Flow Transitions and Bifurcations of Buoyancy-induced Flows from an Eclosed Cylindrical Heat Source

The study presents a numerical analysis of the dynamics of transitional natural convection flow regimes, generated by a confined thermal source. The system considered is a 2D enclosure of square cross-section, containing a horizontal cylindrical source,placed in central position. The heat carrier fluid is air with Prandtl number Pr = 0:7. The resulting flow is investigated withrespect to the variation of the Rayleigh number, based on the minimum gap width H between the cylinder and the enclosurewalls. Three values of the aspect ratio A are considered (A = 2:5; 3:¯3; 5;). The numerical scheme is based on a second orderfinite-volume discretization of the Navier-Stokes equations, solved on orthogonal Cartesian grids. Internal boundaries nonalignedwith the grid are subjected to special treatment. The first bifurcation of the low-Ra fixed-point solution is tracked foreach A-value. The transition to unsteady, chaotic flow is detailed for A = 2:5. The supercritical behaviour of the system isinvestigated using nonlinear analysis tools and phase space representations of the computed time series, and the effect of the flow features on heat transfer is discussed.