The use of lasers in materials processing has become widespread in recent
years, so that an understanding of the nature of heat and mass transfer in
this branch of modern technology is of increasing importance. The aim of the
authors of this book is to concentrate on the physical processes; these can be
developed from a mathematical point of view, or from direct experimentallyderived
observation. The two approaches are complementary; each can provide
insights and the synthesis of the two can lead to a very powerful understanding
of the processes involved. Mathematical modelling of physical processes has
had an important role to play in the development of technology over the
centuries and particularly so in the last one hundred and fifty years or so.
It can be argued that it is more important today than ever before since the
availability of high-speed computers allows accurate numerical simulation of
industrial processes at a fraction of the cost of the corresponding experiments.
This is one aspect of mathematical modelling, high profile and much valued,
but it is not the only one.
In the past mathematical modelling had to rely on qualitative investigation,
very special analytical solutions, or inaccurate and time-consuming
calculations performed with little in the way of tabulated or mechanical
assistance. Log tables and slide rules are still remembered by people working
today, though there are surely few who regret their disappearance.