Low-Prandtl number natural convection in volumetrically heated rectangular enclosures: II. Square cavity, AR=1

Following a previous study for a slender enclosure (AR=4), direct numerical two-dimensional simulations were conducted for the free convective flow of a low-Prandtl number fluid (Pr=0.0321) with internal heat generation in a square cavity having adiabatic top and bottom walls and isothermal side walls. The Grashof number, Gr, based on conductive maximum temperature and cavity width, ranged from 105 to 109. For Gr up to ∼107, the flow was steady and exhibited left–right symmetry. For Gr≈3×107, the spatial symmetry was broken and asymmetric steady-state flow patterns were obtained. For Gr≈5×107, the asymmetric flow became time-periodic. Finally, for Gr≥108, chaotic flow was predicted; the time-averaged velocity and temperature fields were still markedly asymmetric at Gr=108, but reattained bilateral symmetry at higher Gr (109), when developed two-dimensional turbulence was observed. For Grashof numbers above ∼106, the friction coefficient averaged along the vertical walls scaled roughly with Gr−1/3 (as in the AR=4 cavity), while the Nusselt number (overall/conductive heat transfer) increased roughly as Gr1/7, i.e. slightly less markedly than in the slender cavity.