Barbara Lazzari

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

Abstract 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.

Second-order approximation for heat conduction: dissipation principle and free energies

In the context of new models of heat conduction, the second-order approximation of Tzous theory, derived by Quintanilla and Racke, has been studied recently by two of the present authors, where it was proved equivalent to a fading memory material. The importance of determining free energy functionals for such materials, and indeed for any material with memory, is emphasized. Because the kernel does not satisfy certain convexity restrictions that allow us to obtain various traditional free energies for materials with fading memory, it is necessary to restrict the study to the minimum and related free energies, which do not require these restrictions. Thus, the major part of this work is devoted to deriving an explicit expression for the minimum free energy. Simple modifications of this expression also give an intermediate free energy and the maximum free energy for the material. These derivations differ in certain important respects from earlier work on such free energies.

Energy decay in Green–Naghdi thermoelasticity with diffusion and dissipative boundary controls

ABSTRACT We study the asymptotic behavior of the solutions of a three-dimensional hyperbolic system arising in the Green–Naghdi models of thermoelasticity with diffusion of type-II and III, in the presence of dissipative boundary controls and prove that the energy exponentially decays in time.