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 ixNomenclature xiChapter 1 Introduction to Heat Transfer 11.1 Introduction 11.2 Definitions 11.2.1 Temperature field 11.2.2 Temperature gradient 11.2.3 Heat flux 21.3 Formulation of a heat transfer problem 31.3.1 Energy balance 31.3.2 Expression of energy flows 3Chapter 2 Steady-State Conduction Heat Transfer 92.1 The heat equation 92.2 Unidirectional transfer 112.2.1 Simple wall 112.2.2 Multilayer wall 132.2.3 Composite wall 152.2.4 Long hollow cylinder (tube) 162.2.5 Multilayer hollow cylinder 172.2.6 General case 182.2.7 Consideration of radiative transfer 192.3 Multi-directional transfer 202.3.1 Method of separation of variables 202.3.2 Shape coefficient method 242.3.3 Numerical methods 262.4 The fins 302.4.1 The bar equation 302.4.2 Flow extracted by a fin 322.4.3 Efficiency of a fin 362.4.4 Electrical analogy 382.4.5 Choice of fins 432.5 Corrected exercises 432.5.1 Heat supply in an air-conditioned room 432.5.2 Heat losses from an oil pipeline 462.5.3 Critical insulation thickness 462.5.4 Hot wire anemometry 472.5.5 Calculation of a fin 512.5.6 Temperature of teapot handles 522.5.7 Thermal resistance of a finned tube 542.5.8 Heat input in a cold room 572.5.9 Pipe insulation 592.5.10 Heat losses from a pipe 602.5.11 Effect of a fin and radiation on a thermocouple 622.5.12 Internal heat transfer in a pipe 662.5.13 Buried pipes 692.5.14 Measurement of the thermal conductivity of a rock 71Chapter 3 Heat Transfer by Conduction in Transient Regime 813.1 Unidirectional conduction in transient regime without change of state 813.1.1 Uniform temperature medium 813.1.2 Semi-infinite medium 833.1.3 Unidirectional transfer in limited media: plate, cylinder, sphere 933.1.4 Complex systems: quadrupole method 1203.1.5 Established periodic state 1283.1.6 Systems with temperature-dependent thermal properties 1303.2 Multidirectional conduction in transient regime 1333.2.1 Von Neuman’s theorem 1333.2.2 Integral transformations and separation of variables 1343.3 Corrected exercises 1383.3.1 Age of the Earth: “Kelvin ambiguity” (1864) 1383.3.2 Periodic variation of temperature in the ground 1403.3.3 Measurement of thermal diffusivity by sinusoidal excitation 1413.3.4 Freezing a lake 1433.3.5 Freezing water pipes in dry ground 1453.3.6 Freezing water pipes in wet ground 1463.3.7 Firewall 1493.3.8 Fire from a wooden beam 1503.3.9 Flash method 1513.3.10 Heat treatment of landing gear 1563.3.11 Heat treatment of a carbon block 1573.3.12 Heat treatment of a thin layer 1613.3.13 Quenching of a ball 1623.3.14 Brake pad heating 1683.3.15 Hot plate method 1713.3.16 Measurement of the thermal diffusivity of a thin plate 1763.3.17 Regular regime method 1773.3.18 Hot wire modeling 1803.3.19 Intermittent heating of a chalet 1833.3.20 Heat loss through the floor of a house 1913.3.21 Periodic temperature variation in an unconditioned room 1993.3.22 Periodic flow variation in an air-conditioned room 202Chapter 4 Convective Heat Transfer 2054.1 Reminders on dimensional analysis 2054.1.1 Fundamental dimensions 2054.1.2 Principle of the method 2054.1.3 Application example 2064.1.4 Advantages of using reduced quantities 2094.2 Convection without phase change 2104.2.1 Generalities and definitions 2104.2.2 Expression of heat flow rate 2114.2.3 Calculation of heat flow rate in forced convection 2134.2.4 Calculation of heat flow rate in natural convection 2204.3 Convection with phase change 2234.3.1 Condensation 2234.3.2 Boiling 2274.4 Corrected exercises 2314.4.1 Forced convection in and around a tube 2314.4.2 Water flow in a heating tube 2334.4.3 Air cooling in a duct 2364.4.4 Permeable-dynamic insulation of a house 2384.4.5 Convection in a chimney 2414.4.6 Modeling natural convection in double glazing 2424.4.7 Calculation of exchanges by convection in double glazing 2494.4.8 Study of an electric kettle 253Appendices 259References 299Index 303Summary of Volume 2 305

