Laminar free convection in confined regions

Abstract

We investigate the development of density stratification in a confined fluid due to a buoyancy source which gives rise to a vertical convective boundary layer. We find that the stratification is significantly different when the boundary layer is laminar rather than turbulent. In particular, the magnitude of the density gradient in the fluid interior increases rather than decreases in the direction of flow of the boundary layer, and this density gradient varies smoothly so that there is no density front between the stratified fluid and the unmodified homogeneous fluid. Laboratory experiments are described in which homogeneous fluid in a rectangular container was heated at a vertical sidewall. Vertical temperature profiles and streak photographs were taken which show the dominant features of the stratification mechanism under laminar flow conditions. We review similarity theory for a vertical, laminar, free-convection boundary layer in a homogeneous environment, and develop new similarity solutions for convective boundary layers in stratified environments. We use these analytic results to interpret qualitative features of the experimentally observed flow fields and to develop an expression for the depth of the stratified layer as a function of time.