Fundamentals of Heat and Mass Transfer

Cover......Page 1
Title Page......Page 3
Copyright......Page 4
Contents......Page 13
Symbols......Page 23
CHAPTER 1 Introduction......Page 27
1.1 What and How?......Page 28
1.2.1 Conduction......Page 29
1.2.2 Convection......Page 32
1.2.3 Radiation......Page 34
1.3 Relationship to Thermodynamics......Page 38
1.3.1 Relationship to the First Law of Thermodynamics (Conservation of Energy)......Page 39
1.3.2 Relationship to the Second Law of Thermodynamics and the Efficiency of Heat Engines......Page 57
1.4 Units and Dimensions......Page 62
1.5 Analysis of Heat Transfer Problems: Methodology......Page 64
1.6 Relevance of Heat Transfer......Page 67
1.7 Summary......Page 71
References......Page 74
Problems......Page 75
CHAPTER 2 Introduction to Conduction......Page 93
2.1 The Conduction Rate Equation......Page 94
2.2.1 Thermal Conductivity......Page 96
2.2.2 Other Relevant Properties......Page 104
2.3 The Heat Diffusion Equation......Page 108
2.4 Boundary and Initial Conditions......Page 116
2.5 Summary......Page 120
Problems......Page 121
CHAPTER 3 One-Dimensional, Steady-State Conduction......Page 137
3.1.1 Temperature Distribution......Page 138
3.1.2 Thermal Resistance......Page 140
3.1.3 The Composite Wall......Page 141
3.1.4 Contact Resistance......Page 143
3.1.5 Porous Media......Page 145
3.2 An Alternative Conduction Analysis......Page 158
3.3.1 The Cylinder......Page 162
3.3.2 The Sphere......Page 167
3.5 Conduction with Thermal Energy Generation......Page 168
3.5.1 The Plane Wall......Page 169
3.5.2 Radial Systems......Page 175
3.5.4 Application of Resistance Concepts......Page 176
3.6 Heat Transfer from Extended Surfaces......Page 180
3.6.1 A General Conduction Analysis......Page 182
3.6.2 Fins of Uniform Cross-Sectional Area......Page 184
3.6.3 Fin Performance......Page 190
3.6.4 Fins of Nonuniform Cross-Sectional Area......Page 193
3.6.5 Overall Surface Efficiency......Page 196
3.7 The Bioheat Equation......Page 204
3.8 Thermoelectric Power Generation......Page 208
3.9.1 Conduction Through Thin Gas Layers......Page 215
3.10 Summary......Page 216
Problems......Page 219
CHAPTER 4 Two-Dimensional, Steady-State Conduction......Page 255
4.1 Alternative Approaches......Page 256
4.2 The Method of Separation of Variables......Page 257
4.3 The Conduction Shape Factor and the Dimensionless Conduction Heat Rate......Page 261
4.4.1 The Nodal Network......Page 267
4.4.2 Finite-Difference Form of the Heat Equation......Page 268
4.4.3 The Energy Balance Method......Page 269
4.5.1 Formulation as a Matrix Equation......Page 276
4.5.2 Verifying the Accuracy of the Solution......Page 277
4.6 Summary......Page 282
Problems......Page 283
CHAPTER 5 Transient Conduction......Page 305
5.1 The Lumped Capacitance Method......Page 306
5.2 Validity of the Lumped Capacitance Method......Page 309
5.3 General Lumped Capacitance Analysis......Page 313
5.3.2 Negligible Radiation......Page 314
5.3.4 Additional Considerations......Page 315
5.4 Spatial Effects......Page 324
5.5 The Plane Wall with Convection......Page 325
5.5.2 Approximate Solution......Page 326
5.5.4 Additional Considerations......Page 328
5.6.1 Exact Solutions......Page 329
5.6.3 Total Energy Transfer......Page 330
5.6.4 Additional Considerations......Page 331
5.7 The Semi-Infinite Solid......Page 336
5.8.1 Constant Temperature Boundary Conditions......Page 343
5.8.2 Constant Heat Flux Boundary Conditions......Page 345
5.8.3 Approximate Solutions......Page 346
5.9 Periodic Heating......Page 353
5.10.1 Discretization of the Heat Equation: The Explicit Method......Page 356
5.10.2 Discretization of the Heat Equation: The Implicit Method......Page 363
5.11 Summary......Page 371
Problems......Page 372
CHAPTER 6 Introduction to Convection......Page 403
6.1.1 The Velocity Boundary Layer......Page 404
6.1.2 The Thermal Boundary Layer......Page 405
6.1.3 The Concentration Boundary Layer......Page 406
6.2.1 Heat Transfer......Page 408
6.2.2 Mass Transfer......Page 409
6.2.3 The Problem of Convection......Page 411
6.3.1 Laminar and Turbulent Velocity Boundary Layers......Page 415
6.3.2 Laminar and Turbulent Thermal and Species Concentration Boundary Layers......Page 417
