Fractal mixtures for optimal heat draining

The aim of this paper is to optimize the shape of a highly conductive interface in order to drain the maximum amount of heat. Given the ubiquity of irregular interfaces in heat transmission processes, we model such interfaces by Koch-mixture fractal layers. We propose a dynamics that iteratively refines these mixtures in order to maximize the temperature reduction in the bulk. We obtain that asymmetric Koch-mixtures drain heat effectively when properly refined. In addition, we show that the conductivity of the interface plays a significant role in the refinement of the optimal shape.