Transient buoyant convection in an enclosure by sudden imposition of gravity

Abstract

Transient buoyant convection in a rectangular cavity is considered. The vertical side walls are at two different temperatures, and the horizontal end walls are thermally insulated. At the initial state, the fluid is motionless and under zero gravity, and a conduction-controlled, horizontally linear temperature profile exists. At t = 0, gravity g is imposed on the system, and the flow is initiated at large Rayleigh number. A scale analysis is performed. Numerical solutions to the governing Navier-Stokes equations are acquired. In the present setup, due to the presence of the preexisting cavity-scale horizontal temperature gradient, strong bulk flows occur in much of the interior core within a relatively short time duration. The peak value of the Nusselt number is order-of-magnitude larger than that of the conventional heat-up model. Detailed evolutionary flow patterns are illustrated. Physical rationalizations, with the aid of the scale analysis, are offered.