NUMERICAL COMPUTATION OF OSCILLATORY RAYLEIGH-BENARD NATURAL CONVECTION OF GALLIUM IN A RECTANGULAR REGION WITH ASPECT RATIOS EQUAL TO FIVE

Present paper considers unsteady fully three-dimensional natural convection of the low-Prandtl number fluid in a shallow rectangular region with an aspect ratio (width/depth) of five heated from below and cooled from above. Four vertical boundaries were assumed to be dragless and thermally insulated to simulate the convection in an infinite wide shallow fluid layer heated from below. The model equations consist of equation of continuity, three-directional momentum equations and energy equation. These simultaneous nonlinear partial differential equations were approximated with HSMAC finite difference scheme with second order central difference for the inertial terms. Numerical grids of 41×41×16 were employed after several tests on the grid size effects. Sample computations were carried out for Pr = 0.023 and Ra = 2100, 2200, 2500 and 3000. Oscillatory responses were successfully obtained for all cases studied.