Unphysical effects of the dual-phase-lag model of heat conduction

We consider the model of heat conduction, based on the first-order approximation to the dual-phase-lag (DPL) constitutive relation. This model is described by the Jeffreys-type equation. We study an initial value problem for the three-dimensional Jeffreys-type equation with a positive localized source of short duration. We demonstrate that solutions to the problem manifest unphysical behavior with negative values of temperature. We conclude that the DPL model in the form of the Jeffreys-type equation is not in general an appropriate model of heat conduction.