Nanoscale Graphene Disk: A Natural Functionally Graded Material–How is Fourier’s Law Violated along Radius Direction of 2D Disk

In this Paper, we investigate numerically and analytically the thermal conductivity of nanoscale graphene disks (NGDs), and discussed the possibility to realize functionally graded material (FGM) with only one material, NGDs. Different from previous studies on divergence/non-diffusive of thermal conductivity in nano-structures with different size, we found a novel non-homogeneous (graded) thermal conductivity along the radius direction in a single nano-disk structure. We found that, instead of a constant value, the NGD has a graded thermal conductivity along the radius direction. That is, Fourier's law of heat conduction is not valid in two dimensional graphene disk structures Moreover, we show the dependent of NGDs' thermal conductivity on radius and temperature. Our study might inspire experimentalists to develop NGD based versatile FGMs, improve understanding of the heat removal of hot spots on chips, and enhance thermoelectric energy conversion efficiency by two dimensional disk with a graded thermal conductivity.