Stability and Thermodynamic Restrictions for a Dual-Phase-Lag Thermal Model

In this paper, the seeming inconsistency highlighted by Fabrizio and Lazzari (Stability and second law of thermodynamics in dual-phase-lag heat conduction, Int. J. Heat Mass Transfer 74 (2014), 484–489) and Quintanilla and Racke (A note on stability of dual-phase-lag heat conduction, Int. J. Heat Mass Transfer 49 (2007), 1209–1213) for a thermoelastic material, between the thermodynamic restrictions and the stability conditions is studied. Actually, we show as these results are due to the use of different formulations of the thermodynamic principles, which are not always equivalent. So that, we prove by the model considered in the paper that these two formulations do not lead to the same restrictions on the constitutive equations. This analysis allowed us to restore the compatibility by an appropriate and wide representation of the Second Law.