We study the propagation of acoustic waves in a viscous heat-conducting gas at non-adiabatic conditions. Considering a planar slab configuration, constant wall heating is applied at the confining walls to maintain non-uniform temperature and density reference distributions. Acoustic excitation is then imposed via small-amplitude harmonic wall oscillations and normal heat-flux perturbations. Focusing on continuum-limit conditions of small Knudsen numbers and high actuation frequencies (yet small compared with the mean collision frequency), the gas domain affected by wall excitation is confined to a thin layer (termed “acoustic layer”) in the vicinity of the excited boundary, and an approximate solution is derived based on asymptotic expansion of the acoustic fields. The application of thermoacoustic wall excitation necessitates the formation of an ever thinner “thermal layer” that governs the transmission of wall unsteady heat flux into sound waves. The results of the approximate analysis, supported by continuum-model finite-differences and direct simulation Monte Carlo calculations, clarify the impacts of system non-adiabaticity and gas kinetic model of interaction on sound propagation. Primarily, reference wall heating results in an extension of the acoustic layer and consequent sound wave radiation over larger distances from the wall source. Considering the entire range of inverse power law (repulsion point center) interactions, it is also found that wave attenuation is affected by the kinetic model of gas collisions, yielding stronger decay rates in gases with softer molecular interactions. The results are used to generalize the counterpart adiabatic-system findings for the amount of boundary heat-flux required for the silencing of vibroacoustic sound at non-adiabatic reference conditions.

中文翻译：

---

非绝热条件下的声波传播：薄声层的连续极限

我们研究了非绝热条件下声波在粘性导热气体中的传播。考虑到平面平板构造，在限制壁处施加恒定的壁加热以保持温度和密度参考分布不均匀。然后，通过小振幅谐波壁振荡和正常的热通量扰动施加声激励。着眼于小Knudsen数和高致动频率（但与平均碰撞频率相比还很小）的连续极限条件，受壁激发影响的气域被限制在该区域附近的薄层（称为“声层”）中。激发边界，并基于声场的渐近展开导出近似解。热声壁激励的应用需要形成越来越薄的“热层”，该“热层”控制壁的不稳定热通量向声波的传输。在连续模型有限差分和直接模拟蒙特卡洛计算的支持下，近似分析的结果阐明了系统的非绝热性和相互作用的气体动力学模型对声音传播的影响。首先，参考壁加热会导致声层的扩展，从而导致声波辐射距离壁源的距离更大。考虑到整个逆功率定律（排斥点中心）相互作用的整个范围，还发现波衰减受气体碰撞动力学模型的影响，在分子相互作用较弱的气体中产生更强的衰减率。