Chapman and Hall/CRC
304 pages | 150 B/W Illus.
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.
"The book is written very transparently, it uses adequate mathematical sophistication and physical background. … [R]ecommended to engineers and material scientists at the Ms. or Ph.D. level, or to mathematicians interested in technological problems."
- Zentralblatt MATH, 1054
Dimensions and Dimensionless Numbers
Summary of Equations and Conditions
THE TEMPERATURE IN BLOCKS AND PLATES
The Temperature Distribution
The Point Source Solution
The Temperature Distribution in Plates
The Line Source Solution
TIME DEPENDENT SOLUTIONS IN BLOCKS
Time Dependent One-Dimensional Solutions
Surface Heating from Cold
Time-Dependent Point and Line Sources
The Thermal History of a Material Element
MOVING BOUNDARY PROBLEMS
SIMPLE MODELS OF LASER KEYHOLE WELDING
Laser Keyhole Welding
Point and Line Source Models
The Relation between Power Absorbed and Keyhole Radius
The Liquid/Vapor Interface
THE FLUID REGIONS IN KEYHOLE WELDING
Flow in the Weld Pool
Interaction of Motion in the Weld Pool with the Keyhole
Laser Heating of the Vapor in the Keyhole
The Scabbing of Concrete
Stresses in a Metal Work Piece
APPENDIX 1: VALUES OF MATERIAL PROPERTIES
APPENDIX 2: ELASTIC GREEN'S FUNCTIONS FOR A SEMI-INFINITE DOMAIN