Natural convection in a semielliptic cavity

Natural convective steady-state motion inside a bidimensional semielliptic cavity is investigated numerically by means of a finite-element algorithm. The ceiling of the cavity is kept at a known temperature with a sinusoidal spatial distribution and the floor is assumed thermally insulated. A parametric study is carried out by varying the aspect ratio and the Grashof number. The convective motion is found to be composed of a main cell plus two small corner cells, one of which disappears at high Grashof numbers or aspects ratios. Heat is transferred mainly across the upper part of the cavity, the lower portion remaining essentially isothermal