Heat transfer

Table of Contents......Page 6
Preface......Page 18
Acknowledgments......Page 20
Study Guide......Page 22
Nomenclature......Page 26
1.1.2 Thermal Conductivity......Page 37
1.2.2 The Plane Wall......Page 41
References (E23)......Page 0
1.2.3 The Resistance Concept......Page 45
1.2.4 Resistance to Radial Conduction through a Cylinder......Page 46
1.2.5 Resistance to Radial Conduction through a Sphere......Page 47
1.2.6 Other Resistance Formulae......Page 49
1.2.6.2 Contact Resistance......Page 50
1.2.6.3 Radiation Resistance......Page 52
1.3.2 Uniform Thermal Energy Generation in a Plane Wall......Page 60
1.3.3 Uniform Thermal Energy Generation in Radial Geometries......Page 65
1.3.4 Spatially Non-Uniform Generation......Page 73
1.4.1 Introduction......Page 80
1.4.2 Numerical Solutions in EES......Page 81
1.4.3 Temperature-Dependent Thermal Conductivity......Page 91
1.4.4 Alternative Rate Models......Page 96
1.5.1 Introduction......Page 104
1.5.2 Numerical Solutions in Matrix Format......Page 105
1.5.3 Implementing a Numerical Solution in MATLAB......Page 107
1.5.4 Functions......Page 113
1.5.5 Sparse Matrices......Page 116
1.5.6 Temperature-Dependent Properties......Page 118
1.6.2 The Extended Surface Approximation......Page 128
1.6.3 Analytical Solution......Page 131
1.6.4 Fin Behavior......Page 139
1.6.5 Fin Efficiency and Resistance......Page 141
1.6.6 Finned Surfaces......Page 149
1.7.2 Additional Thermal Loads......Page 158
1.7.3 Moving Extended Surfaces......Page 169
1.8.2 Series Solutions......Page 175
1.8.3 Bessel Functions......Page 178
1.8.4 Rules for Using Bessel Functions......Page 186
1.9.1 Introduction......Page 200
Problems......Page 221
References......Page 237
2.1 Shape Factors......Page 238
2.2.1 Introduction......Page 243
2.2.2 Separation of Variables......Page 244
2.2.2.1 Requirements for Using Separation of Variables......Page 245
2.2.2.2 Separate the Variables......Page 247
2.2.2.3 Solve the Eigenproblem......Page 248
2.2.2.4 Solve the Non-Homogeneous Problem for Each Eigenvalue......Page 249
2.2.2.5 Obtain Solution for Each Eigenvalue......Page 250
2.2.2.6 Create the Series Solution and Enforce the Remaining Boundary Conditions......Page 251
2.2.2.7 Summary of Steps......Page 258
2.2.3 Simple Boundary Condition Transformations......Page 260
2.4.1 Introduction......Page 278
2.4.2 Superposition for 2-D Problems......Page 281
2.5.1 Introduction......Page 286
2.5.2 Numerical Solutions with EES......Page 287
2.6.2 Numerical Solutions with MATLAB......Page 296
2.6.3 Numerical Solution by Gauss-Seidel Iteration......Page 304
2.8.1 Introduction......Page 305
2.8.2 Isothermal and Adiabatic Resistance Limits......Page 308
2.8.3 Average Area and Average Length Resistance Limits......Page 311
2.9.1 Effective Thermal Conductivity......Page 314
Problems......Page 326
References......Page 337
3.1.2 The Lumped Capacitance Assumption......Page 338
3.1.3 The Lumped Capacitance Problem......Page 339
3.1.4 The Lumped Capacitance Time Constant......Page 340
3.2.2 Numerical Integration Techniques......Page 353
3.2.2.1 Euler's Method......Page 354
3.2.2.2 Heun's Method......Page 358
3.2.2.3 Runge-Kutta Fourth Order Method......Page 362
3.2.2.4 Fully Implicit Method......Page 364
3.2.2.5 Crank-Nicolson Method......Page 366
3.2.2.6 Adaptive Step-Size and EES' Integral Command......Page 368
3.2.2.7 MATLAB's Ordinary Differential Equation Solvers......Page 371
3.3.2 The Diffusive Time Constant......Page 384
3.3.3 The Self-Similar Solution......Page 390
3.3.4 Solution to other Semi-Infinite......Page 397
3.4.1 Introduction......Page 405
3.4.2 The Laplace Transformation......Page 406
3.4.2.2 Laplace Transformations with Maple......Page 407
3.4.3 The Inverse Laplace Transform......Page 408
3.4.3.1 Inverse Laplace Transform with Tables and the Method of Partial Fractions......Page 409
