  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.
