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

Abstract

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 10 6 to 10 11. The flow was steady for Gr up to 3×10 9, time-periodic for Gr≈10 10 and chaotic for Gr⩾3×10 10. 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 ∼10 7, the Nusselt number (overall/conductive heat transfer) increased roughly as Gr 1/5, i.e., slightly more markedly than for the previous aspect ratios and in agreement with the behaviour expected in the separated-boundary layer regime.