Numerically computed multiple steady states of vertical buoyancy-induced flows in cold pure water

Abstract

The laminar, boundary-layer, natural convection flow adjacent to a vertical, heated or cooled, flat surface submerged in quiescent cold water was studied. The results demonstrate for the first time the existence of multiple steady-state solutions in a natural convection flow. The calculated velocity profiles, over a range of the parameters, are compared with recent corresponding velocity measurements of Wilson & Vyas (1979) and of Carey & Gebhart (1981). The newly found additional steady-state solutions are of considerable practical interest because the heat-transfer rates for a pair of solutions (with determining physical parameters and boundary conditions otherwise identical) are sometimes vastly different. An important consequence of this study is the possible relationship of multiple steady-state solutions to the recently observed unsteadiness in some such flows.