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  • Author: G. Lebon x
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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.


Our main objective is to describe non-Fickean thermodiffusion in binary fluids within the framework of three recent theories of non-equilibrium thermodynamics, namely Extended Irreversible Thermodynamics (EIT), GENERIC (General Equation for the Non-Equilibrium Reversible Irreversible Coupling) and Thermodynamics with Internal Variables (IVT). In the first part presented in this paper, we develop the EIT description. For pedagogical reasons, we start from the simplest situation to end with the most intricate one. Therefore, we first examine the simple problem of mass diffusion at uniform temperature. Then we study heat transport in a one-component fluid before considering the more complex coupled heat and mass transfer. In Part II developed in the accompanying paper, we follow the same hierarchy of situations from the point of view of GENERIC. Finally, in Part III, we present the point of view of the thermodynamic theory of internal variables. Similarities and differences between EIT, GENERIC and IVT are stressed. In the present work, we have taken advantage of the problem of heat conduction to revisit the notion of caloric.