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

Thirteen different real industrial problems from real industries are considered in this book. The order chosen for the articles presented is related to ordinary and partial differential equation classification. A very useful introduction precedes the thirteen chapters, in which all the preliminaries are presented: the continuum model, diffusion, flow and deformation of solids and fluids, incompressible linear viscous fluid and linear elasticity. The book is divided into three parts. In the first part, chapters 1-4 concern models based on essentially elliptic partial differential equations. The models presented are: Fluid-Mechanical Modelling of the Scroll Compressor, Determining the Viscosity of a Carbon Paste Used in Smelting, the Vibrating element densitometer and Acoustic Emission from Damaged FRP-Hoop-Wrapped Cylinders. In the second part, chapters 5-10 all involve some form of diffusion, with nonlinear effects, convection and reaction, and finally radiation being successively introduced. The models presented are: Modelling the Cooking of a Single Cereal Grain, Epidemic Waves in Animal Populations, Dynamics of Automotive Catalytic Converters, Analysis of an Endothermic Reaction in a Packed Column, Simulation of the Temperature Behaviour of Hot Glass and Water Equilibrium in Vapor-Diffusion Crystal Growth. In the third part, chapter 11 contains equations with both parabolic and hyperbolic features, while chapters 12 and 13 address two hyperbolic problems. The models presented are: Modelling of Quasi-Static and Dynamic Load Responses of Filled Viscoelastic Materials, A Gasdynamic-Acoustic Model of a Bird Scare Gun and Paper Tension Variations in a Printing Press. In each chapter there is a clear description of the process of modelling an industrial problem. This procedure is beginning with a short preface and an extended introduction where there is the description of the problem and the first mathematical equations appear. The modelling is completed step by step with respect to the real problem, the solution follows and the chapter ends with significant remarks, results, conclusions and even proposed open problems for further work. A detailed list of references is provided at the end of each chapter, giving the chance for an analytical further study. A very interesting and wide variety of areas are studied in this book through industrial problems, giving a clear and attractive picture of the whole procedure of the contemporary mathematical modelling. (Zentralblatt)

Bibliogr. et index