The Mathematics of Thermal Modeling

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

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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 more

Product details

  • Hardback | 304 pages
  • 161 x 245.9 x 21.6mm | 562.46g
  • Taylor & Francis Inc
  • CRC Press Inc
  • Bosa Roca, United States
  • English
  • 150 black & white illustrations, 1 black & white tables, 1 black & white halftones
  • 1584882301
  • 9781584882305

Review quote

"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, 1054show more

Table of contents

THERMAL MODELING Introduction Dimensions and Dimensionless Numbers Two Examples PHYSICAL PRINCIPLES Governing Equations Boundary Conditions Summary of Equations and Conditions THE TEMPERATURE IN BLOCKS AND PLATES The Temperature Distribution The Point Source Solution The Temperature Distribution in Plates Fresnel Absorption 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 Stefan Problems Neumann's Problem 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 Keyhole Numerical Examples 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 THERMO-ELASTIC PROBLEMS Thermal Expansion The Scabbing of Concrete Two-Dimensional Models Stresses in a Metal Work Piece Conclusion APPENDIX 1: VALUES OF MATERIAL PROPERTIES APPENDIX 2: ELASTIC GREEN'S FUNCTIONS FOR A SEMI-INFINITE DOMAIN BIBLIOGRAPHY INDEXshow more