Three-dimensional natural convection between parallel cold plates containing a cross-shaped cylinder was investigated for vertical offsets y =-0.3−0.3 at Rayleigh number from 10 4 to 10 6 . The immersed boundary method was applied, and the results revealed strong sensitivity of plume behavior and heat transfer to both buoyancy and cylinder position. At low Ra , transport is conduction-dominated, whereas at high Ra , plume bifurcation and vortex tilting generate enhanced three-dimensionality. Vertical offset modulates these dynamics, as a result, negative y extends plume paths and amplifies lateral exchange, central positioning yields nearly symmetric structures, and positive y promotes early impingement with confined circulation. exhibit non-monotonic dependence on y , while follow monotonic variations controlled by plume impingement. A compact empirical correlation is proposed to predict the Nusselt number as a function of Rayleigh number and vertical offset. The results provide physical insight into plume–geometry interactions and practical guidance for cross-like structures in thermal management systems.
Seo et al. (Sun,) studied this question.