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Cole and Caleb PrefaceThis book is devoted to an account of theories of heat conduction where the temperature may travel as a wave with a finite speed. This area of nonclassical diffusion is very topical in the research literature. With the advent of micro-scale technology there is increasing evidence that thermal motion is via a wave mechanism as opposed to by diffusion. We survey many of the theories which have been proposed as candidates to describe thermal motion as a wave. These theories are linked to solid mechanics (elasticity) and also to fluid mechanics.Wave motion in the form of acceleration waves and of shock waves is discussed. An exposition of numerical work in the area of thermal waves is also included. Analytical methods for establishing uniqueness, continuous dependence, growth, spatial decay and other results are described.Two important chapters are the final two. These focus firstly on where nanofluids and heat transfer are relevant. Hyperbolic temperature equations have been linked to the recent and "hot" area of nanofluids. The final chapter investigates applications of "heat wave -like" ideas to other areas, particularly those in mathematical biology are also investigated.I should like to thank a referee for several pointed remarks and suggestions for rewriting which have substantially helped with this book. My early work on heat waves was influenced greatly by discussions with the late Dario Graffi of the University of Bologna. I have benefitted over the years by many discussions on heat waves with several people and I would especially like to thank
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