Formal Evolutionary Development of Low-Entropy Dendritic Thermal Systems

Abstract

The present work contributes to the formal evolutionary development of complex thermal physical systems by using a bioinspired evolutionary method. The bioinspired method combines Lindenmayer systems with a turtle interpretation for the modeling of the complex dendritic structures, plus a finite element method for the analysis of the structure and an evolutionary algorithm to evolve the topology of the dendritic structure. With the proposed method, the optimal planar topology of a conductive dendritic structure for draining thermal energy from a fixed-area subject to uniform heat generation, a problem originally addressed by constructal theory, is investigated. The results show that the evolutionary approach can yield complex dendritic topologies that excel in performance and robustness. Moreover, our results demonstrate that a better performance in heat removal implies an increased complexity, up to an optimal level, of the draining system. Indeed, it is shown also that there is an optimal level of complexity beyond which the performance of the system is not substantially improved, which is in agreement with results reported in the literature. Finally, the robustness of hierarchical, dendritic complex topologies for heat transfer systems is discussed and quantified.