Industrial Mathematics: Case Studies in the Diffusion of Heat and Matter

by Glenn R. Fulford , Philip Broadbridge

• ISBN13: 9780521807173
• ISBN10: 0521807174
• Format: Hardcover
• Copyright: 2002-01-28
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Preface	ix
Preliminaries	1	(48)
Heat and diffusion - A bird's eye view	1	(2)
Mathematics in industry	3	(2)
Overview of the case studies	5	(2)
Units and dimensions	7	(3)
Diffusion equations	10	(6)
Heat conduction equations	16	(5)
Boundary conditions	21	(6)
Solving the heat/diffusion equation	27	(2)
Scaling equations	29	(4)
Dimensional analysis	33	(5)
Problems for Chapter 1	38	(11)
Case Study: Continuous Casting	49	(36)
Introduction to the case study problem	49	(7)
The Boltzmann similarity solution	56	(8)
A moving boundary problem	64	(5)
The pseudo-steady-state approximate solution	69	(1)
Solving the continuous casting case study	70	(6)
Problems for chapter 2	76	(9)
Case Study: Water Filtration	85	(27)
Introduction to the case study problem	85	(5)
Stretching transformations	90	(6)
Diffusion from a point source	96	(6)
Solving the water filtration case study	102	(4)
Problems for Chapter 3	106	(6)
Case Study: Laser Drilling	112	(30)
Introduction to the case study problem	112	(6)
Method of perturbations	118	(5)
Boundary perturbations	123	(7)
Solving the laser drilling case study	130	(6)
Problems for Chapter 4	136	(6)
Case Study: Factory Fires	142	(30)
Introduction to the case study problem	142	(6)
Bifurcations and spontaneous ignition	148	(7)
Ignition with conduction	155	(7)
Solving the factory fire case study	162	(4)
Problems for Chapter 5	166	(6)
Case Study: Irrigation	172	(17)
Introduction to the case study problem	172	(4)
The Kirchhoff transformation	176	(2)
Fourier series solutions	178	(4)
Solving the crop irrigation case study	182	(4)
Problems for Chapter 6	186	(3)
Conclusions	189	(6)
Introduction	189	(2)
A survey of mathematical techniques	191	(2)
Mathematics in some other industries	193	(2)
References	195	(4)
Index	199