Size effects and beyond-Fourier heat conduction in room-temperature experiments

TL;DR

This paper investigates size-dependent heat conduction phenomena beyond Fourier's law through room-temperature experiments on heterogeneous materials, revealing complex behaviors and proposing empirical relations for better modeling.

Contribution

It provides experimental evidence of size effects in heat conduction beyond Fourier's law and introduces an empirical relation between Fourier and non-Fourier parameters.

Findings

Size-dependent thermal behavior observed in various materials.

Empirical relation between Fourier and non-Fourier parameters established.

Both Fourier and non-Fourier heat conduction can occur depending on size.

Abstract

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 modelled 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 behaviour 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.