The Global Optimal Structural Morphogenesis for Heat Conduction

Heat conduction, being one of the most common types of energy, occurs everywhere at any time in nature. On the long journey to explore the optimal structural design for the ubiquitous heat conduction problem, many insights have been reported, yet still identifying the best structural morphogenesis remains pending and thought-provoking. Here, we investigate this subject with respect to the index of thermal compliance using mathematics and physics-based topology optimization methods. The discussion is carried out by both analytical deduction and numerical simulation. By contrast, the numerical results show very close performances to corresponding analytical solutions and reveal that the global optimal structural morphogenesis for heat conduction consists of countless hair-like fibres forming an independent rather than hierarchical system. Interestingly, inspired by the numerical results, we believe that the leaf vein of the tropical fruit banana might stand the best chance to win a contest of heat conduction in the natural environment as a result of consistency with the optimized solution. Despite the global optimality of the solutions, countless hair-like structures are manufacturing unfriendly for practical engineering applications due to their topological complexity and length scales. To address this issue, we introduce a simple numerical strategy through which the optimized solutions become remarkably simplified without much loss of performance. The present findings are theoretically meaningful, and we expect that they refresh people’s knowledge on heat conduction. Also, the method employed herein can be useful in engineering industries