Investigating the Reynolds analogy for Triply Periodic Minimal Surfaces in low-Reynolds flow regime

In the case of a coolant flow on hot surfaces with negligible pressure gradient, the dimensionless velocity profile is similar to the dimensionless temperature profile as the hydraulic and thermal boundary layers develop similarly, according to the Reynolds analogy. Here the case of a surface belonging to a periodic lattice is considered, and namely a lattice constituted by a solid gyroid, which is a very common structure among the Triply Periodic Minimal Surfaces family. A single lattice cell is investigated by Computational Fluid Dynamics for an incompressible flow at low Reynolds numbers, unitary Prandtl number and constant thermophysical properties. The dimensionless velocity field is compared to the dimensionless temperature field computed for imposed wall temperature. The friction coefficient and the Stanton number are computed at different porosities and Reynolds number values, and a modified Reynolds analogy is derived for these structures.