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.