Low-Prandtl number natural convection in volumetrically heated rectangular enclosures III. Shallow cavity, AR=0.25

Following previous studies for enclosures of aspect ratios 4 and 1, direct numerical two-dimensional simulations were conducted for the free convection flow of a low-Prandtl number fluid with internal heat generation in a shallow cavity (AR=0.25) having adiabatic top and bottom walls and isothermal side walls. The Prandtl number was 0.0321 and the Grashof number, Gr, based on power density and cavity width, ranged from 106 to 1011. The flow was steady for Gr up to 3×109, time-periodic for Gr≈1010 and chaotic for Gr⩾3×1010. In both the steady and the periodic regimes, the flow was instantaneously symmetric with respect to the vertical centreline of the enclosure; in the chaotic regime the instantaneous flow was asymmetric, but bilateral symmetry was recovered in the time-averaged velocity and temperature fields. For Grashof numbers above ∼107, the Nusselt number (overall/conductive heat transfer) increased roughly as Gr1/5, i.e., slightly more markedly than for the previous aspect ratios and in agreement with the behaviour expected in the separated-boundary layer regime.