Generalized Fourier's law for nondiffusive thermal transport: Theory and experiment

Fourier's law, which relates the heat flux and temperature fields at macroscopic length scales, is fundamental to the mathematical description of heat transport. While it is well-known that Fourier's law breaks down at lengths comparable to the mean free path of the heat carriers, an appropriate modification has remained unknown until now. In the present work, the authors derive analytically a generalized Fourier's law that is valid over transport regimes spanning ballistic to diffusive. This relation shows that in the nondiffusive regime the heat flux and temperature fields not only have a nonlocal relationship but also depend on the properties of the heat source itself, a prediction that is verified by thermal spectroscopy experiments. This constitutive law provides a theoretical basis to understand nonlocal effects in the transport of heat at mesoscopic length scales.