In order to distinguish the interaction responses between unsteady thermal waves and thermal diffusion in graphene, the relaxation time of the heat flux vector τ_q and the relaxation time of the temperature gradient τ_T are introduced based on the Fourier's law, and a two-phase relaxation theoretical model is established. Using parameter B, which describes the ratio of relaxation times between two phases, to reveal the influence of the interaction between thermal waves and thermal diffusion and to investigate the regulation 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 the 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 reveal the coupling behaviors between thermal waves and thermal diffusion. The calculation parameters of the two-phase relaxation theoretical model are calibrated. The temperature field following the second sound is the outcome of the combined action of thermal waves and thermal diffusion. It is worth noting that except for the out-of-plane thermal wave, which has a higher speed than the out-of-plane transverse elastic wave, the speeds of the other two thermal waves are both lower than their corresponding elastic wave velocities.

The above results indicate that the two-phase relaxation model can accurately depict the non-equilibrium thermal behaviors of micro-and nano-scale devices and can provide a theoretical basis for protecting micro-components in integrated circuits against thermal radiation and thermal diffusion.