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Mathematical Modeling : Case Studies from Industry - Ellis Cumberbatch

Mathematical Modeling

Case Studies from Industry

By: Ellis Cumberbatch (Editor), Alistair Fitt (Editor)

Paperback Published: 29th October 2001
ISBN: 9780521011730
Number Of Pages: 316

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Industrial Mathematics is growing enormously in popularity around the world. This book deals with real industrial problems from real 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.

'This is a fascinating, even inspiring, book for the graduate mathematician.' A. H. Harker, Contemporary Physics '... this book is an excellent introduction to mathematical modelling, with a wealth of interesting case studies and lovely mathematics that will appeal to many of its target audience - final year undergraduates, Masters and PhD students working in 'practical' mathematical modelling.' The Mathematical Gazette

Contributorsp. xi
Prefacep. xv
Introductionp. 1
Mathematical Preliminariesp. 5
The Continuum Modelp. 5
Conservation Lawsp. 5
Diffusionp. 6
Flow and Deformation of Solids and Fluidsp. 9
Equations of Motionp. 10
Incompressible Linear Viscous Fluidp. 11
Inviscid Incompressible Fluidp. 13
Inviscid Incompressible Irrotational Flowp. 14
Compressible Viscous Flowp. 14
Compressible Inviscid Flowp. 15
The Reynolds Number and Flow in a Viscous Boundary Layerp. 16
Viscous Flow at Low Reynolds Numberp. 17
Viscous Flow in a Thin Layerp. 18
Linear Elasticityp. 19
Summaryp. 20
Referencesp. 20
Fluid-Mechanical Modelling of the Scroll Compressorp. 22
Prefacep. 22
Introductionp. 22
Leakage between Chambersp. 25
Governing Equations and Boundary Conditionsp. 26
Dimensionless Parametersp. 28
Dimensionless Equationsp. 30
Solution in the Quasi-Steady Limitp. 32
Conservation Equations for the Chambersp. 33
The Coupled Problemp. 34
The Small Coupling Limitp. 36
Numerical Resultsp. 37
Conclusionsp. 43
Acknowledgementsp. 44
Referencesp. 44
Determining the Viscosity of a Carbon Paste Used in Smeltingp. 46
Prefacep. 46
Continuous Electrode Smeltingp. 46
Problem Formulationp. 49
Simplified Analysisp. 51
Corner Solutionsp. 51
Special Geometriesp. 54
Further Analysis of the Velocity Testp. 56
Analysis of the Viscometer Testp. 57
Analysis of the Plasticity Testp. 58
The Boundary Layer at the Base of the Samplep. 58
Numerical Analysis and Resultsp. 60
Finite-Element Methodp. 60
Resultsp. 61
Final Conclusionsp. 63
Acknowledgementp. 64
Referencesp. 65
The Vibrating Element Densitometerp. 66
Prefacep. 66
Introductionp. 66
Resonancep. 70
Added Mass Modelp. 71
Fluid--Plate Modelp. 72
Plate Equationp. 72
Fluid Equationp. 73
Fluid--Plate Interactionp. 73
Simple Analysis: Incorrect Boundary Conditionsp. 74
Solution with Clamped Boundary Conditionsp. 76
Remarksp. 77
Appendixp. 78
Referencesp. 79
Acoustic Emission from Damaged FRP-Hoop-Wrapped Cylindersp. 80
Prefacep. 80
Introductionp. 80
Problem Descriptionp. 83
Problem Solutionp. 89
Further Analysisp. 91
Conclusionp. 94
Referencesp. 96
Modelling the Cooking of a Single Cereal Grainp. 97
Prefacep. 97
Introductionp. 97
The Problemp. 98
Backgroundp. 99
Heating a Single Grainp. 100
Spherep. 102
Ellipsoidp. 102
Timescales for Wetting and Heating--Linear Modelsp. 103
Wetting the Grains--a Nonlinear Modelp. 104
Numerical Solutionsp. 105
