Two-temperature thermoelastic model without energy dissipation including higher order time-derivatives and two phase-lags

In the current analysis, we have constructed a new general thermoelastic heat conduction model with two-temperature including higher order time-derivatives and two phase-lags. The thermoelastic models established by Chen and Gurtin Chen, Gurtin 1968. Z. Angew. Math. Phys. 19:614-627, Green and Naghdi of type III Green and Naghdi 1993. J. Elast. 31:189-208 and dual-phase-lag model proposed by Tzou 1995. ASME J. Heat. Transf. 117:8-16 are extended. The proposed model has been restructured by the theory of fading memory, where the heat flow vector depends on the history of the gradient of thermal displacement. The problem of the infinite medium with a cylindrical cavity exposed to a decaying exponentially laser pulse is treated based on the resulting formulation. To explain the validity and accuracy of the derived model, the impacts of various physical parameters on the field variables are discussed in detailed and presented in tabular and graphical forms.