Time-domain finite-difference formulation for dynamic thermoelastic theory coupled with a dual-phase lag heat conduction model

Abstract

Our research group investigated the fundamental equations for simulating the propagation behavior of heat waves, which has been a major issue with the classical Fourier law. We focused on the dual-phase lag (DPL) model introduced by Tzou, and derived a partial differential equation that coupled it with the dynamic thermoelastic equation. Therefore, an exact solution for the one dimensional (1D) bar problem was obtained using the Laplace transform technique. However, it is difficult to obtain an exact solution for more general problems in 3D space. In this study, we analyzed the propagation of heat and stress waves in a 1D bar using discretized equations derived from the finite difference time domain (FDTD) method. We also discussed stability conditions to ensure the accuracy of the FDTD results. The results are as follows: We simulated the propagation of heat and stress waves over time in a 1D bar model and discovered that the wave propagation behavior and its waveform differ significantly based on the combination of relaxation times and coupling terms. Subsequently, we focused on the peak value of the stress wave and investigated the attenuation of the peak value associated with propagation. It was determined that the attenuation increased as the coupling parameter connected between thermo-elastic and heat transfer equations and the two relaxation times in the DPL model increased.