| Contributors | p. xi |
| Preface | p. xv |
| Introduction | p. 1 |
| Mathematical Preliminaries | p. 5 |
| The Continuum Model | p. 5 |
| Conservation Laws | p. 5 |
| Diffusion | p. 6 |
| Flow and Deformation of Solids and Fluids | p. 9 |
| Equations of Motion | p. 10 |
| Incompressible Linear Viscous Fluid | p. 11 |
| Inviscid Incompressible Fluid | p. 13 |
| Inviscid Incompressible Irrotational Flow | p. 14 |
| Compressible Viscous Flow | p. 14 |
| Compressible Inviscid Flow | p. 15 |
| The Reynolds Number and Flow in a Viscous Boundary Layer | p. 16 |
| Viscous Flow at Low Reynolds Number | p. 17 |
| Viscous Flow in a Thin Layer | p. 18 |
| Linear Elasticity | p. 19 |
| Summary | p. 20 |
| References | p. 20 |
| Fluid-Mechanical Modelling of the Scroll Compressor | p. 22 |
| Preface | p. 22 |
| Introduction | p. 22 |
| Leakage between Chambers | p. 25 |
| Governing Equations and Boundary Conditions | p. 26 |
| Dimensionless Parameters | p. 28 |
| Dimensionless Equations | p. 30 |
| Solution in the Quasi-Steady Limit | p. 32 |
| Conservation Equations for the Chambers | p. 33 |
| The Coupled Problem | p. 34 |
| The Small Coupling Limit | p. 36 |
| Numerical Results | p. 37 |
| Conclusions | p. 43 |
| Acknowledgements | p. 44 |
| References | p. 44 |
| Determining the Viscosity of a Carbon Paste Used in Smelting | p. 46 |
| Preface | p. 46 |
| Continuous Electrode Smelting | p. 46 |
| Problem Formulation | p. 49 |
| Simplified Analysis | p. 51 |
| Corner Solutions | p. 51 |
| Special Geometries | p. 54 |
| Further Analysis of the Velocity Test | p. 56 |
| Analysis of the Viscometer Test | p. 57 |
| Analysis of the Plasticity Test | p. 58 |
| The Boundary Layer at the Base of the Sample | p. 58 |
| Numerical Analysis and Results | p. 60 |
| Finite-Element Method | p. 60 |
| Results | p. 61 |
| Final Conclusions | p. 63 |
| Acknowledgement | p. 64 |
| References | p. 65 |
| The Vibrating Element Densitometer | p. 66 |
| Preface | p. 66 |
| Introduction | p. 66 |
| Resonance | p. 70 |
| Added Mass Model | p. 71 |
| Fluid--Plate Model | p. 72 |
| Plate Equation | p. 72 |
| Fluid Equation | p. 73 |
| Fluid--Plate Interaction | p. 73 |
| Simple Analysis: Incorrect Boundary Conditions | p. 74 |
| Solution with Clamped Boundary Conditions | p. 76 |
| Remarks | p. 77 |
| Appendix | p. 78 |
| References | p. 79 |
| Acoustic Emission from Damaged FRP-Hoop-Wrapped Cylinders | p. 80 |
| Preface | p. 80 |
| Introduction | p. 80 |
| Problem Description | p. 83 |
| Problem Solution | p. 89 |
| Further Analysis | p. 91 |
| Conclusion | p. 94 |
| References | p. 96 |
| Modelling the Cooking of a Single Cereal Grain | p. 97 |
| Preface | p. 97 |
| Introduction | p. 97 |
| The Problem | p. 98 |
| Background | p. 99 |
| Heating a Single Grain | p. 100 |
| Sphere | p. 102 |
| Ellipsoid | p. 102 |
| Timescales for Wetting and Heating--Linear Models | p. 103 |
| Wetting the Grains--a Nonlinear Model | p. 104 |
| Numerical Solutions | p. 105 |
| Analytic Solutions--Mean Action Time | p. 106 |
| Log Mean Diffusivity | p. 108 |
| Degree of Overcook for the Present Process | p. 109 |
| Temperature Dependence of Wetting Times | p. 111 |
| Sensitivity Analysis | p. 112 |
| Conclusions and Further Extensions | p. 112 |
| Acknowledgements | p. 114 |
| References | p. 114 |
| Epidemic Waves in Animal Populations: A Case Study | p. 115 |
| Preface | p. 115 |
| History of RHD and its Introduction into New Zealand | p. 116 |
| What is Known about the Disease | p. 117 |
