Natural Convection in a Shallow Cavity

We present numerical solutions of natural convection in a shallow enclosure heated from a side. As a result of hydrodynamic instability transverse cells appear in the flow if the Prandtl number is sufficiently small. Both conducting and insulated top and bottom boundaries were considered. For fluids of small Prandtl number the differences in the flow patterns in these two cases are slight, the strength of the circulation in the cells being somewhat weaker when the boundaries are insulated. This is a result of a more stable flow in this case, caused by the kinetic energy being more vigorously expended in the work against the buoyant forces. Insulated boundaries allow the temperature field to adjust more freely in the end regions leading to crowding of the isotherms there and consequently to larger heat transfer than when the boundaries are conducting