It is a long-lasting task to understand heat conduction phenomena beyond Fourier. Besides the low-temperature experiments on extremely pure crystals, it has turned out recently that heterogeneous materials with macro-scale size can also show thermal effects that cannot be modeled by the Fourier equation. This is called over-diffusive propagation, different from low-temperature observations, and is found in numerous samples made from metal foam, rocks, and composites. The measured temperature history is indeed similar to what Fourier’s law predicts but the usual evaluation cannot provide reliable thermal parameters. This paper is a report on our experiments on several rock types, each type having multiple samples with different thicknesses. We show that size-dependent thermal behavior can occur for both Fourier and non-Fourier situations. Moreover, based on the present experimental data, we find an empirical relation between the Fourier and non-Fourier parameters, which may be helpful in later experiments to develop a more robust and reliable evaluation procedure.

中文翻译：

---

室温实验中的尺寸效应和超傅里叶热传导

了解傅里叶以外的热传导现象是一项长期的任务。除了对极纯晶体的低温实验外，最近发现具有宏观尺寸的异质材料也可以显示出傅里叶方程无法模拟的热效应。这被称为过度扩散传播，与低温观测不同，在许多由金属泡沫、岩石和复合材料制成的样品中都可以找到。测得的温度历史确实与傅立叶定律预测的相似，但通常的评估无法提供可靠的热参数。本文是我们对几种岩石类型进行实验的报告，每种类型都有多个不同厚度的样品。我们表明，傅立叶和非傅立叶情况都可能发生与尺寸相关的热行为。而且，