We investigate a recently proposed model of second-sound at the nanoscale—One that goes beyond the usual Maxwell–Catteneo theory of hyperbolic heat transfer. The model in question is based on a dynamical non-equilibrium temperature, denoted herein by β, that takes into account the effects of relaxation and nonlocality, both of which play an important role in heat-transport phenomena at the nanoscale. Employing a combination of analytical and numerical methodologies, we examine the propagation of both traveling waves and temperature-rate waves in a class of (thermally conducting) rigid solids; the impact of nonlocality on these waveforms is illustrated via comparisons with results predicted by Maxwell–Cattaneo theory. In particular, we show that nonlocality can: alter the speed at which second-sound propagates; lead to bounded but increasing, semi-compact, traveling wave profiles; and impact the evolution of temperature-rate wave amplitudes. Lastly, we review connections between our findings and known results in other fields, possible follow-on studies are noted, and a paradox revealed by our traveling wave analysis is discussed.

我们研究了最近提出的纳米级第二声音模型，该模型超越了通常的麦克斯韦-卡特尼诺双曲线传热理论。所讨论的模型基于动态非平衡温度，此处用β表示，考虑到弛豫和非局部性的影响，这两者在纳米级的热传递现象中都起着重要作用。结合分析和数值方法，我们研究了行波和温度率波在（导热）刚性固体中的传播。通过与Maxwell–Cattaneo理论预测的结果进行比较，说明了非局部性对这些波形的影响。特别是，我们表明非本地性可以：改变第二声音的传播速度；导致有界但不断增加的半紧凑行波剖面；并影响温度率波幅的变化。最后，我们回顾了我们的发现与其他领域的已知结果之间的联系，并指出了可能的后续研究，