Evolutionary design of radial fins for forced and natural convection using generative methods

Flows in Nature often use two transport mechanisms: one fast and one slow, convection and diffusion. The fast regime spreads through branching pathways that divide and redivide to improve access, resembling dendritic patterns seen in lungs, lightning and river basins. For the area-to-point problem, channels self-organize into tree-like structures. For circle-to-point transport, branches extend radially, forming fin-like structures reminiscent of snowflakes. This study advances a generative framework for radial fins in annular domains. A variational autoencoder is trained on bio-inspired trees to capture hierarchical branching. Exponential conformal mapping adapts these patterns to circular geometries while preserving branching features. Evolutionary algorithms refine the designs in silico using a finite element solver. In forced convection, designs balance heat dissipation with flow resistance; in natural convection, they balance conduction with buoyancy-driven circulation, producing asymmetric structures adapted to gravity. Integrating constructal theory, generative models, and evolutionary search, this approach advances automated design of circular domains with applications in latent heat exchangers, circular heat sinks, and turbine discs. It is shown that high-performing intricate structures are created and controlled with a low number of degrees of freedom ( ). Beyond heat transfer, these generative constructal designs confirm that humans, computers, and Nature shape their fins the same way, toward increased access to what flows.