Analysis of heterogeneous structures described by the two-temperature model

We consider the homogenization problem for composite structures described by the two-temperature model of heat conduction. Our theory is based on the most general solutions of the standard two-temperature equations for the spherical geometry. This methodology allows us to thoroughly analyse different configurations. In particular, we prove two equivalence theorems for homogeneous and composite (core-shell structure) two-temperature spheres, which paradigmatically represent particles dispersed in standard particulate materials. As a matter of fact, the core-shell structure is essential to model interface deficiencies such as mixing phenomena and imperfect transport conditions at the particle-matrix contact surface. Then, we take into consideration a dispersion of particles and we examine the effects of the interfaces characterized by mixing and imperfect transport phenomena. We also discuss in detail the scale effects in heterogeneous systems composed of two-temperature components. The results here established can be used for designing and improving materials or, conversely, for interpreting experimental data in terms of the thermal behavior of their constituents.