Mathematical models in the manufacturing of glass : C.I.M.E. Summer School, Montecatini Terme, Italy 2008 / Angiolo Farina ...[and others] ; editor: Antonio Fasano.

Format:

Book

Conference/Event

Contributor:

Farina, Angiolo.

Fasano, A. (Antonio)

Conference Name:

EMS-CIME Course on Mathematical Models in the Manufacturing of Glass, Polymers and Textiles (2008 : Montecatini Terme, Italy)

Series:

Lecture notes in mathematics (Springer-Verlag) ; 2010.

Lecture notes in mathematics, 0075-8434 ; 2010

Language:

English

Subjects (All):

Glass manufacture--Mathematical models--Congresses.

Glass manufacture.

Glass--Technological innovations--Congresses.

Glass.

Glass--Technological innovations.

Mathematical models.

Genre:

Conference papers and proceedings.

Physical Description:

xi, 227 pages : illustrations (some color) ; 24 cm.

Place of Publication:

Heidelberg ; New York : Springer-Verlag, [2011]

Summary:

Lecture Notes in Mathematics This series reports on new developments in mathematical research and teaching - quickly, informally and at a high level. The type of material considered for publication includes

1. Research monographs

2. Lectures on a new field or presentations of a new angle in a classical field

3. Summer schools and intensive courses on topics of current research.

Texts that are out of print but still in demand may also be considered.

The timeliness of a manuscript is sometimes more important than its form, which may in such cases be preliminary or tentative.

Details of the editorial policy and how to submit to the series can be found on the last pages of a current volume. We recommend contacting the publisher or the series editors at an early stage of your project.

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Latex style files may be found at www.springer.com > Authors> Author Guidelines.

This volume presents a review of advanced technological problems in the glass industry and of the mathematics involved. It is amazing that such a seemingly small research area is extremely rich and, ails for an impressively large variety of mathematical methods, including numerical simulations of considerable complexity. The problems treated here are very typical of the field of glass manufacturing and cover a large spectrum of complementary subjects; injection molding by various techniques, radiative heat transfer in glass, nonisothermal flows and fibre spinning. The book can certainly be useful not only to applied mathematicians, but also to Physicists and engineers, who can find in it an overview of the most advanced models and methods. Book jacket.

Contents:

Mathematical Modelling-of Glass Forming Processes / J.A.W.M. Groot Groot, J.A.W.M., Robert M.M. Mattheij, Mattheij, Robert M.M., K.Y. Laevsky Laevsky, K.Y. 1

1 Introduction 2

1.1 Glass Forming 2

1.2 Process Simulation 6

1.3 Outline 7

2 Mathematical Model 8

2.1 Geometry, Problem Domains and Boundaries 8

2.2 Balance Laws 9

3 Parison Press Model 16

3.1 Mathematical Model 16

3.2 Slender-Geometry Approximation 18

3.3 Motion of the Plunger 23

3.4 Simulation Model 26

3.5 Results 30

4 Blow Model 31

4.1 Mathematical Model 31

4.2 Glass-Air Interfaces 36

4.3 Variational Formulation 39

4.4 Simulation Model 42

4.5 Results 45

5 Direct Press Model 46

5.1 Mathematical Model 47

5.2 Simulation Model 49

5.3 Results 51

Radiative Heat Transfer and Applications for Glass Production Processes / Martin Frank Frank, Martin, Axel Klar Klar, Axel 57

1 Introduction 57

2 Radiative Heat Transfer Equations for Glass 58

2.1 Fundamental Quantities 59

2.2 Blackbody Radiation 61

2.3 The Transfer Equation 62

2.4 Overall Energy Conservation 65

2.5 Boundary Conditions 66

2.6 Summary 68

Direct Numerical Methods 70

3.1 Ordinates and Space Discretizations 71

3.2 Linear System Forulation 73

3.3 Preconditioning Techniques 77

3.4 A Fast Multilevel Preconditioner 82

3.5 Numerical Results 85

4 Higher-Order Diffusion Approximations 92

4.1 Asymptotic Analysis and Derivation of the SP_n Approximations 94

4.2 Boundary Conditions for SP_n Approximations 100

5 Moment Models 104

5.1 Spherical Harmonics 105

5.2 Minimum Entropy losure 107

5.3 Flux-Limited Diffusion and Entropy Minimization 108

5.4 Partial Moments 110

5.5 Partial Moment P_N Closure 112

5·6 Partial Moment Entropy Closure 113

6 Frequency-Averaged Moment Equations 115

6.1 Entropy Minimization 116

6.2 Inversion of the System 117

6.3 Properties 118

7 Numerical Comparisons 119

7.1 Numerical Results 119

7.2 Grey Transport 119

7.3 Grey Cooling 120

7.4 MUltigroup Transport 123

7.5 MUltigroup Cooling 125

7.6 Adaptive methods for the Simulations of 2-d and 3-d Cooling Process 125

References 131

Radiative Heat Transfer and Applications for Glass Production Process II 135

1 Introduction 135

2 Models for Fast Radiative Heat Transfer Simulation 137

2.1 Introduction 137

3 Indirect Temperature Measurement of Hot Glasses 148

3.1 Introduction 148

3.2 The Basic Equation of Spectral Remote Temperature Sensing 149

3.3 Some Basics of Inverse Problems 150

3.4 Spectral Remote Sensing 159

3.5 Reconstruction of Initial Temperature 161

3.6 Conclusions 170

Non-Isothermal Flow of Molten Glass: Mathematical Challenges and Industrial Questions / Angio Farina Farina, Angio, Antonio Fasano Fasano, Antonio, Andro Mikelic Mikelic, Andro 173

1 Introduction 173

2 Mathematical Modelling 176

2.1 Definitions and Basic Equations 176

2.2 Fluids Physical Properties and Constitutive Equations 177

2.3 The General Model 181

2.4 Scaling and Dimensionless Formulation 183

3 Study of the Stationary Non-Isothermal Molten Glass Flow in a Die 187

3.1 Existence and Uniqueness Result for the Stationary Problem 189

3.2 Oberbeck-Boussinesq Model 194

4 Modelling the Viscous Jet at the Exit of the Die 198

4.1 Definition of L and Jet's Profile at the End of Stage (c) 201

5 Terminal Phase of the Fiber Drawing 207

5.1 Derivation of the Model of Matovich-Pearson for the Thermal Case 209

5.2 Solvability of the Boundary Value Problems for the Stationary Effective Equations 216.

Notes:

The EMS-CIME Course on Mathematical Models in the Manufacturing of Glass, Polymers, and Textiles was held in Montecatini Terme (Italy) from September 8 to September 19, 2008.

Includes bibliographical references.

ISBN:

9783642159664

3642159664

OCLC:

668191356