| Overview | p. 1 |
| Introduction | p. 1 |
| Systematics and Boundary Conditions of This Book | p. 3 |
| Some Important 3D Continuum Equations | p. 6 |
| References | p. 15 |
| Melting and Fining | p. 17 |
| Modeling of the Melting Process in Industrial Glass Furnaces | p. 17 |
| Application of Process Simulation Models for Glass Furnaces | p. 18 |
| Modeling of Heat Transfer and Convection Flows in Glass-Melting Tanks | p. 23 |
| Sand-Grain Dissolution, Behavior of Gas Bubbles in Glass Melts, and Glass-Quality Index | p. 47 |
| Models for Evaporation and Superstructure Refractory Attack by Vapors | p. 61 |
| Dynamic Modeling | p. 71 |
| Concluding Remarks | p. 72 |
| Mathematical Modeling of Batch Melting in Glass Tanks | p. 73 |
| Motivation and Requirements on Batch Modeling | p. 74 |
| Survey of Batch Melting | p. 76 |
| Theoretical Basis of Batch Modeling | p. 93 |
| Key Values and Non-Dimensional Numbers | p. 105 |
| Batch Models | p. 110 |
| High-Frequency Melting of Glass in Crucibles Frank-Thomas Lentes | p. 126 |
| Basics of Electrodynamics | p. 126 |
| Mathematical Formulation of the Simulation Model | p. 129 |
| Simulation Results | p. 134 |
| Conclusion and Outlook | p. 136 |
| Model-Based Glass Melter Control Ton Backx | p. 137 |
| Model Concepts | p. 138 |
| Model-Predictive Control | p. 142 |
| Extensions of the MPC Technology | p. 148 |
| Application of MPC in the Glass Industry | p. 150 |
| References | p. 155 |
| Homogenizing and Conditioning | p. 165 |
| The Intensity of Mixing Processes | p. 165 |
| Description and Quantification of Mixing Processes | p. 165 |
| Flows and Particle Paths in Stirrers | p. 169 |
| Statistics of Residence Time and Dispersion | p. 173 |
| Deformation of Infinitesimal Test Bodies Along Particle Paths | p. 176 |
| Deformation Statistics | p. 187 |
| Example: a Simple Paddle Stirrer | p. 189 |
| Outlook | p. 192 |
| Instabilities and Stabilization of Glass Pipe Flows | p. 193 |
| Stationary Temperature and Pressure Profiles in the Pipe | p. 193 |
| A Stability Phenomenon | p. 197 |
| Appendix: Derivation of Several Equations | p. 205 |
| Shape Optimization of Flanges | p. 208 |
| General Shape Optimization: Continuously Varying Thicknesses and Contours | p. 209 |
| Finite-Dimensional Shape Optimization: the 3-Ring/Spoke Flange | p. 230 |
| References | p. 237 |
| Shaping at Low Viscosities | p. 239 |
| Heat Transfer Between Glass and Mold During Hot Forming | p. 239 |
| Heat Transfer Coefficient Between Glass and Mold | p. 241 |
| Physics and Mathematics of the Heat Transfer | p. 245 |
| Sample Computations | p. 252 |
| Radiative Contributions to the Heat Transfer | p. 255 |
| Laboratory Experiments | p. 259 |
| Remote Spectral Temperature Profile Sensing | p. 262 |
| Thermal Radiation in Hot Glass | p. 263 |
| The Inverse Problem of Spectral Temperature Sensing | p. 266 |
| Sample Computations | p. 273 |
| Laboratory Experiment | p. 275 |
| Spectral Imaging of Hot Glass | p. 279 |
| Heat Transfer During Casting Experiments | p. 286 |
| Experimental Set Up | p. 287 |
| Comparison Between "Exact" Modeling and Measurement | p. 289 |
| Alternative Modeling Using the Active Thermal Conductivity | p. 290 |
| Thin-Layer Flows of Glass | p. 293 |
| Example of a Thin-Layer Model | p. 294 |
| Simplified Energy Balance | p. 298 |
| Validation of the Model | p. 300 |
| Fiber- and Tube-Drawing Models | p. 302 |
| More Comprehensive Thin-Layer Flow Models | p. 305 |
| Pressing of Drinking-Glass Stems | p. 306 |
| Model 1: Finite-Element Modeling | p. 309 |
| Model 2: Analytical Modeling | p. 310 |
| Comparison of Model 1 and Model 2 | p. 316 |
