HEAT TRANSFER SECOND
EDITION
A Practical Approach
YUNUS A. CENGEL
, CONTENTS
Preface xviii
Nomenclature xxvi
CHAPTER TWO
HEAT CONDUCTION EQUATION 61
2-1 Introduction 62
CHAPTER ONE Steady versus Transient Heat Transfer 63
Multidimensional Heat Transfer 64
BASICS OF HEAT TRANSFER 1 Heat Generation 66
2-2 One-Dimensional
1-1 Thermodynamics and Heat Transfer 2
Heat Conduction Equation 68
Application Areas of Heat Transfer 3
Heat Conduction Equation in a Large Plane Wall 68
Historical Background 3
Heat Conduction Equation in a Long Cylinder 69
1-2 Engineering Heat Transfer 4 Heat Conduction Equation in a Sphere 71
Combined One-Dimensional
Modeling in Heat Transfer 5 Heat Conduction Equation 72
1-3 Heat and Other Forms of Energy 6 2-3 General Heat Conduction Equation 74
Specific Heats of Gases, Liquids, and Solids 7 Rectangular Coordinates 74
Energy Transfer 9 Cylindrical Coordinates 75
Spherical Coordinates 76
1-4 The First Law of Thermodynamics 11
2-4 Boundary and Initial Conditions 77
Energy Balance for Closed Systems (Fixed Mass) 12
Energy Balance for Steady-Flow Systems 12 1 Specified Temperature Boundary Condition 78
Surface Energy Balance 13 2 Specified Heat Flux Boundary Condition 79
3 Convection Boundary Condition 81
1-5 Heat Transfer Mechanisms 17 4 Radiation Boundary Condition 82
5 Interface Boundary Conditions 83
1-6 Conduction 17 6 Generalized Boundary Conditions 84
Thermal Conductivity 19 2-5 Solution of Steady One-Dimensional
Thermal Diffusivity 23
Heat Conduction Problems 86
1-7 Convection 25 2-6 Heat Generation in a Solid 97
1-8 Radiation 27 2-7 Variable Thermal Conductivity, k(T) 104
1-9 Simultaneous Heat Transfer Mechanisms 30 Topic of Special Interest:
A Brief Review of Differential Equations 107
1-10 Problem-Solving Technique 35 Summary 111
References and Suggested Reading 112
A Remark on Significant Digits 37 Problems 113
Engineering Software Packages 38
Engineering Equation Solver (EES) 39
Heat Transfer Tools (HTT) 39 CHAPTER THREE
Topic of Special Interest:
Thermal Comfort 40 STEADY HEAT CONDUCTION 127
Summary 46
References and Suggested Reading 47
3-1 Steady Heat Conduction in Plane Walls 128
Problems 47 The Thermal Resistance Concept 129
vii
, viii
CONTENTS
Thermal Resistance Network 131 4 Complications 268
Multilayer Plane Walls 133 5 Human Nature 268
3-2 Thermal Contact Resistance 138 5-2 Finite Difference Formulation of
3-3 Generalized Thermal Resistance Networks 143 Differential Equations 269
3-4 Heat Conduction in Cylinders and Spheres 146 5-3 One-Dimensional Steady Heat Conduction 272
Multilayered Cylinders and Spheres 148 Boundary Conditions 274
3-5 Critical Radius of Insulation 153 5-4 Two-Dimensional
Steady Heat Conduction 282
3-6 Heat Transfer from Finned Surfaces 156
Boundary Nodes 283
Fin Equation 157 Irregular Boundaries 287
Fin Efficiency 160
Fin Effectiveness 163 5-5 Transient Heat Conduction 291
Proper Length of a Fin 165 Transient Heat Conduction in a Plane Wall 293
3-7 Heat Transfer in Common Configurations 169 Two-Dimensional Transient Heat Conduction 304
Topic of Special Interest:
Topic of Special Interest: Controlling Numerical Error 309
Heat Transfer Through Walls and Roofs 175 Summary 312
Summary 185 References and Suggested Reading 314
References and Suggested Reading 186 Problems 314
Problems 187
CHAPTER FOUR
TRANSIENT HEAT CONDUCTION 209 CHAPTER SIX
FUNDAMENTALS OF CONVECTION 333
4-1 Lumped System Analysis 210
Criteria for Lumped System Analysis 211 6-1 Physical Mechanism on Convection 334
Some Remarks on Heat Transfer in Lumped Systems 213
Nusselt Number 336
4-2 Transient Heat Conduction in 6-2 Classification of Fluid Flows 337
Large Plane Walls, Long Cylinders,
Viscous versus Inviscid Flow 337
