Three-dimensional conductive heat transfer topology optimisation in a cubic domain for the volume-to-surface problem

In this paper, three-dimensional topology optimisation was investigated with regard to heat conduction for the volume-to-point or volume-to-surface problem in a cubic three-dimensional domain. The positioning of high conductive material in a solid with low thermal conductivity and high heat generation was optimised via the method of moving asymptotes (MMA) algorithm in order to reduce the average internal temperature. Both partial and full Dirichlet temperature boundaries were considered. Thermal conductivity ratios ranging from 5 to 3000 and volumetric constraint between 5% and 30% were covered. The high conductive material distributions were found to resemble those of natural tree-structures, with the four primary branches extending towards the furthest corners of the domain when a single seed-location was used. Multiple seed locations (two and four) were also considered. It was found that each seed location resulted in a separate conduction tree, each of which also had four primary branches. By increasing the number of seed locations from one to four, the thermal performance of the optimised internal architecture improved by up to 20% for a volumetric constraint of 5%.