| The Use of Remeshing Methods in Pressing Simulations | p. 317 |
| Some Technical Aspects of the Method | p. 319 |
| Example: Pressing of a Tumbler | p. 320 |
| Example: Pressing of an "Axisymmetric TV Screen" | p. 321 |
| Chill Ripples in Pressing and Casting Processes | p. 326 |
| A Simple Casting Process | p. 328 |
| A Model for Kluge's Experimental Set-Up | p. 330 |
| References | p. 335 |
| 5 | p. 339 |
| Temperature-Dependent Elasticity in Reshaping Simulations | p. 339 |
| Model | p. 339 |
| Simulation Results | p. 341 |
| Sagging and Pressing of Glass Sheets | p. 343 |
| Model and Boundary Conditions | p. 344 |
| Results of the Model Computations | p. 345 |
| Calibration of Glass Tubes ThoralfJohansson | p. 349 |
| Model Description | p. 349 |
| Results of the Model Computations | p. 350 |
| Thermal Treatment | p. 359 |
| Verification of Relaxation Models | p. 359 |
| Mathematical Models | p. 359 |
| Experiments in the Lehr | p. 362 |
| Simulation | p. 363 |
| Measuring Stress and Compaction | p. 363 |
| Results | p. 363 |
| Stresses and Crack Growth in Continuously Formed Slabs | p. 367 |
| Cooling a Continuous Strip | p. 369 |
| Crack Growth | p. 370 |
| Modified Temperature Program in Order to Avoid Cracking | p. 371 |
| Cutting the Strip into Slabs | p. 372 |
| Thermal Tempering of Drinking Glasses | p. 374 |
| Principles of Thermal Tempering | p. 375 |
| Results for Spatially Inhomogeneous Quenching | p. 376 |
| Realization of a Quenching Process | p. 378 |
| Post-Processing by Laser Cutting | p. 381 |
| Rough Estimation of Process Parameters | p. 381 |
| Stress Levels | p. 381 |
| Laser-Beam Profiling | p. 382 |
| Selection of Laser | p. 384 |
| Numerical Analysis of Cutting Processes | p. 385 |
| Calculation of Temperature Distributions | p. 386 |
| Calculation of Stress Distributions | p. 391 |
| Condition for Cut Elongation | p. 396 |
| Calculation of Stress Intensities for Laser Cutting | p. 399 |
| Practical Realization | p. 404 |
| Appendix: Fundamentals of Fracture Mechanics | p. 408 |
| Fracture Mechanics for Brittle Solids | p. 408 |
| FEA Calculation of Stress-Intensity Factors | p. 410 |
| Prediction of the Crack Path | p. 411 |
| Glass Products Under Mechanical and Thermal Loads | p. 413 |
| Strength Optimization of Airbag Igniters | p. 413 |
| FEA for Axial-Symmetric Models | p. 413 |
| FEA of 3D Models | p. 420 |
| Pull-Out Tests | p. 423 |
| Push-Out Tests | p. 432 |
| Pressure Tests | p. 435 |
| Appendix: Statistical Procedure | p. 437 |
| Stiffness and Weight Optimization of a Reticle Stage for Optical Lithography | p. 438 |
| Requirements for a (9 × 9)" Reticle Stage | p. 439 |
| Design of a Prototype | p. 440 |
| FEM Optimization Without Additional Masses | p. 442 |
| FEM Analysis With Additional Masses | p. 444 |
| References | p. 446 |
| Simulation and Test of the Spinning Process Applied to Platinum Metals | p. 449 |
| Necessity to Shape Materials | p. 449 |
| Qualitative Description of the Spinning Process | p. 449 |
| Essential Assumptions for the Modeling of the Spinning Process | p. 451 |
| General Relations for the Model of the Spinning Process | p. 453 |
| Approximations | p. 455 |
| First Approximation: Quasi-Homogeneous Deformation | p. 455 |
| Second Approximation: Linearly Decreasing Deformation | p. 458 |
| A Practical Example for the First and Second Approximations | p. 460 |
| Experimental Observations and Discussion | p. 464 |
| References | p. 465 |
| List of Contributors | p. 467 |
| Sources of Figures and Tables | p. 471 |
| Index | p. 473 |
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