Vertical transient natural convection flows in cold water

Abstract

The initial, transient natural convection flow resulting from a sudden change of the boundary condition at a vertical surface has been examined. The ambient medium is cold water, giving rise to a density variation with temperature which may not be linearized. Closed-form solutions for flow velocity have been obtained from the known temperature solutions. Two important surface conditions have been considered. These are: (a) an initial step in the surface energy generation rate, both for zero and finite thermal capacity surfaces and, (b) a step in the surface temperature. Flow results have been computed for the entire range of ambient temperature conditions around that at the density extremum point. For suddenly heated surfaces, ambient temperatures larger than the extremum temperature result in upflow for all later times, although the velocities are much smaller than those obtained at higher temperature levels for identical heating conditions. For condition (a), ambient temperatures below the extremum result in a pure downflow for short times, followed by a bidirectional flow. For condition (b), by suitably transforming the velocity and distance variables, self-similar profiles are obtained. Conditions resulting in upflow, bidirectional flow and downflow are then examined. Dimensional comparisons of present results with those at higher ambient temperatures show the inapplicability of the Boussinesq formulation around the extremum point. In addition, it is shown necessary to use an accurate density equation by comparing the results with those using a parabolic density equation for water around 4°C.