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 ixNomenclature xiChapter 1 Introduction to Heat Transfer 11.1 Introduction 11.2 Definitions 11.2.1 Temperature field 11.2.2 Temperature gradient 11.2.3 Heat flux 21.3 Formulation of a heat transfer problem 31.3.1 Energy balance 31.3.2 Expression of energy flows 3Chapter 2 Steady-State Conduction Heat Transfer 92.1 The heat equation 92.2 Unidirectional transfer 112.2.1 Simple wall 112.2.2 Multilayer wall 132.2.3 Composite wall 152.2.4 Long hollow cylinder (tube) 162.2.5 Multilayer hollow cylinder 172.2.6 General case 182.2.7 Consideration of radiative transfer 192.3 Multi-directional transfer 202.3.1 Method of separation of variables 202.3.2 Shape coefficient method 242.3.3 Numerical methods 262.4 The fins 302.4.1 The bar equation 302.4.2 Flow extracted by a fin 322.4.3 Efficiency of a fin 362.4.4 Electrical analogy 382.4.5 Choice of fins 432.5 Corrected exercises 432.5.1 Heat supply in an air-conditioned room 432.5.2 Heat losses from an oil pipeline 462.5.3 Critical insulation thickness 462.5.4 Hot wire anemometry 472.5.5 Calculation of a fin 512.5.6 Temperature of teapot handles 522.5.7 Thermal resistance of a finned tube 542.5.8 Heat input in a cold room 572.5.9 Pipe insulation 592.5.10 Heat losses from a pipe 602.5.11 Effect of a fin and radiation on a thermocouple 622.5.12 Internal heat transfer in a pipe 662.5.13 Buried pipes 692.5.14 Measurement of the thermal conductivity of a rock 71Chapter 3 Heat Transfer by Conduction in Transient Regime 813.1 Unidirectional conduction in transient regime without change of state 813.1.1 Uniform temperature medium 813.1.2 Semi-infinite medium 833.1.3 Unidirectional transfer in limited media: plate, cylinder, sphere 933.1.4 Complex systems: quadrupole method 1203.1.5 Established periodic state 1283.1.6 Systems with temperature-dependent thermal properties 1303.2 Multidirectional conduction in transient regime 1333.2.1 Von Neuman’s theorem 1333.2.2 Integral transformations and separation of variables 1343.3 Corrected exercises 1383.3.1 Age of the Earth: “Kelvin ambiguity” (1864) 1383.3.2 Periodic variation of temperature in the ground 1403.3.3 Measurement of thermal diffusivity by sinusoidal excitation 1413.3.4 Freezing a lake 1433.3.5 Freezing water pipes in dry ground 1453.3.6 Freezing water pipes in wet ground 1463.3.7 Firewall 1493.3.8 Fire from a wooden beam 1503.3.9 Flash method 1513.3.10 Heat treatment of landing gear 1563.3.11 Heat treatment of a carbon block 1573.3.12 Heat treatment of a thin layer 1613.3.13 Quenching of a ball 1623.3.14 Brake pad heating 1683.3.15 Hot plate method 1713.3.16 Measurement of the thermal diffusivity of a thin plate 1763.3.17 Regular regime method 1773.3.18 Hot wire modeling 1803.3.19 Intermittent heating of a chalet 1833.3.20 Heat loss through the floor of a house 1913.3.21 Periodic temperature variation in an unconditioned room 1993.3.22 Periodic flow variation in an air-conditioned room 202Chapter 4 Convective Heat Transfer 2054.1 Reminders on dimensional analysis 2054.1.1 Fundamental dimensions 2054.1.2 Principle of the method 2054.1.3 Application example 2064.1.4 Advantages of using reduced quantities 2094.2 Convection without phase change 2104.2.1 Generalities and definitions 2104.2.2 Expression of heat flow rate 2114.2.3 Calculation of heat flow rate in forced convection 2134.2.4 Calculation of heat flow rate in natural convection 2204.3 Convection with phase change 2234.3.1 Condensation 2234.3.2 Boiling 2274.4 Corrected exercises 2314.4.1 Forced convection in and around a tube 2314.4.2 Water flow in a heating tube 2334.4.3 Air cooling in a duct 2364.4.4 Permeable-dynamic insulation of a house 2384.4.5 Convection in a chimney 2414.4.6 Modeling natural convection in double glazing 2424.4.7 Calculation of exchanges by convection in double glazing 2494.4.8 Study of an electric kettle 253Appendices 259References 299Index 303Summary of Volume 2 305

