Heat transfer along the route to chaos of a swaying thermal plume

Abstract

Detailed analyses have been recently reported on the low order dynamics of a thermal plume arising from a horizontal cylindrical heat source concentric to an air-filled isothermally cooled square enclosure, together with those of the related flow structures, in the limit of the 2D approximation. In particular, within the range of 0 < Ra < 3Racr, with Racr corresponding to the loss of stability of the stationary buoyant plume, the entire evolution from a periodic limit cycle (P1) to the birth of chaos through a period-doubling cascade has been fully explored. With this respect, special attention has been given to the window of quasiperiodic dynamics onto a T2-torus that is observed to separate the monoperiodic dynamics from the biperiodic dynamics onto a P1 and a P2-limit cycle, respectively. The results of these analyses hint at the bimodal nature of the overall dynamics, in general, and of the subharmonic cascade, in particular, which are still under investigation. Although relevant on a dynamical perspective, a with a main reflection on the laminar-turbulent transition, the observed oscillations appear to be characterised by comparable amplitudes and to be determined by similar evolutions of the flow pattern evolutions, so that their role on the overall heat transfer rate is expected to be marginal. Within this frame, the present study aims at reporting the influence played by the observed dynamics of the thermal plume and of the flow structures on the global heat transfer rate. In particular, the aim is the assessment of the correlation between the Rayleigh number and the average Nusselt number on the cylinder surface, as well as the effect on the latter of the observed series of bifurcations.