Enhancing the degrees of freedom of topology optimization via variable-porosity metal foams: Design of heat conduction paths in a volume-to-point problem

Abstract

Abstract Multi-material topology optimization determines the optimal distribution of different materials within a design domain in order to achieve specific performance goals. This work takes advantage of such technique to enhance the thermal performance of a benchmark heat conduction problem. The aim is to investigate the impact of enhancing the degrees of freedom introducing different materials, i.e., variable-porosity metal foams in addition to the high-conductivity solid, in the design of heat conduction paths under a constant weight constraint. The study leverages a well-established case study – volume-to-point problem – in the field of thermal management, ensuring a consistent basis for comparison. It consists of a square domain with a uniform heat source and a Dirichlet condition at a point on the boundary. Interpolation functions – ordered solid isotropic material with penalization (SIMP) type – allow the properties – in this case thermal conductivity – of materials to be correctly assigned. The distinction between materials is made by means of different thresholds on the projection function. By varying the foam porosity, we investigate the trade-offs between weight and heat dissipation efficiency. The objective is to find the ideal combination of materials that maximizes heat transfer – minimizing the average domain temperature – while conforming to weight constraints. Findings reveal that multi-material topology optimization – when applied to heat conduction problems – can outperform other design approaches, such as the growth-based algorithm, the evolved constructal tree, and the classical topology optimization (with one solid material), thereby paving the ground to innovative heat sink designs in weight-constrained environments.