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Modeling in Materials Processing - Jonathan A. Dantzig

Modeling in Materials Processing

Paperback Published: 8th April 2002
ISBN: 9780521779234
Number Of Pages: 363

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Mathematical modeling and computer simulation are useful tools for improving materials processing. While courses in materials processing have covered modeling, they have traditionally been devoted to one particular class of materials, that is, polymers, metals, or ceramics. This text offers a new approach, presenting an integrated treatment of metallic and non-metallic materials. The authors show that a common base of knowledge - specifically, the fundamentals of heat transfer and fluid mechanics - provides a unifying theme for these seemingly disparate areas. Emphasis is placed on understanding basic physical phenomena and knowing how to include them in a model. The book also treats selected numerical methods, showing the relationship between the physical system, analytical solution, and the numerical scheme. A wealth of practical, realistic examples are provided, as well as homework exercises. Students, and practising engineers who must deal with a wide variety of materials and processing problems, will benefit from the unified treatment presented in this book.

'The book is highly recommended.' Zeitschrift fuer Angewandte Mathematik und Mechanik

Prefacep. ix
Principal Nomenclaturep. xi
Introductionp. 1
What Is a Model?p. 1
A Simple Pendulump. 2
One-Dimensional Traffic Flowp. 6
Summaryp. 19
Bibliographyp. 19
Exercisesp. 20
Governing Equationsp. 24
Preliminariesp. 24
Mass Balancep. 29
Momentum Balancep. 33
Energy Balancep. 45
Summaryp. 52
Bibliographyp. 53
Exercisesp. 53
Appendixp. 58
Scaling and Model Simplificationp. 60
Introductionp. 60
Basic Scaling Analysisp. 62
Small Parameters and Boundary Layersp. 69
Classical Dimensionless Groupsp. 76
Nondimensionalization for Numerical Solutions (Advanced)p. 78
Summaryp. 81
Bibliographyp. 81
Exercisesp. 81
Heat Conduction and Materials Processingp. 87
Steady Heat Conduction in Solidsp. 90
Transient Heat Conductionp. 93
Conduction with Phase Changep. 106
Summaryp. 120
Bibliographyp. 121
Exercisesp. 121
Appendixp. 130
Isothermal Newtonian Fluid Flowp. 132
Newtonian Flow in a Thin Channelp. 132
Other Slow Newtonian Flowsp. 143
Free Surfaces and Moving Boundariesp. 149
Flows with Significant Inertiap. 161
Summaryp. 177
Bibliographyp. 178
Exercisesp. 178
Non-Newtonian Fluid Flowp. 190
Non-Newtonian Behaviorp. 190
The Power Law Modelp. 192
Power Law Solutions for Other Simple Geometriesp. 200
Principles of Non-Newtonian Constitutive Equationsp. 202
More Non-Newtonian Constitutive Equationsp. 209
The Generalized Hele-Shaw Approximationp. 217
Summaryp. 228
Bibliographyp. 228
Exercisesp. 229
Heat Transfer with Fluid Flowp. 239
Uncoupled Advectionp. 239
Temperature-Dependent Viscosity and Viscous Dissipationp. 250
Buoyancy-Driven Flowp. 259
Summaryp. 275
Bibliographyp. 275
Exercisesp. 276
Mass Transfer and Solidification Microstructuresp. 282
Governing Equations for Diffusionp. 282
Solid-State Diffusionp. 285
Solidification Microstructure Developmentp. 295
Summaryp. 319
Bibliographyp. 320
Exercisesp. 321
Mathematical Backgroundp. 327
Scalars, Vectors, and Tensors: Definitions and Notationp. 327
Vector and Tensor Algebrap. 331
Differential Operations in Rectangular Coordinatesp. 335
Vectors and Tensors in Cylindrical and Spherical Coordinatesp. 337
The Divergence Theoremp. 339
Curvature of Curves and Surfacesp. 339
The Gaussian Error Functionp. 343
Bibliographyp. 345
Exercisesp. 345
Balance and Kinematic Equationsp. 348
Continuity Equation: General Formp. 348
Continuity Equation: Constant [rho]p. 348
Rate-of-Deformation Tensorp. 349
Vorticity Tensorp. 350
General Equation of Motionp. 350
Navier-Stokes Equation: Constant [rho] and [mu]p. 352
Heat Flux Vector: Isotropic Materialp. 353
Energy Balance: General Formp. 354
Energy Balance: Constant [rho], [kappa] and [mu]p. 355
Bibliographyp. 356
Indexp. 357
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521779234
ISBN-10: 0521779235
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 363
Published: 8th April 2002
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 25.5 x 17.7  x 2.4
Weight (kg): 0.71