Heat Transfer 1

Preface ix Introduction xiii Chapter 1. The Problem of Thermal Conduction: General Comments 1 1.1. The fundamental problem of thermal conduction 1 1.2. Definitions 2 1.2.1. Temperature, isothermal surface and gradient 2 1.2.2. Flow and density of flow 4 1.3. Relation to thermodynamics 5 1.3.1. Calorimetry 5 1.3.2. The first principle 6 1.3.3. The second principle 6 Chapter 2. The Physics of Conduction 9 2.1. Introduction 9 2.2. Fourier's law 9 2.2.1. Experiment 9 2.2.2. Temperature profile 12 2.2.3. General expression of the Fourier law 14 2.3. Heat equation 16 2.3.1. General problem 16 2.3.2. Mono-dimensional plane problem 18 2.3.3. Case of the axisymmetric system 24 2.3.4. Case of the spherical system 25 2.4. Resolution of a problem 26 2.5. Examples of application 29 2.5.1. Problems involving spherical symmetry 40 Chapter 3. Conduction in a Stationary Regime 53 3.1. Thermal resistance 53 3.1.1. Thermal resistance: plane geometry 53 3.1.2. Thermal resistance: axisymmetric geometry. The case of a cylindrical wall 62 3.1.3. Thermal resistance to convection 65 3.1.4. Critical radius 67 3.2. Examples of the application of thermal resistance in plane geometry 69 3.3. Examples of the application of the thermal resistance in cylindrical geometry 85 3.4. Problem of the critical diameter 92 3.5. Problem with the heat balance 99 Chapter 4. Quasi-stationary Model 103 4.1. We can perform a simplified calculation, adopting the following hypotheses 103 4.2. Method: instantaneous thermal balance 104 4.3. Resolution 106 4.4. Applications for plane systems 107 4.5. Applications for axisymmetric systems 152 Chapter 5. Non-stationary Conduction 183 5.1. Single-dimensional problem 183 5.1.1. Temperature imposed at the interface at instant t = 0 184 5.2. Non-stationary conduction with constant flow density 190 5.3. Temperature imposed on the wall: sinusoidal variation 193 5.4. Problem with two walls stuck together 200 5.5. Application examples 204 5.5.1. Simple applications 204 5.5.2. Some scenes from daily life 213 Chapter 6. Fin Theory: Notions and Examples 237 6.1. Notions regarding the theory of fins 237 6.1.1. Principle of fins 237 6.1.2. Elementary fin theory 238 6.1.3. Parallelepiped fin 242 6.2. Examples of application 249 Appendices 263 Appendix 1. Heat Equation of a Three-dimensional System 265 Appendix 2. Heat Equation: Writing in the Main Coordinate Systems 273 Appendix 3. One-dimensional Heat Equation 283 Appendix 4. Conduction of the Heat in a Non-stationary Regime: Solutions to Classic Problems 291 Appendix 5. Table of erf (x), erfc (x) and ierfc (x) Functions 295 Appendix 6. Complementary Information Regarding Fins 297 Appendix 7. The Laplace Transform 301 Appendix 8. Reminders Regarding Hyperbolic Functions 309 References 313 Index 315