瞬时加热半无限长自由端Hooke链的非定常热输运
Unsteady thermal transport in an instantly heated semi-infinite free end Hooke chain
摘要：
研究了具有任意初始温度分布的半无限长虎克链的非定常弹道热输运问题。动力学温度的演变提出了离散（精确）和连续（近似）配方的分析描述。通过对动力学温度场离散描述和连续描述的比较，揭示了后者的局限性。具体而言，远场动力学温度是很好地描述了连续的解决方案，然而，偏离附近和自由端（边界）。分析表明，热波从边界反射后，动力学温度的离散解在自由端附近发生跳跃。比较了半无限和无限虎克链中热传播的描述。目前的文件的结果，预计提供洞察非稳态热输运的半无限晶格。
英文摘要：
We consider unsteady ballistic heat transport in a semi-infinite Hooke chain with free end and arbitrary initial temperature profile. An analytical description of the evolution of the kinetic temperature is proposed in both discrete (exact) and continuum (approximate) formulations. By comparison of the discrete and continuum descriptions of kinetic temperature field, we reveal some restrictions to the latter. Specifically, the far-field kinetic temperature is well described by the continuum solution, which, however, deviates near and at the free end (boundary). We show analytically that, after thermal wave reflects from the boundary, the discrete solution for the kinetic temperature undergoes a jump near the free end. A comparison of the descriptions of heat propagation in the semi-infinite and infinite Hooke chains is presented. Results of the current paper are expected to provide insight into non-stationary heat transport in the semi-infinite lattices.
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