Heat Transfer Explained A Computational Perspective

About the Author xi

Preface xiii

Acknowledgments xv

1 Introduction 1

1.1 What Is Heat Transfer? 1

1.2 Three Basic Heat Transfer Modes 2

1.3 Relations to Thermodynamics 6

1.3.1 The First Law of Thermodynamics 6

1.3.2 Zeroth Law and Second Law 10

1.4 A Brief Review of the Prerequisite 11

1.4.1 Coordinate Systems 11

1.4.2 Units and Dimensions 11

1.4.3 Integration 12

1.4.4 Solving Second-order Ordinary Differential Equations 13

1.4.5 The Problem Solution Procedure 15

1.5 Summary 15

Bibliography 16

2 Introduction to Conduction 17

2.1 Thermal Conductivity 17

2.2 General Description of Conduction 20

2.2.1 General Form of Fourier's Law 20

2.2.2 Derivation of Heat Equation 22

2.2.3 Boundary Conditions and Initial Conditions 24

2.3 General Solution Procedure to 1D Steady-state Heat Equation 27

2.4 Steady-state Conduction with No Internal Source: The Thermal Resistance Network Method 28

2.5 Summary 33

Bibliography 33

3 Multidimensional Conduction 35

3.1 Conduction Beyond Steady-state One-dimensional Problems 35

3.1.1 Zero-dimensional Transient Conduction: The Lumped Capacitance Method 36

3.1.2 Steady-state 2D Conduction 40

3.1.3 Transient 1D Conduction Without Source/Sink 41

3.1.4 Transient 3D Conduction with Moving Source 44

3.1.5 A Note on Analytical Solutions 45

3.2 Numerical Methods 45

3.2.1 Approximation to Derivatives 46

3.2.2 Finite Volume Method 48

3.2.3 Treatment of Time 53

3.2.4 Accuracy Versus Stability 56

3.2.5 Virtual Laboratory: 1D Transient Conduction in a Semi-infinite Wall 57

3.3 Summary 61

Bibliography 61

4 Introduction to Convective Heat Transfer 63

4.1 Boundary Layers 63

4.2 Nusselt Number 68

4.3 Connecting Momentum Transport and Heat Transfer: Prandtl Number 69

4.4 Reynolds Analogy 71

4.5 Impact of Turbulence 72

4.6 Virtual Laboratory: Boundary Layer Measurement 73

4.7 Summary 77

Bibliography 77

5 Forced Convection 79

5.1 External Convection 81

5.1.1 Flat Plate 81

5.1.2 Other Bluff Bodies 85

5.1.3 Virtual Laboratory: Determination of the Convective Heat Transfer Coefficient for a Rotating Disk 87

5.2 Internal Convection 91

5.2.1 Pipes 93

5.2.2 Ducts with Other Cross-sectional Shape 94

5.2.3 Total Heat Transfer Rate 95

5.2.4 Virtual Laboratory: Heat Transfer Characteristics for Detonation in Narrow Channel 97

5.3 Summary 101

Bibliography 102

6 Natural Convection and Phase Change 105

6.1 The Physical Processes of Natural Convection and Phase Change 105

6.1.1 Relevant Scales for Natural Convection 105

6.1.2 Relevant Scales for Boiling and Condensation 108

6.2 Correlations for Natural Convection 111

6.2.1 External Natural Convection 111

6.2.2 Internal Natural Convection 113

6.2.3 Mixed Regime Convection 114

6.2.4 Virtual Laboratory: Natural Convection in an Ethylene-Air Pool Fire 114

6.3 Correlations for Phase Change Process 118

6.4 Summary 119

Bibliography 119

7 Introduction to Radiative Heat Transfer 121

7.1 The Physical Process of Thermal Radiation 121

7.2 Basic Concepts in Radiation 122

7.2.1 Solid Angle 122

7.2.2 The Electromagnetic Spectrum 123

7.2.3 Radiative Intensity 124

7.3 The Idealized "Blackbody" 125

7.3.1 Fraction of Blackbody Emissive Power 126

7.3.2 Virtual Laboratory: Key Observations for Blackbody Radiation 126

7.4 Surface Properties 128

7.4.1 Spectral and Directional Dependence of Surface Properties 129

7.4.2 Kirchhoff's Law 130

7.4.3 Virtual Laboratory: Measuring Emissivity of Semiconductor Wafer 131

7.5 Summary 133

Bibliography 133

8 Radiative Exchange Between Surfaces 135

8.1 View Factor 135

8.1.1 Properties of View Factor 137

8.1.2 Two-dimensional Geometries: The Crossed-string Method 138

8.1.3 The Monte Carlo Method for Determination of View Factors 140

8.2 Surface Exchange Between Gray Diffuse Surfaces 144

8.2.1 Surface Exchange Between Black Surfaces 144

8.2.2 Analytical Methods for Surface Exchange Between Gray Diffuse Surfaces 145

8.2.3 The Monte Carlo Methods for Surface Exchange Between Gray Diffuse Surfaces 147

8.3 Virtual Laboratory: Radiation Within a Backward-facing Step Combustor 148

8.4 Summary 150

Bibliography 150

9 Radiation in Participating Media 151

9.1 The Characteristics of Gaseous Radiation 151

9.2 The Characteristics of Radiative Interactions with Particles 153

9.3 The Characteristics of Radiation in Semitransparent Medium 154

9.4 Radiative Absorption: The Beer's Law 154

9.5 Radiative Emission 156

9.6 Virtual Laboratory: Measurement of Wall Temperature in a Combustor Using IR Camera 157

9.7 Summary 159

Bibliography 159

10 Applications: Fin and Heat Exchanger 161

10.1 Fins 162

10.1.1 Heat Transfer Rate 163

10.1.2 Efficiency and Effectiveness 167

10.1.3 Virtual Laboratory: Determination of Efficiency and Effectiveness for Fins with Arbitrary Shape 168

10.2 Heat Exchanger 173

10.2.1 Classification 173

10.2.2 Overall Heat Transfer Coefficient 174

10.2.3 Log-mean Temperature Difference 175

10.2.4 Effectiveness-NTU Method 177

10.2.5 A Practical Example 181

10.3 Summary 186

Bibliography 187

11 Contemporary Application of Heat Transfer 189

11.1 A Simplified Energy Balance for Earth 191

11.2 Conjugate Heat Transfer Within a Thermal Barrier Coating Layer 196

11.3 Electronics Cooling 201

11.4 Thermal Runaway of Lithium-ion Batteries 208

11.5 Summary 213

Bibliography 213

Index 215