The Mathematics of Thermal Modeling: An Introduction to the Theory of Laser Material Processing, 1st Edition (Hardback) book cover

The Mathematics of Thermal Modeling

An Introduction to the Theory of Laser Material Processing, 1st Edition

By John Michael Dowden

Chapman and Hall/CRC

304 pages | 150 B/W Illus.

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Hardback: 9781584882305
pub: 2001-05-24
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pub: 2001-05-24
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Description

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.

Reviews

"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

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

INDEX

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied
TEC021000
TECHNOLOGY & ENGINEERING / Material Science