3.4.3.2 Inverse Laplace Transformation with Maple......Page 412
3.4.4 Properties of the Laplace Transformation......Page 414
3.4.5 Solution to Lumped Capacitance Problems......Page 416
3.4.6 Solution to Semi-Infinite Body Problems......Page 422
3.5.1 Introduction......Page 431
3.5.2.1 The Plane Wall......Page 432
3.5.2.2 The Cylinder......Page 437
3.5.2.3 The Sphere......Page 439
3.5.3 Separation of Variables Solutions in Cartesian Coordinates......Page 444
3.5.3.1 Requirements for Using Separation of Variables......Page 445
3.5.3.2 Separate the Variables......Page 446
3.5.3.3 Solve the Eigenproblem......Page 447
3.5.3.4 Solve the Non-Homogeneous Problem for Each Eigenvalue......Page 449
3.5.3.6 Create the Series Solution and Enforce the Initial Condition......Page 450
3.5.3.7 Limit Behaviors of the Separation of Variables Solution......Page 453
3.5.4 Separation of Variables Solutions in Cylindrical Coordinates......Page 463
3.8.1 Introduction......Page 464
3.8.2 Transient Conduction in a Plane Wall......Page 465
3.8.2.1 Euler's Method......Page 468
3.8.2.2 Fully Implicit Method......Page 474
3.8.2.3 Heun's Method......Page 478
3.8.2.4 Runge-Kutta 4th Order Method......Page 481
3.8.2.5 Crank-Nicolson Method......Page 485
3.8.2.6 EES' Integral Command......Page 488
3.8.2.7 MATLAB's Ordinary Differential Equation Solvers......Page 489
3.8.3 Temperature-Dependent Properties......Page 499
3.9 Reduction of Multi-Dimensional Transient Problems......Page 504
Problems......Page 505
References......Page 518
4.1.1 Introduction......Page 519
4.1.2 The Laminar Boundary Layer......Page 520
4.1.2.1 A Conceptual Model of the Laminar Boundary Layer......Page 521
4.1.2.2 A Conceptual Model of the Friction Coefficient and Heat Transfer Coefficient......Page 524
4.1.2.3 The Reynolds Analogy......Page 528
4.1.3 Local and Integrated Quantities......Page 530
4.2.2.1 The Continuity Equation......Page 531
4.2.2.2 The Momentum Conservation Equations......Page 532
4.2.2.3 The Thermal Energy Conservation Equation......Page 534
4.2.3.1 The Continuity Equation......Page 536
4.2.3.2 The x-Momentum Equation......Page 537
4.2.3.3 The y-Momentum Equation......Page 538
4.2.3.4 The Thermal Energy Equation......Page 539
4.3.1 Introduction......Page 542
4.3.2.1 The Dimensionless Continuity Equation......Page 544
4.3.2.3 The Dimensionless Thermal Energy Equation in the Boundary Layer......Page 545
4.3.3.1 The Friction and Drag Coefficients......Page 547
4.3.3.2 The Nusselt Number......Page 549
4.3.4 The Reynolds Analogy (Revisited)......Page 556
4.4.1 Introduction......Page 557
4.4.2.2 The Similarity Variables......Page 558
4.4.2.3 The Problem Transformation......Page 562
4.4.2.4 Numerical Solution......Page 566
4.4.3.1 The Problem Statement......Page 571
4.4.3.3 The Problem Transformation......Page 572
4.4.3.4 Numerical Solution......Page 574
4.5.1 Introduction......Page 578
4.5.2 A Conceptual Model of the Turbulent Boundary Layer......Page 579
4.6.1 Introduction......Page 584
4.6.2 The Averaging Process......Page 585
4.6.2.1 The Reynolds Averaged Continuity Equation......Page 586
4.6.2.2 The Reynolds Averaged Momentum Equation......Page 587
4.6.2.3 The Reynolds Averaged Thermal Energy Equation......Page 590
4.7.1 Introduction......Page 592
4.7.2 Inner Variables......Page 593
4.7.3 Eddy Diffusivity of Momentum......Page 596
4.7.4 The Mixing Length Model......Page 597
4.7.5 The Universal Velocity Profile......Page 598
4.7.6 Eddy Diffusivity of Momentum Models......Page 601
4.7.7 Wake Region......Page 602
4.7.8 Eddy Diffusivity of Heat Transfer......Page 603
4.7.9 The Thermal Law of the Wall......Page 604
4.8.2.1 Derivation of the Integral Form of the Momentum Equation......Page 607
4.8.2.2 Application of the Integral Form of the Momentum Equation......Page 611
4.8.3.1 Derivation of the Integral Form of the Energy Equation......Page 620
4.8.3.2 Application of the Integral Form of the Energy Equation......Page 623
