The Mathematics of Thermal Modeling: An Introduction to the Theory of Laser Material Processing

John Michael Dowden1584882301, 9781584882305, 9781420035629

The use of lasers for various applications in materials processing has grown rapidly in recent years. Lasers are by nature particularly well suited to automation, but to ensure repeatability and reliability, the engineers employing them must not simply rely on numerical analysis software. They must have a firm grasp on the physical principles involved. Mathematics of Thermal Modelling: An Introduction to the Theory of Laser Material Processing introduces the mathematics needed to formulate and exploit the physical principles important to modelling various aspects of laser material processing. The author shows how to gain insight by constructing and analyzing simple models. He demonstrates how to extract qualitative information from the models, how the underlying principles can be extended to more complex modelling, and how these principles can be applied to processes such as laser welding, surface treatment, drilling, and cutting. Written at a level accessible to graduate students, this book shows that simple mathematical investigation– based primarily on analytical methods backed by relatively simple numerical methods–can greatly illuminate the processes being studied. Regardless of the stage of your career development, if you are confronting the modelling of thermal process in this field for the first time, Mathematics of Thermal Modelling will build the foundation you need.

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Table of contents :
COVER……Page 1
The Mathematics of Thermal Modeling: An Introduction to the Theory of Laser Material Processing……Page 2
THE AUTHOR……Page 4
TABLE OF CONTENTS……Page 6
PREFACE……Page 9
1.1 INTRODUCTION……Page 11
Table of contents……Page 0
1.2 DIMENSIONS AND DIMENSIONLESS NUMBERS……Page 14
1.3 TWO EXAMPLES……Page 25
2.1.1 Conservation equations……Page 30
2.1.2 The equation of conservation of mass……Page 36
2.1.3 The equation of heat conduction……Page 38
2.1.4 Dynamics of a continuous medium……Page 40
2.1.5 Euler’s Equation for an ideal fluid…….Page 46
2.1.6 The Navier-Stokes equations for a viscous fluid……Page 48
2.1.7 Equations of linear thermoelasticity……Page 49
2.1.8 Plasticity……Page 62
2.2.1 General considerations……Page 65
2.2.2 Thermal boundary conditions……Page 67
2.2.3 Dynamical boundary conditions……Page 73
2.2.5 Comments on the fluid boundary conditions……Page 76
2.2.6 Elastic boundary conditions……Page 79
2.3.1 General……Page 80
2.3.2 Thermal equations and conditions……Page 81
2.3.3 Fluid motion……Page 82
2.3.4 Thermoelasticity……Page 84
3.1 THE TEMPERATURE DISTRIBUTION……Page 86
3.2.1 Special solutions……Page 87
3.2.2 Applications of the point source solution……Page 94
3.3 THE TEMPERATURE DISTRIBUTION IN PLATES……Page 102
3.4 FRESNEL ABSORPTION……Page 107
3.5 THE LINE SOURCE SOLUTION……Page 109
4.1 TIME-DEPENDENT ONE-DIMENSIONAL SOLUTIONS……Page 122
4.2 SURFACE HEATING FROM COLD……Page 126
4.3 TIME-DEPENDENT POINT AND LINE SOURCES……Page 131
4.4 THE THERMAL HISTORY OF A MATERIAL ELEMENT……Page 138
5.1 STEFAN PROBLEMS……Page 145
5.2 NEUMANN’S PROBLEM 7……Page 154
6.1 LASER KEYHOLE WELDING……Page 158
6.2 POINT AND LINE SOURCE MODELS……Page 161
6.3.1 The line source as a model of the keyhole……Page 172
6.3.2 The Davis-Noller solution……Page 174
6.3.3 Other two-dimensional thermal models for the solid and liquid phases……Page 180
6.4 THE LIQUID/VAPOR INTERFACE……Page 181
6.5 THE KEYHOLE……Page 185
6.6 NUMERICAL EXAMPLES……Page 192
The weld pool……Page 196
The keyhole……Page 197
7.1 FLOW IN THE WELD POOL……Page 198
7.2 INTERACTION OF MOTION IN THE WELD POOL WITH THE KEYHOLE……Page 207
7.3. LASER HEATING OF THE VAPOR IN THE KEYHOLE……Page 232
The keyhole……Page 247
8.1 THERMAL EXPANSION……Page 248
8.2 THE SCABBLING OF CONCRETE……Page 251
8.3 TWO-DIMENSIONAL MODELS……Page 258
8.4 STRESSES IN A METAL WORKPIECE……Page 267
8.5 CONCLUSION……Page 268
APPENDIX 1: VALUES OF MATERIAL PROPERTIES……Page 269
APPENDIX 2: ELASTIC GREEN’S FUNCTIONS FOR A SEMI-INFINITE DOMAIN……Page 275
BIBLIOGRAPHY……Page 280