In order to distinguish the interaction responses between unsteady thermal waves and thermal diffusion in graphene, the relaxation time of the heat flux vector τq and the relaxation time of the temperature gradient τT are introduced based on the Fourier's law, and a two-phase relaxation theoretical model is established. Parameter B describing ratio of the two phase relaxation times is employed to reveal the influencing rules of the interaction between thermal waves and thermal diffusion, and to investigate the regulatory mechanism of heat transport modes. When B approaches zero, the thermal wave effect dominates the heat transfer. When B approaches 0.5, the thermal diffusion characteristics are significant. When B is between zero and 0.5, both of them jointly dominate heat transfer, and the interaction between the two is of great significance. The results uncover the rules of thermal diffusion induced wave attenuation and thermal wave promoted thermal diffusion. They exhibit strong coupling characteristics. The unique contribution of third-order partial derivatives to local thermal wave disturbances is also revealed. A molecular dynamics model of short-pulse thermal shock for zigzag graphene is developed to unveil the coupling behaviors of thermal waves and thermal diffusion. The calculation parameters of two-phase relaxation theoretical model are calibrated. The main findings are presented in the figure below. The black, red, and yellow lines correspond to the in-plane longitudinal vibration, in-plane transverse vibration, and out-of-plane transverse vibration of carbon atoms, respectively. The solid lines denote elastic waves, while the dashed lines represent the second sound. The temperature field following the second sound is the outcome of the combined action of thermal waves and thermal diffusion. It merits attention that except for speed of the out-of-plane thermal wave is higher than that of the out-of-plane transverse elastic wave, speeds of the other two thermal waves are both lower than their elastic wave velocities.
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