Anomalous Transient Heat Conduction in Fractal Metamaterials

Wuxi Lin

Shengpeng Huang

Jie Ren Email

Center for Phononics and Thermal Energy Science, China-EU Joint Center for Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Sciences and Engineering, Tongji University, Shanghai 200092, China


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.

Anomalous Transient Heat Conduction in Fractal Metamaterials