4.8.4 Integral Solutions for Turbulent Flows......Page 627
4.9.2.1 Friction Coefficient......Page 629
4.9.2.2 Nusselt Number......Page 634
4.9.2.4 Constant Heat Flux......Page 642
4.9.2.5 Flow over a Rough Plate......Page 643
4.9.3 Flow across a Cylinder......Page 645
4.9.3.1 Drag Coefficient......Page 647
4.9.3.2 Nusselt Number......Page 649
4.9.3.4 Non-Circular Extrusions......Page 653
4.9.4 Flow Past a Sphere......Page 654
Problems......Page 660
References......Page 669
5.1.2 Momentum Considerations......Page 671
5.1.2.1 The Mean Velocity......Page 673
5.1.2.3 Turbulent Internal Flow......Page 674
5.1.2.4 The Turbulent Hydrodynamic Entry Length......Page 676
5.1.2.5 The Friction Factor......Page 677
5.1.3.1 The Mean Temperature......Page 680
5.1.3.2 The Heat Transfer Coefficient and Nusselt Number......Page 681
5.1.3.3 The Laminar Thermal Entry Length......Page 682
5.1.3.4 Turbulent Internal Flow......Page 684
5.2.1 Introduction......Page 685
5.2.3 Friction Factor......Page 686
5.2.3.1 Laminar Flow......Page 687
5.2.3.2 Turbulent Flow......Page 690
5.2.3.3 EES' Internal Flow Convection Library......Page 692
5.2.4 The Nusselt Number......Page 697
5.2.4.1 Laminar Flow......Page 698
5.2.4.2 Turbulent Flow......Page 703
5.3.2 The Energy Balance......Page 707
5.3.3 Prescribed Heat Flux......Page 709
5.3.4.1 Constant Wall Temperature......Page 710
5.3.5 Prescribed External Temperature......Page 711
5.4.2 The Momentum Equation......Page 722
5.4.2.1 Fully Developed Flow between Parallel Plates......Page 723
5.4.3 The Thermal Energy Equation......Page 725
5.4.3.1 Fully Developed Flow through a Round Tube with a Constant Heat Flux......Page 727
5.4.3.2 Fully Developed Flow between Parallel Plates with a Constant Heat Flux......Page 731
5.5.1 Introduction......Page 733
5.5.2 Hydrodynamically Fully Developed Laminar Flow......Page 734
5.5.2.1 EES' Integral Command......Page 738
5.5.2.2 The Euler Technique......Page 740
5.5.2.3 The Crank-Nicolson Technique......Page 742
5.5.2.4 MATLAB's Ordinary Differential Equation Solvers......Page 746
5.5.3 Hydrodynamically Fully Developed Turbulent Flow......Page 748
Problems......Page 759
References......Page 770
6.1.2 Dimensionless Parameters for Natural Convection......Page 771
6.1.2.1 Identification from Physical Reasoning......Page 772
6.1.2.2 Identification from the Governing Equations......Page 775
6.2.2 Plate......Page 777
6.2.2.1 Heated or Cooled Vertical Plate......Page 778
6.2.2.2 Horizontal Heated Upward Facing or Cooled Downward Facing Plate......Page 780
6.2.2.3 Horizontal Heated Downward Facing or Cooled Upward Facing Plate......Page 781
6.2.2.4 Plate at an Arbitrary Tilt Angle......Page 783
6.2.3 Sphere......Page 788
6.2.4.1 Horizontal Cylinder......Page 793
6.2.4.2 Vertical Cylinder......Page 794
6.2.5 Open Cavity......Page 796
6.2.5.1 Vertical Parallel Plates......Page 797
6.2.6 Enclosures......Page 802
6.2.7 Combined Free and Forced Convection......Page 804
6.4 Integral Solution......Page 808
Problems......Page 809
References......Page 813
7.1 Introduction......Page 814
7.2.1 Introduction......Page 815
7.2.2 The Boiling Curve......Page 816
7.2.3 Pool Boiling Correlations......Page 820
7.3.1 Introduction......Page 826
7.3.2 Flow Boiling Correlations......Page 827
7.4.1 Introduction......Page 834
7.4.2 Solution for Inertia-Free Film Condensation on a Vertical Wall......Page 835
7.4.3.1 Vertical Wall......Page 841
7.4.3.2 Horizontal, Downward Facing Plate......Page 846
7.4.3.6 Single Horizontal Finned Tube......Page 847
7.5.1 Introduction......Page 848
7.5.2 Flow Condensation Correlations......Page 849
Problems......Page 851
References......Page 857
8.1.2 Applications of Heat Exchangers......Page 859
8.1.3 Heat Exchanger Classifications and Flow Paths......Page 860
8.1.4 Overall Energy Balances......Page 864
8.1.5.1 Fouling Resistance......Page 867
