Mathematical models in the manufacturing of glass: C.I.M.E. Summer School, Montecatini Terme, Italy, September 8 - 19, 2008
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2011
|
| Series: | Lecture notes in mathematics
2010 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XI, 227 S. Ill., graph. Darst. |
| ISBN: | 9783642159664 |
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Record in the Search Index
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IMAGE 1
CONTENTS
MATHEMATICAL MODELLING OF GLASS FORMING PROCESSES 1
J.A.W.M. GROOT, ROBERT M.M. MATTHEIJ, AND K.Y. LAEVSKY 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 32
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
REFERENCES 53
RADIATIVE HEAT TRANSFER AND APPLICATIONS FOR GLASS PRODUCTION PROCESSES
57
MARTIN FRANK AND AXEL KLAR 1 INTRODUCTION 57
2 RADIATIVE HEAT TRANSFER EQUATIONS FOR GLASS 58
2.1 FUNDAMENTAL QUANTITIES 59
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1005647097
DIGITALISIERT DURCH
IMAGE 2
VIII CONTENTS
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
3 DIRECT NUMERICAL METHODS 70
3.1 ORDINATES AND SPACE DISCRETIZATIONS 71
3.2 LINEAR SYSTEM FORMULATION 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 SPN APPROXIMATIONS 94
4.2 BOUNDARY CONDITIONS FOR SPN APPROXIMATIONS 100
5 MOMENT MODELS 104
5.1 SPHERICAL HARMONICS 105
5.2 MINIMUM ENTROPY CLOSURE 107
5.3 FLUX-LIMITED DIFFUSION AND ENTROPY MINIMIZATION 108 5.4 PARTIAL
MOMENTS 110
5.5 PARTIAL MOMENT PN 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 GREYCOOLING 120
7.4 MULTIGROUP TRANSPORT 123
7.5 MULTIGROUP COOLING 125
7.6 ADAPTIVE METHODS FOR THE SIMULATION OF 2-D AND 3-D COOLING PROCESSES
125
REFERENCES 131
RADIATIVE HEAT TRANSFER AND APPLICATIONS FOR GLASS PRODUCTION PROCESSES
H 135
NORBERT SIEDOW 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
IMAGE 3
CONTENTS IX
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
REFERENCES 170
NON-ISOTHERMAL FLOW OF MOLTEN GLASS: MATHEMATICAL CHALLENGES AND
INDUSTRIAL QUESTIONS 173
ANGIOLO FARINA, ANTONIO FASANO, AND ANDRO MIKELIC 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
REFERENCES 223
LIST OF PARTICIPANTS 225 |
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| dewey-full | 666.12015118 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 666 - Ceramic & allied technologies |
| dewey-raw | 666.12015118 |
| dewey-search | 666.12015118 |
| dewey-sort | 3666.12015118 |
| dewey-tens | 660 - Chemical engineering |
| discipline | Chemie / Pharmazie Physik Mathematik Werkstoffwissenschaften / Fertigungstechnik Industrien, sonstige |
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| spelling | Mathematical models in the manufacturing of glass C.I.M.E. Summer School, Montecatini Terme, Italy, September 8 - 19, 2008 Angiolo Farina ... Ed.: Antonio Fasano Berlin [u.a.] Springer 2011 XI, 227 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2010 Glasschmelze (DE-588)4122177-1 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2008 Montecatini Terme gnd-content Glasschmelze (DE-588)4122177-1 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Farina, Angiolo Sonstige (DE-588)143181491 oth Fasano, Antonio Sonstige (DE-588)111188962 oth Centro Internazionale Matematico Estivo Sonstige (DE-588)1025933-8 oth Erscheint auch als Online-Ausgabe 978-3-642-15967-1 Lecture notes in mathematics 2010 (DE-604)BV000676446 2010 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3523489&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020804044&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mathematical models in the manufacturing of glass C.I.M.E. Summer School, Montecatini Terme, Italy, September 8 - 19, 2008 Lecture notes in mathematics Glasschmelze (DE-588)4122177-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4122177-1 (DE-588)4114528-8 (DE-588)1071861417 |
| title | Mathematical models in the manufacturing of glass C.I.M.E. Summer School, Montecatini Terme, Italy, September 8 - 19, 2008 |
| title_auth | Mathematical models in the manufacturing of glass C.I.M.E. Summer School, Montecatini Terme, Italy, September 8 - 19, 2008 |
| title_exact_search | Mathematical models in the manufacturing of glass C.I.M.E. Summer School, Montecatini Terme, Italy, September 8 - 19, 2008 |
| title_full | Mathematical models in the manufacturing of glass C.I.M.E. Summer School, Montecatini Terme, Italy, September 8 - 19, 2008 Angiolo Farina ... Ed.: Antonio Fasano |
| title_fullStr | Mathematical models in the manufacturing of glass C.I.M.E. Summer School, Montecatini Terme, Italy, September 8 - 19, 2008 Angiolo Farina ... Ed.: Antonio Fasano |
| title_full_unstemmed | Mathematical models in the manufacturing of glass C.I.M.E. Summer School, Montecatini Terme, Italy, September 8 - 19, 2008 Angiolo Farina ... Ed.: Antonio Fasano |
| title_short | Mathematical models in the manufacturing of glass |
| title_sort | mathematical models in the manufacturing of glass c i m e summer school montecatini terme italy september 8 19 2008 |
| title_sub | C.I.M.E. Summer School, Montecatini Terme, Italy, September 8 - 19, 2008 |
| topic | Glasschmelze (DE-588)4122177-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Glasschmelze Mathematisches Modell Konferenzschrift 2008 Montecatini Terme |
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