Mathematical modeling : case studies from industry / edited by Ellis Cumberbatch, Alistair Fitt.

Format:

Book

Contributor:

Cumberbatch, Ellis.

Fitt, Alistair, 1957-

Language:

English

Subjects (All):

Mathematical models--Industrial applications.

Mathematical models.

Physical Description:

xv, 299 pages : illustrations ; 23 cm

Place of Publication:

Cambridge, UK ; New York : Cambridge University Press, 2001.

Summary:

Industrial Mathematics is growing enormously in popularity around the world. This book deals with \[I\]real\[/I\] industrial problems from \[I\]real\[/I\] industries. Presented as a series of case studies by some of the world's most active and successful industrial mathematicians, this volume shows clearly how the process of mathematical collaboration with industry can not only work successfully for the industrial partner, but also lead to interesting and important mathematics. The book begins with a brief introduction, where the equations that most of the studies are based upon are summarized. Thirteen different problems are then considered, ranging from the cooking of cereal to the analysis of epidemic waves in animal populations. Throughout the work the emphasis is on telling industry what they really want to know. This book is suitable for all final year undergraduates, master's students, and Ph.D. students who are working on practical mathematical modeling.

Contents:

0 Mathematical Preliminaries 5

0.1 The Continuum Model 5

0.1.1 Conservation Laws 5

0.2 Diffusion 6

0.3 Flow and Deformation of Solids and Fluids 9

0.3.1 Equations of Motion 10

0.4 Incompressible Linear Viscous Fluid 11

0.4.1 Inviscid Incompressible Fluid 13

0.4.2 Inviscid Incompressible Irrotational Flow 14

0.4.3 Compressible Viscous Flow 14

0.4.4 Compressible Inviscid Flow 15

0.4.5 The Reynolds Number and Flow in a Viscous Boundary Layer 16

0.4.6 Viscous Flow at Low Reynolds Number 17

0.4.7 Viscous Flow in a Thin Layer 18

0.5 Linear Elasticity 19

1 Fluid-Mechanical Modelling of the Scroll Compressor 22

1.2 Leakage between Chambers 25

1.2.1 Governing Equations and Boundary Conditions 26

1.2.2 Dimensionless Parameters 28

1.2.3 Dimensionless Equations 30

1.2.4 Solution in the Quasi-Steady Limit 32

1.3 Conservation Equations for the Chambers 33

1.4 The Coupled Problem 34

1.4.1 The Small Coupling Limit 36

1.5 Numerical Results 37

2 Determining the Viscosity of a Carbon Paste Used in Smelting 46

2.1 Continuous Electrode Smelting 46

2.2 Problem Formulation 49

2.3 Simplified Analysis 51

2.3.1 Corner Solutions 51

2.4 Special Geometries 54

2.4.1 Further Analysis of the Velocity Test 56

2.4.2 Analysis of the Viscometer Test 57

2.4.3 Analysis of the Plasticity Test 58

2.4.4 The Boundary Layer at the Base of the Sample 58

2.5 Numerical Analysis and Results 60

2.5.1 Finite-Element Method 60

2.5.2 Results 61

3 The Vibrating Element Densitometer 66

3.2 Resonance 70

3.3 Added Mass Model 71

3.4 Fluid

Plate Model 72

3.4.1 Plate Equation 72

3.4.2 Fluid Equation 73

3.4.3 Fluid

Plate Interaction 73

3.5 Simple Analysis: Incorrect Boundary Conditions 74

3.6 Solution with Clamped Boundary Conditions 76

3.7 Remarks 77

4 Acoustic Emission from Damaged FRP-Hoop-Wrapped Cylinders 80

4.2 Problem Description 83

4.3 Problem Solution 89

4.4 Further Analysis 91