Analytic Solutions--Mean Action Timep. 106
Log Mean Diffusivityp. 108
Degree of Overcook for the Present Processp. 109
Temperature Dependence of Wetting Timesp. 111
Sensitivity Analysisp. 112
Conclusions and Further Extensionsp. 112
Acknowledgementsp. 114
Referencesp. 114
Epidemic Waves in Animal Populations: A Case Studyp. 115
Prefacep. 115
History of RHD and its Introduction into New Zealandp. 116
What is Known about the Diseasep. 117
What We Want to Knowp. 117
The Modelling. Analytical/Numericalp. 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 Valuesp. 127
Immunityp. 130
Results and Conclusionsp. 131
Further Workp. 132
Referencesp. 133
Dynamics of Automotive Catalytic Convertersp. 135
Introductionp. 135
Model Equationsp. 137
Single-Oxidand Model and Nondimensionalizationp. 141
Asymptotic Analysis of the Single-Oxidand Modelp. 144
Warm-up Behaviorp. 145
Light-off Behaviorp. 147
Numerical Methods and Resultsp. 150
Further Analysis of the Single-Oxidand Modelp. 154
Concluding Remarksp. 157
Acknowledgementsp. 158
Referencesp. 158
Analysis of an Endothermic Reaction in a Packed Columnp. 160
Introductionp. 160
The Problem and the Modelp. 161
Analysisp. 166
Discussionp. 175
Further Modelling Considerationsp. 176
Referencesp. 178
Simulation of the Temperature Behaviour of Hot Glass during Coolingp. 181
Cooling of Glassp. 182
Mathematical Formulation of the Problemp. 182
Heat and Radiative Transfer Equationsp. 182
Modelling of the Boundary Conditions for the Heat Transfer Equationp. 184
Numerical Solution Methodsp. 187
The Heat Transfer Equationp. 187
Ray Tracingp. 187
A Diffusion Approximationp. 189
Two-Scale Analysisp. 190
Numerical Simulation and Resultsp. 195
Conclusions and Further Questionsp. 196
Referencesp. 197
Water Equilibration in Vapor-Diffusion Crystal Growthp. 199
Prefacep. 199
Introductionp. 199
Formulationp. 203
Analytical Treatmentp. 209
Geometryp. 209
Method of Multiple Timescalesp. 210
Formulationp. 213
Solutionp. 215
Numerical Approachp. 219
Resultsp. 219
Discussionp. 224
Acknowledgementp. 227
Referencesp. 227
Modelling of Quasi-Static and Dynamic Load Responses of Filled Viscoelastic Materialsp. 229
Introductionp. 229
Nonlinear Extension Models, Experiments and Resultsp. 231
Neo-Hookean Extension Modelsp. 231
Approximation of Nonlinear Constitutive Lawsp. 235
Nonlinear and Hysteretic Models, Experiments and Resultsp. 240
Quasi-Static Hysteresis Loopsp. 240
A Dynamic Model with Hysteresisp. 244
Conclusionp. 248
Acknowledgementsp. 250
Referencesp. 250
A Gasdynamic-Acoustic Model of a Bird Scare Gunp. 253
Introductionp. 253
Modelp. 255
Geometryp. 255
Potp. 255
Jetp. 258
Pipep. 259
Radiated Fieldp. 260
Nonlinear Correction in the Pipep. 262
Analysisp. 264
Resultsp. 266
Conclusions and Suggestions for Further Workp. 266
Acknowledgementsp. 268
Referencesp. 268
Paper Tension Variations in a Printing Pressp. 270
Prefacep. 270
Problem Definitionp. 271
Printing Pressesp. 272
Modellingp. 274
Motion over a Rollerp. 275
Motion in a Spanp. 281
The N-Roller Start-up Problemp. 282
Concluding Remarksp. 285
Acknowledgementsp. 288
Referencesp. 289
Indexp. 291
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521011730
ISBN-10: 0521011736
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 316
Published: 29th October 2001
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 1.8
Weight (kg): 0.46