8.1.6 Compact Heat Exchanger Correlations......Page 874
8.2.1 Introduction......Page 877
8.2.2 LMTD Method for Counter-Flow and Parallel-Flow Heat Exchangers......Page 878
8.2.3 LMTD Method for Shell-and-Tube and Cross-Flow Heat Exchangers......Page 883
8.3.1 Introduction......Page 887
8.3.2 The Maximum Heat Transfer Rate......Page 888
8.3.3 Heat Exchanger Effectiveness......Page 889
8.3.4 Further Discussion of Heat Exchanger Effectiveness......Page 897
8.3.4.1 Behavior as C_R Approaches Zero......Page 898
8.3.4.2 Behavior as NTU Approaches Zero......Page 899
8.3.4.3 Behavior as NTU Becomes Infinite......Page 900
8.3.4.4 Heat Exchanger Design......Page 901
8.4.2 Pinch Point Analysis for a Single Heat Exchanger......Page 903
8.4.3 Pinch Point Analysis for a Heat Exchanger Network......Page 908
8.5.2 Sub-Heat Exchanger Model for Phase-Change......Page 912
8.6.2 Numerical Integration of Governing Equations......Page 924
8.6.2.1 Parallel-Flow Configuration......Page 925
8.6.2.2 Counter-Flow Configuration......Page 932
8.6.3.1 Parallel-Flow Configuration......Page 933
8.6.4 Solution with Axial Conduction......Page 938
8.7.1 Introduction......Page 939
8.7.2 Approximate Models for Axial Conduction......Page 941
8.7.2.2 Approximate Model at High lambda......Page 943
8.7.2.3 Temperature Jump Model......Page 945
8.8.1 Introduction......Page 947
8.8.2 Modeling Perforated Plate Heat Exchangers......Page 949
8.9.1 Introduction......Page 955
8.9.2.1 Both Fluids Unmixed with Uniform Properties......Page 956
8.9.2.2 Both Fluids Unmixed with Temperature-Dependent Properties......Page 963
8.9.2.4 Both Fluids Mixed (E21)......Page 972
8.10.1 Introduction......Page 973
8.10.2 Governing Equations......Page 975
8.10.3.1 Utilization and Number of Transfer Units......Page 978
8.10.3.2 Regenerator Effectiveness......Page 980
8.10.4 Correlations for Regenerator Matrices......Page 984
8.10.4.1 Packed Bed of Spheres......Page 986
8.10.4.2 Screens......Page 987
8.10.4.3 Triangular Passages......Page 988
Problems......Page 998
References......Page 1009
Problems......Page 1010
10.1.1 Radiation......Page 1015
10.1.2 The Electromagnetic Spectrum......Page 1016
10.2.1 Introduction......Page 1017
10.2.2.1 Planck's Law......Page 1018
10.2.2.2 Blackbody Emission in Specified Wavelength Bands......Page 1021
10.3.2 View Factors......Page 1025
10.3.2.1 The Enclosure Rule......Page 1026
10.3.2.2 Reciprocity......Page 1027
10.3.2.4 The Crossed and Uncrossed Strings Method......Page 1028
10.3.2.5 View Factor Library......Page 1032
10.3.3.1 The Space Resistance......Page 1037
10.3.3.2 N-Surface Solutions......Page 1042
10.3.4 Radiation Exchange between Non-Isothermal Surfaces......Page 1045
10.4.2.1 Intensity......Page 1048
10.4.2.3 Hemispherical Emissivity......Page 1050
10.4.2.4 Total Hemispherical Emissivity......Page 1051
10.4.2.7 The Semi-Gray Surface......Page 1052
10.4.3 Reflectivity, Absorptivity, and Transmittivity......Page 1054
10.4.3.1 Diffuse and Specular Surfaces......Page 1055
10.4.3.3 Kirchoff's Law......Page 1056
10.4.3.4 Total Hemispherical Values......Page 1058
10.4.3.7 The Semi-Gray Surface......Page 1059
10.5.1 Introduction......Page 1063
10.5.2 Radiosity......Page 1064
10.5.3 Gray Surface Radiation Calculations......Page 1065
10.5.4 The F with circumflex Parameter......Page 1079
10.5.5 Radiation Exchange for Semi-Gray Surfaces......Page 1086
10.6.2 When is Radiation Important?......Page 1091
10.6.3 Multi-Mode Problems......Page 1093
10.7.2 Determination of View Factors with the Monte Carlo Method......Page 1094
10.7.2.2 Select the Direction of the Ray......Page 1096
10.7.2.3 Determine Whether the Ray from Surface 1 Strikes Surface 2......Page 1097
10.7.3 Radiation Heat Transfer Determined by the Monte Carlo Method......Page 1104
Problems......Page 1113
References......Page 1124
Appendices......Page 1125
INDEX......Page 1127