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

Abstract

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 optimized 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 3 000 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 optimized internal architecture improved by up to 20% for a volumetric constraint of 5%.

Heat Exchanger Design with Topology Optimization

“…It is worth noting that although the heat exchanger is a three-dimensional device, 2D modelling was employed for the topology optimization process. Burger et al [89] explored the 3D solution for the volume to point (called volume to surface in this case) utilizing SIMP with method of moving asymptotes (MMAs) implementation. Full and partial Dirichlet boundary conditions were considered.…”

Topology Optimization Formulations for Circuit Board Heat Spreader Design

“…The optimization result is presented in This particular problem formulation for conductive heat transfer has been solved by numerous researchers. 8,9 Though the thermal compliance metric successfully reduces the temperature of the domain through the design of the passive heat spreader, some system design problems may require instead the optimal heat spreader design to reduce the domain temperature as much as possible. To address this, the next optimization study will minimize the maximum temperature on the design domain.…”

Multiobjective optimization of area‐to‐point heat conduction structure using binary quantum‐behaved PSO and Tchebycheff decomposition method

“…Various constructal designs have been derived for volume (area)‐to‐point problems with different constraints, boundary conditions, element shapes, and optimization objectives. [ 3–11 ] Many algorithms, eg, the solid isotropic with material penalization (SIMP) method, [ 12–18 ] rational approximation of material properties method, [ 19 ] evolutionary structural optimization method, [ 20,21 ] level‐set method, [ 22–24 ] cellular automaton algorithm, [ 25,26 ] deep learning approach, [ 27 ] genetic algorithm (GA), [ 28,29 ] simulated annealing (SA), [ 28,30 ] PSO, [ 31 ] bionic optimization, [ 30,32–41 ] and calculus of variations, [ 42,43 ] have been applied to the field of volume (area)‐to‐point heat conduction.…”