The Mathematics of Thermal Modeling

An Introduction to the Theory of Laser Material Processing

By: John Michael Dowden

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Hardcover | 24 May 2001 | Edition Number 1

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304 Pages

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24.77 x 17.15 x 2.54

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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 need.

Industry 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

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Preface
Thermal Modeling
Introduction	p. 1
Dimensions and Dimensionless Numbers	p. 4
Two Examples	p. 15
Physical Principles
Governing Equations	p. 21
Conservation equations	p. 21
The equation of conservation of mass	p. 27
The equation of heat conduction	p. 29
Dynamics of a continuous medium	p. 31
Euler's equation for an ideal fluid	p. 37
The Navier-Stokes equations for a viscous fluid	p. 39
Equations of linear thermoelasticity	p. 40
Plasticity	p. 53
Boundary Conditions	p. 56
General considerations	p. 56
Thermal boundary conditions	p. 58
Dynamical boundary conditions	p. 64
Other conditions	p. 67
Comments on the fluid boundary conditions	p. 67
Elastic boundary conditions	p. 70
Summary of Equations and Conditions	p. 71
General	p. 71
Thermal equations and conditions	p. 72
Fluid motion	p. 73
Thermoelasticity	p. 75
The Temperature in Blocks and Plates
The Temperature Distribution	p. 77
The Point Source Solution	p. 78
Special solutions	p. 78
Applications of the point source solution	p. 85
The Temperature Distribution in Plates	p. 93
Fresnel Absorption	p. 98
The Line Source Solution	p. 100
Time-Dependent Solutions in Blocks
Time-Dependent One-Dimensional Solutions	p. 113
Surface Heating from Cold	p. 117
Time-Dependent Point and Line Sources	p. 122
The Thermal History of a Material Element	p. 129
Moving Boundary Problems
Stefan Problems	p. 137
Neumann's Problem	p. 146
Simple Models of Laser Keyhole Welding
Laser Keyhole Welding	p. 151
Point and Line Source Models	p. 154
The Relation between Power Absorbed and Keyhole Radius	p. 165
The line source as a model of the keyhole	p. 165
The Davis-Noller solution	p. 167
Other two-dimensional thermal models for the solid and liquid phases	p. 173
The Liquid/Vapor Interface	p. 174
The Keyhole	p. 178
Numerical Examples	p. 185
The Fluid Regions in Keyhole Welding
Flow in the Weld Pool	p. 191
Interaction of Motion in the Weld Pool with the Keyhole	p. 200
Laser Heating of the Vapor in the Keyhole	p. 225
Thermoelastic Problems
Thermal Expansion	p. 241
The Scabbling of Concrete	p. 244
Two-Dimensional Models	p. 251
Stresses in a Metal Workpiece	p. 260
Conclusion	p. 261
Values of Material Properties	p. 263
Elastic Green's Functions for a Semi-Infinite Domain	p. 269
Bibliography	p. 275
Index	p. 289
Table of Contents provided by Syndetics. All Rights Reserved.

The Mathematics of Thermal Modeling

An Introduction to the Theory of Laser Material Processing

At a Glance

Hardcover

Industry Reviews

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How to return your order

Defective items

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