Low-Prandtl number natural convection in volumetrically heated rectangular enclosures: I. Slender cavity, AR = 4

Natural convection in a volumetrically heated rectangular enclosure filled with a low-Prandtl number (Pr=0.0321) fluid was studied by direct numerical two-dimensional simulation. The enclosure had isothermal side walls and adiabatic top/bottom walls. The aspect ratio was 4 and the Grashof number Gr, based on conductive maximum temperature and cavity width, ranged from 3.79 × 104 to 1.26 × 109. According to the value of Gr, different flow regimes were obtained: steady-state, periodic, and chaotic. The first instability of the steady-state solution occurred at Gr≈3×105; the resulting time-periodic flow field consisted of a central rising plume and of convection rolls, periodically generated in the upper corners of the cavity and descending regularly along the vertical isothermal walls. Transition from periodic to chaotic motion occurred at Gr≈1×106; up to the highest Grashof numbers studied, the fluid motion exhibited a recognizable dominating frequency, associated with the process of roll renewal and scaling as Gr1/2. The flow field still consisted of a meandering rising plume and of downcoming convection rolls, but these coherent structures were now irregular in shape, size and velocity. For Grashof numbers larger than ∼106 (chaotic flow), the friction coefficient averaged along the vertical walls was found to scale as Gr−1/3 and the Nusselt number (overall/conductive heat transfer) as Gr1/6.