Origin of effective non-Fourier heat conduction phenomena in heterogeneous materials

Abstract

Phenomenological models of non-Fourier heat conduction often lack a strict microstructural foundation, leading to ambiguities when modeling complex heterogeneous materials. In this study, we derive a continuum heat equation beyond Fourier's law using spatial volume averaging for a two-component system. We analytically prove that the experimentally observed static and dynamic thermal diffusivity arise directly from the distinct material properties, concluding that heterogeneous media are inherently over-diffusive. The resulting heat equation is thermodynamically compatible, and the microstructural origin allows the calculation of non-Fourier transport coefficients. Furthermore, we demonstrate that finite-sample boundaries introduce higher-order spatial non-localities, thereby explaining the size dependence of over-diffusion. We validate the model against experimental data across metal and carbon foams, rocks, and metal-organic frameworks.