Natural convection in platonic solids

Abstract

Natural convection in enclosures is a phenomenon significantly affected by the geometry of the physical domain, however, comparing different formats is challenging because features such as the characteristic length varies with the geometry. This study proposes examining natural convection in 3D convex regular polyhedra, also known as Platonic solids, using the number of faces as a parameter. Differentially heated enclosures were analyzed to investigate the effect of shape on fluid flow and energy distribution. By comparing the different solids, it was found that the dodecahedron and the icosahedron exhibit very similar behaviors and tend to be the more efficient shapes for improving convection heat transfer. In contrast, the tetrahedron is much less efficient due to its structure, which does not favor the presence of a single convective cell. In general, increasing the number of faces, which leads to a more spherical shape and eliminates sharp corners, tends to enhance fluid recirculation and increase the average Nusselt number. For example, the icosahedron showed a 12% increase in the Nusselt number compared to the commonly studied hexahedron for Ra = 10⁶. On the other hand, the tetrahedron demonstrated a 50% decrease in the Nusselt number relative to the cube, making it the least efficient shape among those evaluated.

Keywords:

• Computational fluid dynamics
• heat transfer
• natural convection
• numerical simulation
• platonic solids

Disclosure statement

The authors declare no conflict of interest.