Equilibrium and non-equilibrium thermodynamic analysis of high-order dual-phase-lag heat conduction

The compatibility of dual-phase-lag (DPL) heat conduction with the hypothesis of local thermodynamic equilibrium (LTE) and extended irreversible thermodynamic is investigated. The analysis is based on evaluating the entropy production rate (EPR) for a solid slab that is exposed to a sudden temperature gradient at its boundaries. In this regard, an analytical solution is presented for the first-order and second-order approximations of the DPL model. It is shown that by extending the non-Fourier Cattaneo-Vernotte (C-V) wave model to the high-order DPL model, the unphysical values of the slab temperature that exist in the solution of C-V wave model cannot be generally eliminated. However, a set of phase lag times for the DPL model exist based on which these unphysical values can be omitted by increasing the diffusion versus the wavelike features.