The mathematics of thermal modeling : an introduction to the theory of laser material processing

The Mathematics of Thermal Modeling: An Introduction to the Theory of Laser Material Processing......Page 1
THE AUTHOR......Page 3
TABLE OF CONTENTS......Page 5
PREFACE......Page 8
1.1 INTRODUCTION......Page 10
Table of contents......Page 0
1.2 DIMENSIONS AND DIMENSIONLESS NUMBERS......Page 13
1.3 TWO EXAMPLES......Page 24
2.1.1 Conservation equations......Page 29
2.1.2 The equation of conservation of mass......Page 35
2.1.3 The equation of heat conduction......Page 37
2.1.4 Dynamics of a continuous medium......Page 39
2.1.5 Euler’s Equation for an ideal fluid.......Page 45
2.1.6 The Navier-Stokes equations for a viscous fluid......Page 47
2.1.7 Equations of linear thermoelasticity......Page 48
2.1.8 Plasticity......Page 61
2.2.1 General considerations......Page 64
2.2.2 Thermal boundary conditions......Page 66
2.2.3 Dynamical boundary conditions......Page 72
2.2.5 Comments on the fluid boundary conditions......Page 75
2.2.6 Elastic boundary conditions......Page 78
2.3.1 General......Page 79
2.3.2 Thermal equations and conditions......Page 80
2.3.3 Fluid motion......Page 81
2.3.4 Thermoelasticity......Page 83
3.1 THE TEMPERATURE DISTRIBUTION......Page 85
3.2.1 Special solutions......Page 86
3.2.2 Applications of the point source solution......Page 93
3.3 THE TEMPERATURE DISTRIBUTION IN PLATES......Page 101
3.4 FRESNEL ABSORPTION......Page 106
3.5 THE LINE SOURCE SOLUTION......Page 108
4.1 TIME-DEPENDENT ONE-DIMENSIONAL SOLUTIONS......Page 121
4.2 SURFACE HEATING FROM COLD......Page 125
4.3 TIME-DEPENDENT POINT AND LINE SOURCES......Page 130
4.4 THE THERMAL HISTORY OF A MATERIAL ELEMENT......Page 137
5.1 STEFAN PROBLEMS......Page 144
5.2 NEUMANN’S PROBLEM 7......Page 153
6.1 LASER KEYHOLE WELDING......Page 157
6.2 POINT AND LINE SOURCE MODELS......Page 160
6.3.1 The line source as a model of the keyhole......Page 171
6.3.2 The Davis-Noller solution......Page 173
6.3.3 Other two-dimensional thermal models for the solid and liquid phases......Page 179
6.4 THE LIQUID/VAPOR INTERFACE......Page 180
6.5 THE KEYHOLE......Page 184
6.6 NUMERICAL EXAMPLES......Page 191
The weld pool......Page 195
The keyhole......Page 196
7.1 FLOW IN THE WELD POOL......Page 197
7.2 INTERACTION OF MOTION IN THE WELD POOL WITH THE KEYHOLE......Page 206
7.3. LASER HEATING OF THE VAPOR IN THE KEYHOLE......Page 231
The keyhole......Page 246
8.1 THERMAL EXPANSION......Page 247
8.2 THE SCABBLING OF CONCRETE......Page 250
8.3 TWO-DIMENSIONAL MODELS......Page 257
8.4 STRESSES IN A METAL WORKPIECE......Page 266
8.5 CONCLUSION......Page 267
APPENDIX 1: VALUES OF MATERIAL PROPERTIES......Page 268
APPENDIX 2: ELASTIC GREEN’S FUNCTIONS FOR A SEMI-INFINITE DOMAIN......Page 274
BIBLIOGRAPHY......Page 279