Size Effects and Beyond-Fourier Heat Conduction in Room-Temperature Experiments

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.

Automated summary

Understanding heat conduction phenomena beyond Fourier has been a long-lasting task. Recent studies have shown that heterogeneous materials with macro-scale size can exhibit thermal effects that cannot be modeled by the Fourier equation, known as over-diffusive propagation. This phenomenon, different from low-temperature observations, has been found in various samples such as metal foam, rocks, and composites. The study also reveals a size-dependent thermal behavior for both Fourier and non-Fourier situations, and proposes an empirical relation between Fourier and non-Fourier parameters based on experimental data for a more robust and reliable evaluation procedure in future experiments.