Abstract One-dimensional heat equations beyond Fourier law with account for non-relativistic motion of an observer with respect to the media are considered. Some analytical solutions to these heat transport equations are obtained. The effect of the motion of the observer in the media is studied. Heat transport in thin films is modelled by the system of inhomogeneous differential equations (DE), which involve Guyer–Krumhansl-type and Telegrapher's type equations. Analytical solution to this system is found for the initial Gaussian distribution in the case of Cauchy conditions and for zero initial heat flux. The comparative analysis of the obtained solutions is performed in wide range of Knudsen numbers, Kn⊂[0.1–1]. The effect of the relative media–observer speed on the perceived heat transport is explored.

中文翻译：

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考虑恒定非相对论运动的薄膜热传输建模和精确解析解

摘要 考虑了观察者相对于介质的非相对论运动的超越傅立叶定律的一维热方程。获得了这些热传输方程的一些解析解。研究了观察者在媒体中运动的影响。薄膜中的热传输由非齐次微分方程 (DE) 系统建模，其中涉及 Guyer-Krumhansl 型和 Telegrapher 型方程。在柯西条件和零初始热通量的情况下，为初始高斯分布找到了该系统的解析解。在宽范围的 Knudsen 数，Kn⊂[0.1-1] 中对所获得的解进行比较分析。探讨了相对媒体-观察者速度对感知热传输的影响。