and Spheres with Spatial Effects 216
Internal versus External Flow 337
4-3 Transient Heat Conduction in Compressible versus Incompressible Flow 337
Semi-Infinite Solids 228 Laminar versus Turbulent Flow 338
Natural (or Unforced) versus Forced Flow 338
4-4 Transient Heat Conduction in Steady versus Unsteady (Transient) Flow 338
Multidimensional Systems 231 One-, Two-, and Three-Dimensional Flows 338
Topic of Special Interest: 6-3 Velocity Boundary Layer 339
Refrigeration and Freezing of Foods 239
Summary 250 Surface Shear Stress 340
References and Suggested Reading 251 6-4 Thermal Boundary Layer 341
Problems 252
Prandtl Number 341
6-5 Laminar and Turbulent Flows 342
CHAPTER FIVE Reynolds Number 343
NUMERICAL METHODS 6-6 Heat and Momentum Transfer
IN HEAT CONDUCTION 265 in Turbulent Flow 343
6-7 Derivation of Differential
5-1 Why Numerical Methods? 266 Convection Equations 345
1 Limitations 267 Conservation of Mass Equation 345
2 Better Modeling 267 Conservation of Momentum Equations 346
3 Flexibility 268 Conservation of Energy Equation 348
, ix
CONTENTS
6-8 Solutions of Convection Equations 8-4 General Thermal Analysis 426
for a Flat Plate 352 Constant Surface Heat Flux (q·s constant) 427
The Energy Equation 354 Constant Surface Temperature (Ts constant) 428
6-9 Nondimensionalized Convection 8-5 Laminar Flow in Tubes 431
Equations and Similarity 356 Pressure Drop 433
Temperature Profile and the Nusselt Number 434
6-10 Functional Forms of Friction and
Constant Surface Heat Flux 435
Convection Coefficients 357 Constant Surface Temperature 436
6-11 Analogies between Momentum Laminar Flow in Noncircular Tubes 436
and Heat Transfer 358 Developing Laminar Flow in the Entrance Region 436
Summary 361 8-6 Turbulent Flow in Tubes 441
References and Suggested Reading 362 Rough Surfaces 442
Problems 362 Developing Turbulent Flow in the Entrance Region 443
Turbulent Flow in Noncircular Tubes 443
Flow through Tube Annulus 444
Heat Transfer Enhancement 444
CHAPTER SEVEN Summary 449
References and Suggested Reading 450
EXTERNAL FORCED CONVECTION 367 Problems 452
7-1 Drag Force and Heat Transfer
in External Flow 368 CHAPTER NINE
Friction and Pressure Drag 368
Heat Transfer 370
NATURAL CONVECTION 459
7-2 Parallel Flow over Flat Plates 371 9-1 Physical Mechanism of
Friction Coefficient 372 Natural Convection 460
Heat Transfer Coefficient 373
Flat Plate with Unheated Starting Length 375
9-2 Equation of Motion and
Uniform Heat Flux 375 the Grashof Number 463
7-3 Flow across Cylinders and Spheres 380 The Grashof Number 465
Effect of Surface Roughness 382 9-3 Natural Convection over Surfaces 466
Heat Transfer Coefficient 384 Vertical Plates (Ts constant) 467
7-4 Flow across Tube Banks 389 Vertical Plates (q·s constant) 467
Vertical Cylinders 467
Pressure Drop 392 Inclined Plates 467
Topic of Special Interest: Horizontal Plates 469
Reducing Heat Transfer through Surfaces 395 Horizontal Cylinders and Spheres 469
Summary 406
References and Suggested Reading 407 9-4 Natural Convection from
Problems 408 Finned Surfaces and PCBs 473
Natural Convection Cooling of Finned Surfaces
(Ts constant) 473
Natural Convection Cooling of Vertical PCBs
CHAPTER EIGHT (q·s constant) 474
Mass Flow Rate through the Space between Plates 475
INTERNAL FORCED CONVECTION 419
9-5 Natural Convection inside Enclosures 477
8-1 Introduction 420 Effective Thermal Conductivity 478
Horizontal Rectangular Enclosures 479
8-2 Mean Velocity and Mean Temperature 420 Inclined Rectangular Enclosures 479
Laminar and Turbulent Flow in Tubes 422 Vertical Rectangular Enclosures 480
Concentric Cylinders 480
8-3 The Entrance Region 423 Concentric Spheres 481
Entry Lengths 425 Combined Natural Convection and Radiation 481
