Heat conduction at micro and nanoscales: A review through the prism of Extended Irreversible Thermodynamics

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 nano fluids 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.