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, GI, based on conductive maximum temperature and cavity width, ranged from 10(5) to 10(9). For Gr up to similar to 10(7), the flow was steady and exhibited left-right symmetry. For Gr approximate to3 x 10(7), the spatial symmetry was broken and asymmetric steady-state flow patterns were obtained. For Gr approximate to5 x 10(7), the asymmetric flow became time-periodic. Finally, for Gr greater than or equal to 10(8), chaotic flow was predicted; the time-averaged velocity and temperature fields were still markedly asymmetric at Gr = 10(8), but reattained bilateral symmetry at higher Ci (109), when developed two-dimensional turbulence was observed. For Grashof numbers above similar to 10(6), 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 Gr(1/7), i.e. slightly less markedly than in the slender cavity. (C) 2001 Elsevier Science Ltd. All rights reserved.