relations......Page 811
13.2 Blackbody Radiation Exchange......Page 820
13.3 Radiation Exchange Between Opaque, Diffuse, Gray Surfaces in an Enclosure......Page 824
13.3.1 Net Radiation Exchange at a Surface......Page 825
13.3.2 Radiation Exchange Between Surfaces......Page 826
13.3.3 The Two-Surface Enclosure......Page 832
13.3.4 Two-Surface Enclosures in Series and Radiation Shields......Page 834
13.3.5 The Reradiating Surface......Page 836
13.4 Multimode Heat Transfer......Page 841
13.6.1 Volumetric Absorption......Page 844
13.6.2 Gaseous Emission and Absorption......Page 845
13.7 Summary......Page 849
References......Page 850
Problems......Page 851
14. Diffusion Mass Transfer......Page 873
14.1.1 Physical Origins......Page 874
14.1.2 Mixture Composition......Page 875
14.1.3 Fick’s Law of Diffusion......Page 876
14.1.4 Mass Diffusivity......Page 877
14.2.1 Absolute and Diffusive Species Fluxes......Page 879
14.2.2 Evaporation in a Column......Page 882
14.4 Conservation of Species for a Stationary Medium......Page 887
14.4.2 The Mass Diffusion Equation......Page 888
14.4.3 Stationary Media with Specified Surface Concentrations......Page 890
14.5 Boundary Conditions and Discontinuous Concentrations at Interfaces......Page 894
14.5.2 Solubility of Gases in Liquids and Solids......Page 895
14.5.3 Catalytic Surface Reactions......Page 900
14.6 Mass Diffusion with Homogeneous Chemical Reactions......Page 902
14.7 Transient Diffusion......Page 905
14.8 Summary......Page 911
Problems......Page 912
A: Thermophysical Properties of Matter......Page 921
A.1 Thermophysical Properties of Selected Metallic Solids......Page 923
A.2 Thermophysical Properties of Selected Nonmetallic Solids......Page 927
A.3 Thermophysical Properties of Common Materials......Page 929
A.4 Thermophysical Properties of Gases at Atmospheric Pressure......Page 935
A.5 Thermophysical Properties of Saturated Fluids......Page 940
A.6 Thermophysical Properties of Saturated Water......Page 943
A.7 Thermophysical Properties of Liquid Metals......Page 945
A.8 Binary Diffusion Coefficients at One Atmosphere......Page 946
A.10 The Solubility of Selected Gases and Solids......Page 947
A.11 Total, Normal (n) or Hemispherical (h) Emissivity of Selected Surfaces......Page 948
A.12 Solar Radiative Properties for Selected Materials......Page 950
References......Page 951
B: Mathematical Relations and Functions......Page 953
B.1 Hyperbolic Functions......Page 954
B.2 Gaussian Error Function......Page 955
B.3 The First Four Roots of the Transcendental Equation, ξn tan ξn = Bi, for Transient Conduction in a Plane Wall......Page 956
B.4 Bessel Functions of the First Kind......Page 957
B.5 Modified Bessel Functions of the First and Second Kinds......Page 958
C: Thermal Conditions Associated with Uniform Energy Generation in One-Dimensional, Steady-State Systems......Page 959
D: The Gauss–Seidel Method......Page 965
E: The Convection Transfer Equations......Page 967
E.2 Newton’s Second Law of Motion......Page 968
E.3 Conservation of Energy......Page 969
E.4 Conservation of Species......Page 970
F: Boundary Layer Equations for Turbulent Flow......Page 971
G: An Integral Laminar Boundary Layer Solution for Parallel Flow over a Flat Plate......Page 975
Conversion Factors......Page 979
Physical Constants......Page 980
B......Page 981
C......Page 982
E......Page 983
F......Page 984
H - I......Page 985
J - K - L - M......Page 986
N - O - P......Page 987
S......Page 988
T......Page 989
W - Z......Page 990
Student Companion Website......Page 2
SUPPLEMENTAL MATERIAL......Page 992
4S.1.1 Methodology of Constructing a Flux Plot......Page 994
4S.1.2 Determination of the Heat Transfer Rate......Page 995
4S.1.3 The Conduction Shape Factor......Page 996
4S.2 The Gauss-Seidel Method: Example of Usage......Page 998
Problems......Page 1003
5S.1 Graphical Representation of One Dimensional, Transient Conduction in the Plane Wall, Long Cylinder, and Sphere......Page 1005
5S.2 Analytical Solution of Multidimensional Effects......Page 1009
Problems......Page 1015
6S.1.1 Conservation of Mass......Page 1018
6S.1.2 Newton’s Second Law of Motion......Page 1019
6S.1.3 Conservation of Energy......Page 1022
6S.1.4 Conservation of Species......Page 1025
Problems......Page 1029
11S.1 Log Mean Temperature Difference Method for Multipass and Cross-Flow Heat Exchangers......Page 1033
11S.2 Compact Heat Exchangers......Page 1037
Problems......Page 1042
Index......Page 1044