Cooling of a Pr<1 fluid in a rectangular container

Abstract

The flow behaviour associated with the cooling of an initially quiescent isothermal Newtonian fluid with Prandtl number Pr less than unity in a rectangular container by unsteady natural convection with an imposed lower temperature on vertical sidewalls is investigated by scaling analysis and direct numerical simulation. The flow is dominated by two distinct stages of development, i.e. the boundary-layer development stage adjacent to the sidewall and the subsequent cooling-down stage. The first stage can be further divided into a start-up stage, transitional stage, and steady-state stage. The parameters characterizing the flow behaviour are the boundary-layer thickness, the maximum vertical velocity within the boundary layer, the time for the boundary layer to reach the steady state, the Nusselt number across the sidewall at the boundary layer development stage, the time for the fluid in the container to be fully cooled down, and the average fluid temperature over the whole volume of the container.