Anomalous Transient Heat Conduction in Fractal Metamaterials

TL;DR

This paper investigates how fractal dimensionality influences transient heat conduction in metamaterials, revealing anomalous decay behaviors and optimal dimensions for heat absorption, with potential applications in advanced thermal management.

Contribution

It introduces an analytical and numerical framework using non-integer Laplacian operators to study heat conduction in fractal metamaterials, highlighting novel decay behaviors and optimal design parameters.

Findings

Non-exponential decay of heat pulses in fractal media

Identification of an optimal fractal dimension for heat absorption

Potential for controlling heat conduction in hierarchical materials

Abstract

Transient dynamics of heat conduction in isotropic fractal metamaterials is investigated. By using the Laplacian operator in non-integer dimension, we analytically and numerically study the effect of fractal dimensionality on the evolution of the temperature profile, heat flux and excess energy under certain initial and boundary conditions. Particularly, with randomly distributed absorbing heat sinks in the fractal metamaterials, we obtain an anomalous non-exponential decay behavior of the heat pulse diffusion. and an optimal dimension for efficient heat absorption as a function of sink concentrations. Our results may have potential applications in controlling transient heat conduction in fractal media, which will be ubiquitous as porous, composite, networked, hierarchical meta-materials.