Industrial Mathematics: Case Studies in the Diffusion of Heat and Matter (Australian Mathematical Society Lecture Series, Series Number 16)

The Focus In This Text Is On Mathematical Modelling Stimulated By Contemporary Industrial Problems Involving Heat Conduction And Mass Diffusion. These Include Continuous Metal Casting, Laser Drilling, Spontaneous Combustion Of Industrial Waste, Water Filtration And Crop Irrigation. The Industrial Problems Prove To Be An Excellent Setting For The Introduction And Reinforcement Of Modelling Skills, Equation Solving Techniques, Qualitative Understanding Of Partial Differential Equations And Their Dynamical Properties. Mathematical Topics Include Setting Up Partial Differential Equations And Boundary Conditions, Dimensional Analysis, Scaling, Perturbation Expansions, Boundary Value Problems, Fourier Series, Symmetry Reductions, Stefan Problems And Bifurcations. For Students Of Mathematics, Engineering, Or Any Other Related Discipline, This Will Be A Great Introduction To Modelling The Real World. Glenn R. Fulford, Philip Broadbridge. Includes Bibliographical References (p. 195-198) And Index. Contents......Page 7 Preface......Page 9 1.1 Heat and diffusion ?a A bird's eye view......Page 13 1.2 Mathematics in industry......Page 15 1.3 Overview of the case studies......Page 17 1.4 Units and dimensions......Page 19 1.5 Di usion equations......Page 22 1.6 Heat conduction equations......Page 28 1.7 Boundary conditions......Page 33 1.8 Solving the heat/di usion equation......Page 39 1.9 Scaling equations......Page 41 1.10 Dimensional analysis......Page 45 1.11 Problems for Chapter 1......Page 50 2.1 Introduction to the case study problem......Page 61 2.2 The Boltzmann similarity solution......Page 68 2.3 A moving boundary problem......Page 76 2.4 The pseudo-steady-state approximate solution......Page 81 2.5 Solving the continuous casting case study......Page 82 2.6 Problems for Chapter 2......Page 88 3.1 Introduction to the case study problem......Page 97 3.2 Stretching transformations......Page 102 3.3 Di usion from a point source......Page 108 3.4 Solving the water filtration case study......Page 114 3.5 Problems for Chapter 3......Page 118 4.1 Introduction to the case study problem......Page 124 4.2 Method of perturbations......Page 130 4.3 Boundary perturbations......Page 135 4.4 Solving the laser drilling case study......Page 142 4.5 Problems for Chapter 4......Page 148 5.1 Introduction to the case study problem......Page 154 5.2 Bifurcations and spontaneous ignition......Page 160 5.3 Ignition with conduction......Page 167 5.4 Solving the factory fire case study......Page 174 5.5 Problems for Chapter 5......Page 178 6.1 Introduction to the case study problem......Page 184 6.2 The Kirchho transformation......Page 188 6.3 Fourier series solutions......Page 190 6.4 Solving the crop irrigation case study......Page 194 6.5 Problems for Chapter 6......Page 198 7.1 Introduction......Page 201 7.2 A survey of mathematical techniques......Page 203 7.3 Mathematics in some other industries......Page 205 References......Page 207 Index......Page 211 "The focus in this text is on mathematical modelling stimulated by contemporary industrial problems involving heat conduction and mass diffusion. These include continuous metal casting, laser drilling, spontaneous combustion of industrial waste, water filtration and crop irrigation. The industrial problems prove to be an excellent setting for the introduction and reinforcement of modelling skills, equation solving techniques, qualitative understanding of partial differential equations and their dynamical properties. Mathematical topics include setting up partial differential equations and boundary conditions, dimensional analysis, scaling, perturbation expansions, boundary valuer problems, Fourier series, symmetry reductions, Stefan problems and bifurcations. For students of mathematics, engineering, or any other related discipline, this will be a great introduction to modelling the real world."--Publisher description In this chapter we set the scene by introducing the case studies of the following chapters.