| What We Want to Know | p. 117 |
| The Modelling. Analytical/Numerical | p. 118 |
| Case: No Immunity (R(x, t) = 0) and No Breeding (a = 0) | p. 120 |
| Case: No Immunity (R(x, t) = 0) But Breeding Season (a [not equal] 0) | p. 125 |
| Parameter Values | p. 127 |
| Immunity | p. 130 |
| Results and Conclusions | p. 131 |
| Further Work | p. 132 |
| References | p. 133 |
| Dynamics of Automotive Catalytic Converters | p. 135 |
| Introduction | p. 135 |
| Model Equations | p. 137 |
| Single-Oxidand Model and Nondimensionalization | p. 141 |
| Asymptotic Analysis of the Single-Oxidand Model | p. 144 |
| Warm-up Behavior | p. 145 |
| Light-off Behavior | p. 147 |
| Numerical Methods and Results | p. 150 |
| Further Analysis of the Single-Oxidand Model | p. 154 |
| Concluding Remarks | p. 157 |
| Acknowledgements | p. 158 |
| References | p. 158 |
| Analysis of an Endothermic Reaction in a Packed Column | p. 160 |
| Introduction | p. 160 |
| The Problem and the Model | p. 161 |
| Analysis | p. 166 |
| Discussion | p. 175 |
| Further Modelling Considerations | p. 176 |
| References | p. 178 |
| Simulation of the Temperature Behaviour of Hot Glass during Cooling | p. 181 |
| Cooling of Glass | p. 182 |
| Mathematical Formulation of the Problem | p. 182 |
| Heat and Radiative Transfer Equations | p. 182 |
| Modelling of the Boundary Conditions for the Heat Transfer Equation | p. 184 |
| Numerical Solution Methods | p. 187 |
| The Heat Transfer Equation | p. 187 |
| Ray Tracing | p. 187 |
| A Diffusion Approximation | p. 189 |
| Two-Scale Analysis | p. 190 |
| Numerical Simulation and Results | p. 195 |
| Conclusions and Further Questions | p. 196 |
| References | p. 197 |
| Water Equilibration in Vapor-Diffusion Crystal Growth | p. 199 |
| Preface | p. 199 |
| Introduction | p. 199 |
| Formulation | p. 203 |
| Analytical Treatment | p. 209 |
| Geometry | p. 209 |
| Method of Multiple Timescales | p. 210 |
| Formulation | p. 213 |
| Solution | p. 215 |
| Numerical Approach | p. 219 |
| Results | p. 219 |
| Discussion | p. 224 |
| Acknowledgement | p. 227 |
| References | p. 227 |
| Modelling of Quasi-Static and Dynamic Load Responses of Filled Viscoelastic Materials | p. 229 |
| Introduction | p. 229 |
| Nonlinear Extension Models, Experiments and Results | p. 231 |
| Neo-Hookean Extension Models | p. 231 |
| Approximation of Nonlinear Constitutive Laws | p. 235 |
| Nonlinear and Hysteretic Models, Experiments and Results | p. 240 |
| Quasi-Static Hysteresis Loops | p. 240 |
| A Dynamic Model with Hysteresis | p. 244 |
| Conclusion | p. 248 |
| Acknowledgements | p. 250 |
| References | p. 250 |
| A Gasdynamic-Acoustic Model of a Bird Scare Gun | p. 253 |
| Introduction | p. 253 |
| Model | p. 255 |
| Geometry | p. 255 |
| Pot | p. 255 |
| Jet | p. 258 |
| Pipe | p. 259 |
| Radiated Field | p. 260 |
| Nonlinear Correction in the Pipe | p. 262 |
| Analysis | p. 264 |
| Results | p. 266 |
| Conclusions and Suggestions for Further Work | p. 266 |
| Acknowledgements | p. 268 |
| References | p. 268 |
| Paper Tension Variations in a Printing Press | p. 270 |
| Preface | p. 270 |
| Problem Definition | p. 271 |
| Printing Presses | p. 272 |
| Modelling | p. 274 |
| Motion over a Roller | p. 275 |
| Motion in a Span | p. 281 |
| The N-Roller Start-up Problem | p. 282 |
| Concluding Remarks | p. 285 |
| Acknowledgements | p. 288 |
| References | p. 289 |
| Index | p. 291 |
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