6.4.1 Boundary Layer Equations for Laminar Flow......Page 420
6.4.2 Compressible Flow......Page 423
6.5.1 Boundary Layer Similarity Parameters......Page 424
6.5.2 Functional Form of the Solutions......Page 426
6.6 Physical Interpretation of the Dimensionless Parameters......Page 433
6.7 Boundary Layer Analogies......Page 435
6.7.1 The Heat and Mass Transfer Analogy......Page 436
6.7.2 Evaporative Cooling......Page 439
6.7.3 The Reynolds Analogy......Page 442
6.8 Summary......Page 443
References......Page 444
Problems......Page 445
CHAPTER 7 External Flow......Page 459
7.1 The Empirical Method......Page 461
7.2 The Flat Plate in Parallel Flow......Page 462
7.2.1 Laminar Flow over an Isothermal Plate: A Similarity Solution......Page 463
7.2.2 Turbulent Flow over an Isothermal Plate......Page 469
7.2.3 Mixed Boundary Layer Conditions......Page 470
7.2.4 Unheated Starting Length......Page 471
7.2.6 Limitations on Use of Convection Coefficients......Page 472
7.3 Methodology for a Convection Calculation......Page 473
7.4.1 Flow Considerations......Page 481
7.4.2 Convection Heat and Mass Transfer......Page 483
7.5 The Sphere......Page 491
7.6 Flow Across Banks of Tubes......Page 494
7.7.1 Hydrodynamic and Geometric Considerations......Page 503
7.7.2 Convection Heat and Mass Transfer......Page 504
7.8 Packed Beds......Page 508
7.9 Summary......Page 509
Problems......Page 512
CHAPTER 8 Internal Flow......Page 543
8.1.1 Flow Conditions......Page 544
8.1.2 The Mean Velocity......Page 545
8.1.3 Velocity Profile in the Fully Developed Region......Page 546
8.1.4 Pressure Gradient and Friction Factor in Fully Developed Flow......Page 548
8.2 Thermal Considerations......Page 549
8.2.1 The Mean Temperature......Page 550
8.2.3 Fully Developed Conditions......Page 551
8.3.1 General Considerations......Page 555
8.3.2 Constant Surface Heat Flux......Page 556
8.3 .3 Constant Surface Temperature......Page 559
8.4.1 The Fully Developed Region......Page 563
8.4.2 The Entry Region......Page 568
8.5 Convection Correlations: Turbulent Flow in Circular Tubes......Page 570
8.6 Convection Correlations: Noncircular Tubes and the Concentric Tube Annulus......Page 578
8.7 Heat Transfer Enhancement......Page 581
8.8.1 Microscale Convection in Gases (0.1 μm ≤ D[sub(h)] ≤ 100 μm)......Page 584
8.8.2 Microscale Convection in Liquids......Page 585
8.8.3 Nanoscale Convection (D[sub(h)] ≤\n 100 nm)......Page 586
8.9 Convection Mass Transfer......Page 589
8.10 Summary......Page 591
References......Page 594
Problems......Page 595
CHAPTER 9 Free Convection......Page 619
9.1 Physical Considerations......Page 620
9.2 The Governing Equations for Laminar Boundary Layers......Page 623
9.3 Similarity Considerations......Page 624
9.4 Laminar Free Convection on a Vertical Surface......Page 625
9.5 The Effects of Turbulence......Page 628
9.6 Empirical Correlations: External Free Convection Flows......Page 630
9.6.1 The Vertical Plate......Page 631
9.6.2 Inclined and Horizontal Plates......Page 634
9.6.3 The Long Horizontal Cylinder......Page 639
9.6.4 Spheres......Page 643
9.7 Free Convection Within Parallel Plate Channels......Page 644
9.7.1 Vertical Channels......Page 645
9.8.1 Rectangular Cavities......Page 647
9.8.2 Concentric Cylinders......Page 650
9.8.3 Concentric Spheres......Page 651
9.9 Combined Free and Forced Convection......Page 653
9.10 Convection Mass Transfer......Page 654
9.11 Summary......Page 655
References......Page 656
Problems......Page 657
CHAPTER 10 Boiling and Condensation......Page 679
10.1 Dimensionless Parameters in Boiling and Condensation......Page 680
10.2 Boiling Modes......Page 681
10.3.1 The Boiling Curve......Page 682
10.3.2 Modes of Pool Boiling......Page 683
10.4.1 Nucleate Pool Boiling......Page 686
10.4.2 Critical Heat Flux for Nucleate Pool Boiling......Page 688
10.4.4 Film Pool Boiling......Page 689
10.4.5 Parametric Effects on Pool Boiling......Page 690
10.5 Forced Convection Boiling......Page 695
10.5.2 Two-Phase Flow......Page 696
10.6 Condensation: Physical Mechanisms......Page 699
10.7 Laminar Film Condensation on a Vertical Plate......Page 701
10.8 Turbulent Film Condensation......Page 705
