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为研究石墨烯中的非稳态热波和热扩散的相互作用机制，引入热流矢量弛豫时间τq和温度梯度弛豫时间τT，建立了双相弛豫理论模型。分别基于Bromwich积分方法和有限差分方法讨论此模型的解析解和数值解，研究了双相弛豫时间参数B对热波与热扩散相互作用和热输运模式调控机制的影响规律，揭示了三阶偏导项对局部热波扰动的独特贡献。建立锯齿形石墨烯短脉冲热冲击分子动力学模型以揭示热波与热扩散相互作用特征，并校核模型计算参数。研究结果表明：纵波、面内横波、面外横波三种模式中均存在弹性波、热波、热扩散三种热能传递方式；除面外热波波速高于面外横向弹性波波速外，其他两种热波传播速度均低于对应的弹性波波速。分子动力学模拟校核了双相弛豫理论模型计算参数的可靠性，进一步揭示了热波辐射与热扩散的相互耦合作用。本研究表明双相弛豫模型可精确描述微纳器件的非平衡热行为，可为集成电路微器件的热辐射和热扩散防护提供理论参考。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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Keywords:
- The Two-Phase Relaxation Model /
- Thermal Wave /
- Thermal Diffusion /
- Molecular Dynamics Simulation
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