Introduction 11
PART 1. Steady State Conduction 17
Chapter 1. Problem Formulation 21
1.1. Physical modeling 21
1.2. Mathematical analysis 24
1.3. Working example 30
Chapter 2. The Finite Element Method 43
2.1. Finite element approximation 43
2.2. Discrete problem formulation 48
2.3. Solution 53
2.4. Working example 68
Chapter 3. Isoparametric Finite Elements 79
3.1. Definitions 79
3.2. Calculation of element quantities 90
3.3. Some finite elements 99
PART 2. Transient State, Non-linearities, Transport Phenomena 101
Chapter 4. Transient Heat Conduction 105
4.1. Problem formulation . 105
4.2. Time integration 111
4.3. Working example 135
Chapter 5. Non-linearities 143
5.1. Formulation and solution techniques 143
5.2. Traditional non-linearities 153
5.3. A temperature-enthalpy formulation 162
Chapter 6. Transport Phenomena 169
6.1. Highlighting instabilities 169
6.2. Resolution techniques 174
PART 3. Coupled Phenomena 183
Chapter 7. Radiation Exchanges in a Chamber 189
7.1. Modeling radiative heat exchanges in a cavity 189
7.2. Examples 200
Chapter 8. Fluid-Structure Coupling in a Pipe 207
8.1 Modeling the fluid 207
8.2. Example 212
Chapter 9. Thermometallurgical Coupling 215
9.1. Modeling phase changes 215
9.2. Examples 222
Chapter 10. Thermochemical Coupling 231
10.1. Finite element simulation of simultaneous diffusion and precipitation 231
10.2. Calculation of precipitation 236
10.3. Examples 239
Chapter 11. Electrothermal Coupling 243
11.1. Electrokinetic modeling 243
11.2. Resistance welding 248
Chapter 12. Magnetothermal Coupling 253
12.1. Introduction 253
12.2. Magnetic vector potential formulation for magnetodynamics 254
12.3. Coupled finite element-boundary element method 257
12.4. A harmonic balance method for the magnetodynamic problem 261
12.5. Coupling magnetodynamics with heat transfer .263
12.6. Application: induction hardening of a steel cylinder 266
Bibliography 269
Index 277
