Two-temperature discrete model for nonlocal heat conduction

(Received 12 January 1993, revised 2 August 1993, accepted 23 September 1993)

Abstract
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.