Tree-network structure generation for heat conduction by cellular automaton

Abstract

This study proposes a cellular automaton approach to deal with the typical “area-to-point” problem of how to effectively cool a heat generating surface by arranging the configuration of high conductivity material links which discharge the generated heat to a heat sink. To demonstrate the principle and the procedure of the cellular automaton approach, a simple case of square surface with single heat sink is treated: the approach starts with an initial shape of a certain quantity of high conductivity material. By shaping the initial conductive drain through the equipartition of thermal gradients, the high conductivity material evolves step-by-step and forms at convergence a final configuration, which turns out to be a multi-scale tree-like network. The effects of the conductivity ratio k ˆ , the fraction of high conductivity material ϕ 0 as well as the influence of the initial shape are discussed. The cellular automaton approach, which allows increasing the effective overall thermal conductance of an area, is fast, easy to apply and nearly constraint-free. Finally, the present limitations of the cellular automaton are also exposed.