EDITION
A Practical Approach
YUNUS A. CENGEL
, CONTENTS
Preface xviii
Nomenclature xxvi
CHAPTER TWO
HEAT CONDUCTION EQUATION 61
2-1 Introduction 62
CHAPTER ONE Steady versus Transient Heat Transfer 63
Multidimensional Heat Transfer 64
BASICS OF HEAT TRANSFER 1 Heat Generation 66
2-2 One-Dimensional
1-1 Thermodynamics and Heat Transfer 2
Heat Conduction Equation 68
Application Areas of Heat Transfer 3
Heat Conduction Equation in a Large Plane Wall 68
Historical Background 3
Heat Conduction Equation in a Long Cylinder 69
1-2 Engineering Heat Transfer 4 Heat Conduction Equation in a Sphere 71
Combined One-Dimensional
Modeling in Heat Transfer 5 Heat Conduction Equation 72
1-3 Heat and Other Forms of Energy 6 2-3 General Heat Conduction Equation 74
Specific Heats of Gases, Liquids, and Solids 7 Rectangular Coordinates 74
Energy Transfer 9 Cylindrical Coordinates 75
Spherical Coordinates 76
1-4 The First Law of Thermodynamics 11
2-4 Boundary and Initial Conditions 77
Energy Balance for Closed Systems (Fixed Mass) 12
Energy Balance for Steady-Flow Systems 12 1 Specified Temperature Boundary Condition 78
Surface Energy Balance 13 2 Specified Heat Flux Boundary Condition 79
3 Convection Boundary Condition 81
1-5 Heat Transfer Mechanisms 17 4 Radiation Boundary Condition 82
5 Interface Boundary Conditions 83
1-6 Conduction 17 6 Generalized Boundary Conditions 84
Thermal Conductivity 19 2-5 Solution of Steady One-Dimensional
Thermal Diffusivity 23
Heat Conduction Problems 86
1-7 Convection 25 2-6 Heat Generation in a Solid 97
1-8 Radiation 27 2-7 Variable Thermal Conductivity, k(T) 104
1-9 Simultaneous Heat Transfer Mechanisms 30 Topic of Special Interest:
A Brief Review of Differential Equations 107
1-10 Problem-Solving Technique 35 Summary 111
References and Suggested Reading 112
A Remark on Significant Digits 37 Problems 113
Engineering Software Packages 38
Engineering Equation Solver (EES) 39
Heat Transfer Tools (HTT) 39 CHAPTER THREE
Topic of Special Interest:
Thermal Comfort 40 STEADY HEAT CONDUCTION 127
Summary 46
References and Suggested Reading 47
3-1 Steady Heat Conduction in Plane Walls 128
Problems 47 The Thermal Resistance Concept 129
vii
, viii
CONTENTS
Thermal Resistance Network 131 4 Complications 268
Multilayer Plane Walls 133 5 Human Nature 268
3-2 Thermal Contact Resistance 138 5-2 Finite Difference Formulation of
3-3 Generalized Thermal Resistance Networks 143 Differential Equations 269
3-4 Heat Conduction in Cylinders and Spheres 146 5-3 One-Dimensional Steady Heat Conduction 272
Multilayered Cylinders and Spheres 148 Boundary Conditions 274
3-5 Critical Radius of Insulation 153 5-4 Two-Dimensional
Steady Heat Conduction 282
3-6 Heat Transfer from Finned Surfaces 156
Boundary Nodes 283
Fin Equation 157 Irregular Boundaries 287
Fin Efficiency 160
Fin Effectiveness 163 5-5 Transient Heat Conduction 291
Proper Length of a Fin 165 Transient Heat Conduction in a Plane Wall 293
3-7 Heat Transfer in Common Configurations 169 Two-Dimensional Transient Heat Conduction 304
Topic of Special Interest:
Topic of Special Interest: Controlling Numerical Error 309
Heat Transfer Through Walls and Roofs 175 Summary 312
Summary 185 References and Suggested Reading 314
References and Suggested Reading 186 Problems 314
Problems 187
CHAPTER FOUR
TRANSIENT HEAT CONDUCTION 209 CHAPTER SIX
FUNDAMENTALS OF CONVECTION 333
4-1 Lumped System Analysis 210
Criteria for Lumped System Analysis 211 6-1 Physical Mechanism on Convection 334
Some Remarks on Heat Transfer in Lumped Systems 213
Nusselt Number 336
4-2 Transient Heat Conduction in 6-2 Classification of Fluid Flows 337
Large Plane Walls, Long Cylinders,
Viscous versus Inviscid Flow 337
