On the Generalized Thermal Lagging Behavior: Refined Aspects

A fractional hyperbolic two-temperature (FHTT) model, that replaces the well-known one derived by Qiu and Tien (HTT), and results in a model revealing other possible sub-cases in the energy transport in both the photon–electron and electron–phonon interaction processes, is proposed in the present work. The hyperbolicity of HTT-model is accommodated. Tzou idea (the thermal lagging behavior) is modified through an alternative definition that also captures the microstructural effects and the hyperbolic nature of energy transport by electrons. Hence, a fractional Tzou law is suggested, and again, direct correlations are established with the FHTT-model. Ignaczak conditions are modified, fractional generalized Gibbs equation is introduced and some restrictions are imposed on the entropy source term in order to put a rigorous thermodynamical basis for the fractional Qiu–Tien and Tzou models. The Danilovskaya problem is revisited in the framework of the modified dual-phase-lag-thermoelasticity based on the proposed fractional Tzou law. Keywords: Dual-phase-lagFractional calculusHeat conductionTwo-temperature model Acknowledgments This article is dedicated to Professor Hany H. Sherief. The author is indebted to Professor Richard B. Hetnarski and the anonymous referee for their helpful comments/suggestions that have improved the manuscript and caused the existence of some sections. This research is supported by the Alexandria University Research Grants.