Finite Element Simulation of Heat Transfer

Jean-Michel Bergheau is presently Director of Research at Ecole Nationale d'ingenieurs de Saint-Etienne and head of the Computational Mechanics research group of the Laboratory of Tribology and Systems Dynamics. His research interests concern the modeling of coupled physical phenomena applied to the numerical simulation of manufacturing processes such as welding, heat treatment and machining, and the understanding of the mechanical phenomena involved in interfaces.Roland Fortunier conducted research abroad, in Germany and Canada, of the nuclear and the steel industry. He was appointed Professor of the Ecole des Mines in France in 1995.

• Introduction 11PART 1.  Steady State Conduction 17Chapter 1.  Problem Formulation 211.1. Physical modeling 211.2. Mathematical analysis 241.3. Working example 30Chapter 2.  The Finite Element Method 432.1. Finite element approximation 432.2. Discrete problem formulation 482.3. Solution 532.4. Working example 68Chapter 3.  Isoparametric Finite Elements 793.1. Definitions 793.2. Calculation of element quantities 903.3. Some finite elements 99PART 2.  Transient State, Non-linearities, Transport Phenomena 101Chapter 4.  Transient Heat Conduction 1054.1. Problem formulation . 1054.2. Time integration 1114.3. Working example 135Chapter 5.  Non-linearities 1435.1. Formulation and solution techniques 1435.2. Traditional non-linearities 1535.3. A temperature-enthalpy formulation 162Chapter 6. Transport Phenomena 1696.1. Highlighting instabilities 1696.2. Resolution techniques 174PART 3. Coupled Phenomena 183Chapter 7.  Radiation Exchanges in a Chamber 1897.1. Modeling radiative heat exchanges in a cavity 1897.2. Examples 200Chapter 8. Fluid-Structure Coupling in a Pipe 2078.1 Modeling the fluid 2078.2. Example 212Chapter 9. Thermometallurgical Coupling 2159.1. Modeling phase changes 2159.2. Examples 222Chapter 10. Thermochemical Coupling 23110.1. Finite element simulation of simultaneous diffusion and precipitation 23110.2. Calculation of precipitation 23610.3. Examples 239Chapter 11. Electrothermal Coupling 24311.1. Electrokinetic modeling 24311.2. Resistance welding 248Chapter 12. Magnetothermal Coupling 25312.1. Introduction 25312.2. Magnetic vector potential formulation for magnetodynamics 25412.3. Coupled finite element-boundary element method 25712.4. A harmonic balance method for the magnetodynamic problem 26112.5. Coupling magnetodynamics with heat transfer .26312.6. Application: induction hardening of a steel cylinder 266Bibliography 269Index 277