A generalized heat conduction model of higher-order time derivatives and three-phase-lags for non-simple thermoelastic materials

In the current work, a new generalized model of heat conduction has been constructed taking into account the influence of the microscopic structure into the on non-simple thermoelastic materials. The new model was established on the basis of the system of equations that includes three-phase lags of higher-order and two different temperatures, namely thermodynamic and conductive temperature. The two-temperature thermoelastic model presented by Chen and Gurtin (Z Angew Math Phys 19(4):614–627, 1968) and some other previous models have been introduced as special cases from the proposed model. As an application of the new model, we studied the thermoelastic interactions resulting from sudden heating in an isotropic solid subjected to external body force. The influence of the discrepancy parameter and higher-order of the time-derivative has been discussed. This work will enable future investigators to gain insight into non-simple thermoelasticity with different phase delays of higher-order in detail.