5 Modelling the Cooking of a Single Cereal Grain 97

5.2 The Problem 98

5.4 Heating a Single Grain 100

5.4.1 Sphere 102

5.4.2 Ellipsoid 102

5.5 Timescales for Wetting and Heating

Linear Models 103

5.6 Wetting the Grains

a Nonlinear Model 104

5.6.1 Numerical Solutions 105

5.6.2 Analytic Solutions

Mean Action Time 106

5.6.3 Log Mean Diffusivity 108

5.6.4 Degree of Overcook for the Present Process 109

5.7 Temperature Dependence of Wetting Times 111

5.8 Sensitivity Analysis 112

5.9 Conclusions and Further Extensions 112

6 Epidemic Waves in Animal Populations: A Case Study 115

6.1 History of RHD and its Introduction into New Zealand 116

6.2 What is Known about the Disease 117

6.3 What We Want to Know 117

6.4 The Modelling. Analytical/Numerical 118

6.4.1 Case: No Immunity (R(x, t) = 0) and No Breeding (a = 0) 120

6.4.2 Case: No Immunity (R(x, t) = 0) But Breeding Season (a [not equal] 0) 125

6.4.3 Parameter Values 127

6.5 Immunity 130

6.7 Further Work 132

7 Dynamics of Automotive Catalytic Converters 135

7.2 Model Equations 137

7.3 Single-Oxidand Model and Nondimensionalization 141

7.4 Asymptotic Analysis of the Single-Oxidand Model 144

7.4.1 Warm-up Behavior 145

7.4.2 Light-off Behavior 147

7.5 Numerical Methods and Results 150

7.6 Further Analysis of the Single-Oxidand Model 154

8 Analysis of an Endothermic Reaction in a Packed Column 160

8.2 The Problem and the Model 161

8.3 Analysis 166

8.5 Further Modelling Considerations 176

9 Simulation of the Temperature Behaviour of Hot Glass during Cooling 181

9.1 Cooling of Glass 182

9.2 Mathematical Formulation of the Problem 182

9.2.1 Heat and Radiative Transfer Equations 182

9.2.2 Modelling of the Boundary Conditions for the Heat Transfer Equation 184

9.3 Numerical Solution Methods 187

9.3.1 The Heat Transfer Equation 187

9.3.2 Ray Tracing 187

9.3.3 A Diffusion Approximation 189

9.3.4 Two-Scale Analysis 190

9.4 Numerical Simulation and Results 195

9.5 Conclusions and Further Questions 196

10 Water Equilibration in Vapor-Diffusion Crystal Growth 199

10.2 Formulation 203

10.3 Analytical Treatment 209

10.3.1 Geometry 209

10.3.2 Method of Multiple Timescales 210

10.3.3 Formulation 213

10.3.4 Solution 215

10.4 Numerical Approach 219

10.5 Results 219

11 Modelling of Quasi-Static and Dynamic Load Responses of Filled Viscoelastic Materials 229

11.2 Nonlinear Extension Models, Experiments and Results 231

11.2.1 Neo-Hookean Extension Models 231

11.2.2 Approximation of Nonlinear Constitutive Laws 235

11.3 Nonlinear and Hysteretic Models, Experiments and Results 240

11.3.1 Quasi-Static Hysteresis Loops 240

11.3.2 A Dynamic Model with Hysteresis 244

12 A Gasdynamic-Acoustic Model of a Bird Scare Gun 253

12.2 Model 255

12.2.1 Geometry 255

12.2.2 Pot 255

12.2.3 Jet 258

12.2.4 Pipe 259

12.2.5 Radiated Field 260

12.2.6 Nonlinear Correction in the Pipe 262

12.3 Analysis 264

12.4 Results 266

12.5 Conclusions and Suggestions for Further Work 266

13 Paper Tension Variations in a Printing Press 270

13.1 Problem Definition 271

13.2 Printing Presses 272

13.3 Modelling 274

13.3.1 Motion over a Roller 275

13.3.2 Motion in a Span 281

13.4 The N-Roller Start-up Problem 282.

Notes:

Includes bibliographical references and index.

ISBN:

0521650070

0521011736

OCLC:

45700844