Heat is a branch of thermodynamics that occupies a unique position due to its involvement in the field of practice. Being linked to the management, transport and exchange of energy in thermal form, it impacts all aspects of human life and activity. Heat transfers are, by nature, classified as conduction, convection (which inserts conduction into fluid mechanics) and radiation. The importance of these three transfer methods has resulted justifiably in a separate volume being afforded to each of them. This first volume is dedicated to thermal conduction, and, importantly, assumes an analytical approach to the problems presented, and recalls the fundamentals. Heat Transfer 1 combines a basic approach with a deeper understanding of the discipline and will therefore appeal to a wide audience, from technician to engineer, from doctoral student to teacher-researcher.

Heat is a branch of thermodynamics that occupies a unique position dueto its involvement in the field of practice. Being linked to themanagement, transport and exchange of energy in thermal form, itimpacts all aspects of human life and activity.Heat transfers are, by nature, classified as conduction, convection (whichinserts conduction into fluid mechanics) and radiation. The importanceof these three transfer methods has resulted justifiably in a separatevolume being afforded to each of them. This first volume is dedicated tothermal conduction, and, importantly, assumes an analytical approach tothe problems presented, and recalls the fundamentals.Heat Transfer 1 combines a basic approach with a deeper understandingof the discipline and will therefore appeal to a wide audience, fromtechnician to engineer, from doctoral student to teacher-researcher.

Preface ixIntroduction xiiiChapter 1. The Problem of Thermal Conduction: General Comments 11.1. The fundamental problem of thermal conduction 11.2. Definitions 21.2.1. Temperature, isothermal surface and gradient 21.2.2. Flow and density of flow 41.3. Relation to thermodynamics 51.3.1. Calorimetry 51.3.2. The first principle 61.3.3. The second principle 6Chapter 2. The Physics of Conduction 92.1. Introduction 92.2. Fourier's law 92.2.1. Experiment 92.2.2. Temperature profile 122.2.3. General expression of the Fourier law 142.3. Heat equation 162.3.1. General problem 162.3.2. Mono-dimensional plane problem 182.3.3. Case of the axisymmetric system 242.3.4. Case of the spherical system 252.4. Resolution of a problem 262.5. Examples of application 292.5.1. Problems involving spherical symmetry 40Chapter 3. Conduction in a Stationary Regime 533.1. Thermal resistance 533.1.1. Thermal resistance: plane geometry 533.1.2. Thermal resistance: axisymmetric geometry. The case of a cylindrical wall 623.1.3. Thermal resistance to convection 653.1.4. Critical radius 673.2. Examples of the application of thermal resistance in plane geometry 693.3. Examples of the application of the thermal resistance in cylindrical geometry 853.4. Problem of the critical diameter 923.5. Problem with the heat balance 99Chapter 4. Quasi-stationary Model 1034.1. We can perform a simplified calculation, adopting the following hypotheses 1034.2. Method: instantaneous thermal balance 1044.3. Resolution 1064.4. Applications for plane systems 1074.5. Applications for axisymmetric systems 152Chapter 5. Non-stationary Conduction 1835.1. Single-dimensional problem 1835.1.1. Temperature imposed at the interface at instant t = 0 1845.2. Non-stationary conduction with constant flow density 1905.3. Temperature imposed on the wall: sinusoidal variation 1935.4. Problem with two walls stuck together 2005.5. Application examples 2045.5.1. Simple applications 2045.5.2. Some scenes from daily life 213Chapter 6. Fin Theory: Notions and Examples 2376.1. Notions regarding the theory of fins 2376.1.1. Principle of fins 2376.1.2. Elementary fin theory 2386.1.3. Parallelepiped fin 2426.2. Examples of application 249Appendices 263Appendix 1. Heat Equation of a Three-dimensional System 265Appendix 2. Heat Equation: Writing in the Main Coordinate Systems 273Appendix 3. One-dimensional Heat Equation 283Appendix 4. Conduction of the Heat in a Non-stationary Regime: Solutions to Classic Problems 291Appendix 5. Table of erf (x), erfc (x) and ierfc (x) Functions 295Appendix 6. Complementary Information Regarding Fins 297Appendix 7. The Laplace Transform 301Appendix 8. Reminders Regarding Hyperbolic Functions 309References 313Index 315