Thermal performance of fractal metasurface and its mathematical model

Abstract

How can we explain the thermal phenomenon by a fractal meta-surface? This has been puzzling scientists and engineers for at least ten years, and so far no answer has been found. Now, modern mathematics offers a completely new window to physically understand the magical phenomenon that lies far beyond the Fourier law for heat conduction. A fractal-fractional modification of the Fourier law is elucidated, and its extremely high thermal conductivity is mathematically revealed. This article shows that thermal science is the key to nanotechnology.