2-TEMPERATURE DISCRETE MODEL FOR NONLOCAL HEAT-CONDUCTION

The two-temperature discrete model for heat conduction in heterogeneous media is proposed. It is shown that the discrete model contains as limiting cases both hyperbolic and parabolic heat conduction equations for propagative and diffusive regimes, respectively. To obtain these limiting cases two different laws of continuum limit have been introduced. The evolution of the two-temperature system comprises three stages with distinct time scales: fast relaxation of each subsystem to local equilibrium, energy exchange between the subsystems and classical hydrodynamics.