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 ixNomenclature xiChapter 1 Introduction to Heat Transfer 11.1 Introduction 11.2 Definitions 11.2.1 Temperature field 11.2.2 Temperature gradient 11.2.3 Heat flux 21.3 Formulation of a heat transfer problem 31.3.1 Energy balance 31.3.2 Expression of energy flows 3Chapter 2 Steady-State Conduction Heat Transfer 92.1 The heat equation 92.2 Unidirectional transfer 112.2.1 Simple wall 112.2.2 Multilayer wall 132.2.3 Composite wall 152.2.4 Long hollow cylinder (tube) 162.2.5 Multilayer hollow cylinder 172.2.6 General case 182.2.7 Consideration of radiative transfer 192.3 Multi-directional transfer 202.3.1 Method of separation of variables 202.3.2 Shape coefficient method 242.3.3 Numerical methods 262.4 The fins 302.4.1 The bar equation 302.4.2 Flow extracted by a fin 322.4.3 Efficiency of a fin 362.4.4 Electrical analogy 382.4.5 Choice of fins 432.5 Corrected exercises 432.5.1 Heat supply in an air-conditioned room 432.5.2 Heat losses from an oil pipeline 462.5.3 Critical insulation thickness 462.5.4 Hot wire anemometry 472.5.5 Calculation of a fin 512.5.6 Temperature of teapot handles 522.5.7 Thermal resistance of a finned tube 542.5.8 Heat input in a cold room 572.5.9 Pipe insulation 592.5.10 Heat losses from a pipe 602.5.11 Effect of a fin and radiation on a thermocouple 622.5.12 Internal heat transfer in a pipe 662.5.13 Buried pipes 692.5.14 Measurement of the thermal conductivity of a rock 71Chapter 3 Heat Transfer by Conduction in Transient Regime 813.1 Unidirectional conduction in transient regime without change of state 813.1.1 Uniform temperature medium 813.1.2 Semi-infinite medium 833.1.3 Unidirectional transfer in limited media: plate, cylinder, sphere 933.1.4 Complex systems: quadrupole method 1203.1.5 Established periodic state 1283.1.6 Systems with temperature-dependent thermal properties 1303.2 Multidirectional conduction in transient regime 1333.2.1 Von Neuman’s theorem 1333.2.2 Integral transformations and separation of variables 1343.3 Corrected exercises 1383.3.1 Age of the Earth: “Kelvin ambiguity” (1864) 1383.3.2 Periodic variation of temperature in the ground 1403.3.3 Measurement of thermal diffusivity by sinusoidal excitation 1413.3.4 Freezing a lake 1433.3.5 Freezing water pipes in dry ground 1453.3.6 Freezing water pipes in wet ground 1463.3.7 Firewall 1493.3.8 Fire from a wooden beam 1503.3.9 Flash method 1513.3.10 Heat treatment of landing gear 1563.3.11 Heat treatment of a carbon block 1573.3.12 Heat treatment of a thin layer 1613.3.13 Quenching of a ball 1623.3.14 Brake pad heating 1683.3.15 Hot plate method 1713.3.16 Measurement of the thermal diffusivity of a thin plate 1763.3.17 Regular regime method 1773.3.18 Hot wire modeling 1803.3.19 Intermittent heating of a chalet 1833.3.20 Heat loss through the floor of a house 1913.3.21 Periodic temperature variation in an unconditioned room 1993.3.22 Periodic flow variation in an air-conditioned room 202Chapter 4 Convective Heat Transfer 2054.1 Reminders on dimensional analysis 2054.1.1 Fundamental dimensions 2054.1.2 Principle of the method 2054.1.3 Application example 2064.1.4 Advantages of using reduced quantities 2094.2 Convection without phase change 2104.2.1 Generalities and definitions 2104.2.2 Expression of heat flow rate 2114.2.3 Calculation of heat flow rate in forced convection 2134.2.4 Calculation of heat flow rate in natural convection 2204.3 Convection with phase change 2234.3.1 Condensation 2234.3.2 Boiling 2274.4 Corrected exercises 2314.4.1 Forced convection in and around a tube 2314.4.2 Water flow in a heating tube 2334.4.3 Air cooling in a duct 2364.4.4 Permeable-dynamic insulation of a house 2384.4.5 Convection in a chimney 2414.4.6 Modeling natural convection in double glazing 2424.4.7 Calculation of exchanges by convection in double glazing 2494.4.8 Study of an electric kettle 253Appendices 259References 299Index 303Summary of Volume 2 305