Exploring thermal insulation enhancement in differentially heated cavities through topology optimization

The objective of this work is to investigate the optimal distribution of solid material within the cavity that minimizes heat transfer across its vertical boundaries. To this end, we explore the application of topology optimization (TO) – a methodology used to determine the optimal layout of material within a given design domain – to address the challenge of thermal insulation in rectangular cavities subjected to differential heating. By strategically placing material, the aim is to balance the diffusion/convection trade-off between low-velocity air gaps and diffusive solid paths, improving the thermal resistance of the heated cavity. The optimization problem is set based on a conjugate heat transfer formulation, i.e., the governing equations of heat conduction inside solid material, and natural convection inside air domains. Regularization techniques are applied to ensure the obtained solutions possess certain desirable characteristics, e.g., smoothness and discreteness, essential for instance in additive manufacturing for features such as 3D printability. A dimensionless problem is firstly solved to explore how the material distribution changes with the air recirculation magnitude, i.e., changing the Rayleigh number (Ra) value from 105 to 108. Further, the impact of mesh size, objective function selection, and initial design is investigated. Parameters affecting the TO routine are thus calibrated based on these simulations. Resulting designs are compared with baseline solutions consisting of vertical partitions, fixing the same volume of solid material. Material distribution of TO cases strongly differs depending on the Ra value flow strength. Therefore, convective motions are locally obstructed by smart solid features, leading to reduction in the Nusselt number up to 26 % at Ra = 108 © 2025 The Authors