Thermal oscillation and resonance in dual-phase-lagging heat conduction

We examine thermal oscillation and resonance (with respect to time) described by the dual-phase-lagging heat-conduction equations analytically. Conditions and features of underdamped, critically damped and overdamped oscillations are obtained and compared with those described by the classical parabolic heat-conduction equation and the hyperbolic heat-conduction equation. Also derived is the condition for the thermal resonance. Both the underdamped oscillation and the critically damped oscillation cannot appear if the phase lag of the temperature gradient τT is larger than that of the heat flux τq. The modes of underdamped thermal oscillation are limited to a region fixed by two relaxation distances defined by ατT((τq/τT)+(τq/τT)−1) and ατT((τq/τT)−(τq/τT)−1) for the case of τT>0, and by one relaxation distance 2ατq for the case of τT=0. Here α is the thermal diffusivity of the medium.