10.9 Film Condensation on Radial Systems......Page 710
10.10 Condensation in Horizontal Tubes......Page 715
10.11 Dropwise Condensation......Page 716
References......Page 717
Problems......Page 719
CHAPTER 11 Heat Exchangers......Page 731
11.1 Heat Exchanger Types......Page 732
11.2 The Overall Heat Transfer Coefficient......Page 734
11.3 Heat Exchanger Analysis: Use of the Log Mean Temperature Difference......Page 737
11.3.1 The Parallel-Flow Heat Exchanger......Page 738
11.3.2 The Counterflow Heat Exchanger......Page 740
11.3.3 Special Operating Conditions......Page 741
11.4.1 Definitions......Page 748
11.4.2 Effectiveness–NTU Relations......Page 749
11.5 Heat Exchanger Design and Performance Calculations......Page 756
11.6 Additional Considerations......Page 765
11.7 Summary......Page 773
Problems......Page 774
CHAPTER 12 Radiation: Processes and Properties......Page 793
12.1 Fundamental Concepts......Page 794
12.2 Radiation Heat Fluxes......Page 797
12.3.1 Mathematical Definitions......Page 799
12.3.2 Radiation Intensity and Its Relation to Emission......Page 800
12.3.3 Relation to Irradiation......Page 805
12.3.4 Relation to Radiosity for an Opaque Surface......Page 807
12.4 Blackbody Radiation......Page 808
12.4.1 The Planck Distribution......Page 809
12.4.3 The Stefan–Boltzmann Law......Page 810
12.4.4 Band Emission......Page 811
12.5 Emission from Real Surfaces......Page 818
12.6 Absorption, Reflection, and Transmission by Real Surfaces......Page 827
12.6.1 Absorptivity......Page 828
12.6.2 Reflectivity......Page 829
12.6.4 Special Considerations......Page 831
12.7 Kirchhoff’s Law......Page 836
12.8 The Gray Surface......Page 838
12.9 Environmental Radiation......Page 844
12.9.1 Solar Radiation......Page 845
12.9.2 The Atmospheric Radiation Balance......Page 847
12.9.3 Terrestrial Solar Irradiation......Page 849
12.10 Summary......Page 852
Problems......Page 856
CHAPTER 13 Radiation Exchange Between Surfaces......Page 887
13.1.1 The View Factor Integral......Page 888
13.1.2 View Factor Relations......Page 889
13.2 Blackbody Radiation Exchange......Page 898
13.3 Radiation Exchange Between Opaque, Diffuse, Gray Surfaces in an Enclosure......Page 902
13.3.1 Net Radiation Exchange at a Surface......Page 903
13.3.2 Radiation Exchange Between Surfaces......Page 904
13.3.3 The Two-Surface Enclosure......Page 910
13.3.4 Radiation Shields......Page 912
13.3.5 The Reradiating Surface......Page 914
13.4 Multimode Heat Transfer......Page 919
13.6.1 Volumetric Absorption......Page 922
13.6.2 Gaseous Emission and Absorption......Page 923
13.7 Summary......Page 927
References......Page 928
Problems......Page 929
CHAPTER 14 Diffusion Mass Transfer......Page 959
14.1.1 Physical Origins......Page 960
14.1.2 Mixture Composition......Page 961
14.1.3 Fick’s Law of Diffusion......Page 962
14.1.4 Mass Diffusivity......Page 963
14.2.1 Absolute and Diffusive Species Fluxes......Page 965
14.2.2 Evaporation in a Column......Page 968
14.4 Conservation of Species for a Stationary Medium......Page 973
14.4.2 The Mass Diffusion Equation......Page 974
14.4.3 Stationary Media with Specified Surface Concentrations......Page 976
14.5 Boundary Conditions and Discontinuous Concentrations at Interfaces......Page 980
14.5.2 Solubility of Gases in Liquids and Solids......Page 981
14.5.3 Catalytic Surface Reactions......Page 986
14.6 Mass Diffusion with Homogeneous Chemical Reactions......Page 988
14.7 Transient Diffusion......Page 991
14.8 Summary......Page 997
Problems......Page 998
APPENDIX A: Thermophysical Properties of Matter......Page 1007
APPENDIX B: Mathematical Relations and Functions......Page 1039
APPENDIX C: Thermal Conditions Associated with Uniform Energy Generation in One-Dimensional, Steady-State Systems......Page 1045
APPENDIX D: The Gauss–Seidel Method......Page 1051
APPENDIX E: The Convection Transfer Equations......Page 1053
E.2 Newton’s Second Law of Motion......Page 1054
E.3 Conservation of Energy......Page 1055
E.4 Conservation of Species......Page 1056
APPENDIX F: Boundary Layer Equations for Turbulent Flow......Page 1057
APPENDIX G: An Integral Laminar Boundary Layer Solution for Parallel Flow over a Flat Plate......Page 1061
Index......Page 1065