Heat Transfer Mixing in Closed Domain with Circular and Elliptical Cross-Sections

Rayleigh–Bénard convection (RBC) provides a benchmark for studying buoyancy-driven instabilities and heat transport in confined fluids. Heat transfer scaling in cylindrical geometries is well established, whereas the role of the anisotropy induced by the domain geometry, such as elliptical shapes, has not fully explored. This study presents direct numerical simulations of RBC in two domains of equal height, H=0.0124 m, and different cross-sections: a circular cylinder with radius R=3.11×10−3 m and an elliptical cylinder with semi-axes equal to Rmax=3.11×10−3 m, Rmin=1.55×10−3 m, respectively. The simulations, performed at Rayleigh number Ra=2×106 and Prandtl number Pr=1.68 (for water) under the Boussinesq approximation, reveal that (i) the average Nusselt number is comparable in both cases (⟨Nu⟩≈38.23 for the circular case and ⟨Nu⟩≈39.22 for the elliptical one) and (ii) the different domain geometries influence the thermal transport mechanism and flow organization. Specifically, in the cylindrical cell, heat transfer is regulated by a large-scale circulation roll, whereas in the case of the elliptical shape, the domain is populated by thermal plumes driving the convective dynamics. The latter phenomenon is evidenced by larger Nusselt number fluctuations at the lower and upper plates, with a standard deviation increasing from σ≈2.21 in the circular cylinder to σ≈4.57 in the elliptical domain. These results highlight that the geometric anisotropy modifies the coupling between boundary layers and the core flow dynamics, leading to enhanced intermittency without affecting the magnitude of the heat flux. Therefore, the elliptical domain is suitable for applications characterized by enhanced mixing.