Abstract.

This review paper is dedicated to a description of heat transport at micro and nanoscales from the viewpoint of Extended Irreversible Thermodynamics. After a short survey of the classical heat conduction laws, like those of Fourier, Cattaneo, and Guyer–Krumhansl, we briefly overview the hypotheses and objectives of Extended Irreversible Thermodynamics, which is particularly well suited to cope with processes at short length and time scales. A selection of some important items typical of nanomaterials and technology are reviewed. Particular attention is brought to the notion of effective thermal conductivity: its expression in terms of size and frequency dependence is formulated, its significant increase in nanofluids formed by a matrix and nanoparticles is discussed, the problem of pore-size dependence and its incidence on thermal rectifiers is also investigated. Transient heat conduction through thin one-dimensional films receives special treatment. The results obtained from a generalized Fourier law are compared with those provided by a more sophisticated ballistic-diffusion model. Our survey ends with general considerations on boundary conditions whose role is of fundamental importance in nanomaterials.