Topology optimization using variable-porosity metal foams: design of conduction paths for cooling a heat generating disc and comparison with tree-shaped architectures

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Abstract Topology optimization (TO) is a design algorithm providing the optimal material layout within a design domain to minimize/maximize an objective function. In thermal science, for instance, it can be used to optimize the design of heat sinks to minimize thermal compliance, entropy generation, average temperature, etc. Recently, classical TO frameworks have been enhanced in multi-material TO in order to include more materials, thereby enhancing the degrees of freedom of the system, and thus ensuring better thermal performance. This work implements both TO and multi-material TO (MMTO) to address a benchmark heat conduction problem, i.e., the cooling of a circular heat generating volume through heat conduction paths. The heat generation is uniform in the disc, the rim is adiabatic, while the centre is set at a fixed temperature – Dirichlet boundary condition – and serves as heat sink. In TO the choice is between void and high-conductivity material, while in MMTO variable-porosity metal foams are integrated. The interpolation of the materials’ thermal conductivity is conducted via an ordered solid isotropic material penalization (SIMP) algorithm. The distinction between materials is attained by setting different thresholds in the interpolation and projection functions. The dimensionless global thermal resistance and domain average temperature are alternately addressed as objective functions to be minimized at equal weight of the system. The findings unveil that MMTO outperforms TO, which outperforms constructal tree networks, considering in the latter case different configurations of different complexity.