and Spheres with Spatial Effects 216
Internal versus External Flow 337
4-3 Transient Heat Conduction in Compressible versus Incompressible Flow 337
Semi-Infinite Solids 228 Laminar versus Turbulent Flow 338
Natural (or Unforced) versus Forced Flow 338
4-4 Transient Heat Conduction in Steady versus Unsteady (Transient) Flow 338
Multidimensional Systems 231 One-, Two-, and Three-Dimensional Flows 338
Topic of Special Interest: 6-3 Velocity Boundary Layer 339
Refrigeration and Freezing of Foods 239
Summary 250 Surface Shear Stress 340
References and Suggested Reading 251 6-4 Thermal Boundary Layer 341
Problems 252
Prandtl Number 341
6-5 Laminar and Turbulent Flows 342
CHAPTER FIVE Reynolds Number 343
NUMERICAL METHODS 6-6 Heat and Momentum Transfer
IN HEAT CONDUCTION 265 in Turbulent Flow 343
6-7 Derivation of Differential
5-1 Why Numerical Methods? 266 Convection Equations 345
1 Limitations 267 Conservation of Mass Equation 345
2 Better Modeling 267 Conservation of Momentum Equations 346
3 Flexibility 268 Conservation of Energy Equation 348
, ix
CONTENTS
6-8 Solutions of Convection Equations 8-4 General Thermal Analysis 426
for a Flat Plate 352 Constant Surface Heat Flux (q·s constant) 427
The Energy Equation 354 Constant Surface Temperature (Ts constant) 428
6-9 Nondimensionalized Convection 8-5 Laminar Flow in Tubes 431
Equations and Similarity 356 Pressure Drop 433
Temperature Profile and the Nusselt Number 434
6-10 Functional Forms of Friction and
Constant Surface Heat Flux 435
Convection Coefficients 357 Constant Surface Temperature 436
6-11 Analogies between Momentum Laminar Flow in Noncircular Tubes 436
and Heat Transfer 358 Developing Laminar Flow in the Entrance Region 436
Summary 361 8-6 Turbulent Flow in Tubes 441
References and Suggested Reading 362 Rough Surfaces 442
Problems 362 Developing Turbulent Flow in the Entrance Region 443
Turbulent Flow in Noncircular Tubes 443
Flow through Tube Annulus 444
Heat Transfer Enhancement 444
CHAPTER SEVEN Summary 449
References and Suggested Reading 450
EXTERNAL FORCED CONVECTION 367 Problems 452
7-1 Drag Force and Heat Transfer
in External Flow 368 CHAPTER NINE
Friction and Pressure Drag 368
Heat Transfer 370
NATURAL CONVECTION 459
7-2 Parallel Flow over Flat Plates 371 9-1 Physical Mechanism of
Friction Coefficient 372 Natural Convection 460
Heat Transfer Coefficient 373
Flat Plate with Unheated Starting Length 375
9-2 Equation of Motion and
Uniform Heat Flux 375 the Grashof Number 463
7-3 Flow across Cylinders and Spheres 380 The Grashof Number 465
Effect of Surface Roughness 382 9-3 Natural Convection over Surfaces 466
Heat Transfer Coefficient 384 Vertical Plates (Ts constant) 467
7-4 Flow across Tube Banks 389 Vertical Plates (q·s constant) 467
Vertical Cylinders 467
Pressure Drop 392 Inclined Plates 467
Topic of Special Interest: Horizontal Plates 469
Reducing Heat Transfer through Surfaces 395 Horizontal Cylinders and Spheres 469
Summary 406
References and Suggested Reading 407 9-4 Natural Convection from
Problems 408 Finned Surfaces and PCBs 473
Natural Convection Cooling of Finned Surfaces
(Ts constant) 473
Natural Convection Cooling of Vertical PCBs
CHAPTER EIGHT (q·s constant) 474
Mass Flow Rate through the Space between Plates 475
INTERNAL FORCED CONVECTION 419
9-5 Natural Convection inside Enclosures 477
8-1 Introduction 420 Effective Thermal Conductivity 478
Horizontal Rectangular Enclosures 479
8-2 Mean Velocity and Mean Temperature 420 Inclined Rectangular Enclosures 479
Laminar and Turbulent Flow in Tubes 422 Vertical Rectangular Enclosures 480
Concentric Cylinders 480
8-3 The Entrance Region 423 Concentric Spheres 481
Entry Lengths 425 Combined Natural Convection and Radiation 481
