On a multi-phase-lag model of coupled thermoelasticity

Abstract

Various qualitative properties of the dual/three-phase-lag heat equations are discussed. A refined model of coupled thermoelasticity is formulated to consider three delay times: a phase-lag of heat flux, a phase-lag of temperature gradient, and a phase-lag of thermal displacement gradient. Three special cases are considered to deal with all the considered models in the literature. In the first case one can obtain the simple and Tzou's dual-phase-lag, Lord–Shulman and the classical models. The Green–Naghdi type II model of generalized thermoelasticity without energy dissipation is obtained in the second case. Case 3 is devoted to considering the Green–Naghdi type III model. As an application, a unified form to a multi-phase-lag model is presented to yield all the preceding models as well as the Green–Lindsay generalized thermoelasticity model. A validation example is provided to discuss the coupled solution for photothermal semiconducting isotropic beam. Some illustrative flowcharts and plots are added and concluding remarks are presented.