On heat equation in the framework of classic irreversible thermodynamic with internal variables

In this paper, we show that, using a procedure of classical irreversible thermodynamics (CIT) with internal variables, it is possible to describe the relaxation of thermal phenomena, obtaining some well known results of extended irreversible thermodynamics (EIT). In particular, we introduce as internal variables a vector and a second rank tensor, that influence the thermal transport phenomena, and we derive in the anisotropic and isotropic case, the phenomenological equations for these variables. In the case, in which the medium is isotropic, it is obtained that the total heat flux can be split in two parts: a first contribution J(0), governed by Fourier law, and a second contribution J(1), obeying Maxwell–Cattaneo–Vernotte (MCV) equation, in which a relaxation time is present. The obtained results may have applications in describing the thermal behavior in nanosystems (semiconductors, nanotubes, . . . ), where the phenomena are fast and there are high-frequency thermal waves.