Heat waves / Brian Straughan

This book surveys significant modern contributions to the mathematical theories of generalized heat wave equations as an area of non-classical diffusion. The first three chapters form a comprehensive survey of most modern theories, also describing in detail the mathematical properties of each model, which are linked to solid mechanics and fluid mechanics.

The next two chapters focus on acceleration and shock waves. Chapter 4 presents an account of some recent studies employing acceleration waves in theories of heat transport associated with second sound. Chapter 5 is devoted to the study of various continuum theories of thermal shock waves as well as to an exposition of numerical work in the area of thermal waves. In the Chapters 6 and 7, analytical methods for establishing uniqueness, continuous data dependence, growth, spatial decay and other results are described. Chapter 8 focuses on thermal convection in nanofluids. Chapter 9 is devoted to a description of selected applications and the corresponding formation of mathematical models. Illustrations are taken from a broad range that includes nanowires, thin films, porous media, nuclear reactors, traffic flow, biology, and medicine, all of contemporary active technological importance and interest. (zbMath)