Heat Transfer, Volume 1

Yves Jannot is a CNRS research engineer at the Energy, Theoretical and Applied Mechanics Laboratory of the University of Lorraine, France. Christian Moyne is CNRS research director at the Energy, Theoretical and Applied Mechanics Laboratory of the University of Lorraine, France. Alain Degiovanni is professor emeritus at the Energy, Theoretical and Applied Mechanics Laboratory of the University of Lorraine, France, and research director at the International University of Rabat, Morocco.

Preface ix

Nomenclature xi

Chapter 1 Introduction to Heat Transfer 1

1.1 Introduction 1

1.2 Definitions 1

1.2.1 Temperature field 1

1.2.2 Temperature gradient 1

1.2.3 Heat flux 2

1.3 Formulation of a heat transfer problem 3

1.3.1 Energy balance 3

1.3.2 Expression of energy flows 3

Chapter 2 Steady-State Conduction Heat Transfer 9

2.1 The heat equation 9

2.2 Unidirectional transfer 11

2.2.1 Simple wall 11

2.2.2 Multilayer wall 13

2.2.3 Composite wall 15

2.2.4 Long hollow cylinder (tube) 16

2.2.5 Multilayer hollow cylinder 17

2.2.6 General case 18

2.2.7 Consideration of radiative transfer 19

2.3 Multi-directional transfer 20

2.3.1 Method of separation of variables 20

2.3.2 Shape coefficient method 24

2.3.3 Numerical methods 26

2.4 The fins 30

2.4.1 The bar equation 30

2.4.2 Flow extracted by a fin 32

2.4.3 Efficiency of a fin 36

2.4.4 Electrical analogy 38

2.4.5 Choice of fins 43

2.5 Corrected exercises 43

2.5.1 Heat supply in an air-conditioned room 43

2.5.2 Heat losses from an oil pipeline 46

2.5.3 Critical insulation thickness 46

2.5.4 Hot wire anemometry 47

2.5.5 Calculation of a fin 51

2.5.6 Temperature of teapot handles 52

2.5.7 Thermal resistance of a finned tube 54

2.5.8 Heat input in a cold room 57

2.5.9 Pipe insulation 59

2.5.10 Heat losses from a pipe 60

2.5.11 Effect of a fin and radiation on a thermocouple 62

2.5.12 Internal heat transfer in a pipe 66

2.5.13 Buried pipes 69

2.5.14 Measurement of the thermal conductivity of a rock 71

Chapter 3 Heat Transfer by Conduction in Transient Regime 81

3.1 Unidirectional conduction in transient regime without change of state 81

3.1.1 Uniform temperature medium 81

3.1.2 Semi-infinite medium 83

3.1.3 Unidirectional transfer in limited media: plate, cylinder, sphere 93

3.1.4 Complex systems: quadrupole method 120

3.1.5 Established periodic state 128

3.1.6 Systems with temperature-dependent thermal properties 130

3.2 Multidirectional conduction in transient regime 133

3.2.1 Von Neuman’s theorem 133

3.2.2 Integral transformations and separation of variables 134

3.3 Corrected exercises 138

3.3.1 Age of the Earth: “Kelvin ambiguity” (1864) 138

3.3.2 Periodic variation of temperature in the ground 140

3.3.3 Measurement of thermal diffusivity by sinusoidal excitation 141

3.3.4 Freezing a lake 143

3.3.5 Freezing water pipes in dry ground 145

3.3.6 Freezing water pipes in wet ground 146

3.3.7 Firewall 149

3.3.8 Fire from a wooden beam 150

3.3.9 Flash method 151

3.3.10 Heat treatment of landing gear 156

3.3.11 Heat treatment of a carbon block 157

3.3.12 Heat treatment of a thin layer 161

3.3.13 Quenching of a ball 162

3.3.14 Brake pad heating 168

3.3.15 Hot plate method 171

3.3.16 Measurement of the thermal diffusivity of a thin plate 176

3.3.17 Regular regime method 177

3.3.18 Hot wire modeling 180

3.3.19 Intermittent heating of a chalet 183

3.3.20 Heat loss through the floor of a house 191

3.3.21 Periodic temperature variation in an unconditioned room 199

3.3.22 Periodic flow variation in an air-conditioned room 202

Chapter 4 Convective Heat Transfer 205

4.1 Reminders on dimensional analysis 205

4.1.1 Fundamental dimensions 205

4.1.2 Principle of the method 205

4.1.3 Application example 206

4.1.4 Advantages of using reduced quantities 209

4.2 Convection without phase change 210

4.2.1 Generalities and definitions 210

4.2.2 Expression of heat flow rate 211

4.2.3 Calculation of heat flow rate in forced convection 213

4.2.4 Calculation of heat flow rate in natural convection 220

4.3 Convection with phase change 223

4.3.1 Condensation 223

4.3.2 Boiling 227

4.4 Corrected exercises 231

4.4.1 Forced convection in and around a tube 231

4.4.2 Water flow in a heating tube 233

4.4.3 Air cooling in a duct 236

4.4.4 Permeable-dynamic insulation of a house 238

4.4.5 Convection in a chimney 241

4.4.6 Modeling natural convection in double glazing 242

4.4.7 Calculation of exchanges by convection in double glazing 249

4.4.8 Study of an electric kettle 253

Appendices 259

References 299

Index 303

Summary of Volume 2 305