Scaling investigation of the natural convection boundary layer on an evenly heated plate

An investigation of the natural convection boundary layer adjacent to an evenly heated semi-infinite plate with stratified ambient fluid is undertaken using scaling analysis and numerical simulation. The scaling analysis is shown to provide a complete description of the flow from start-up to full development, including the effect of the stratified ambient fluid. In particular it is shown that for the case with non-stratified ambient fluid the fully developed flow is y dependent over the entire plate, where y is the vertical coordinate, while for the case with stratified ambient fluid the fully developed flow is y dependent only in the region of the plate origin. A scaling is also obtained for the y dependent, y independent transition location. All the scalings are validated using a full numerical solution of the governing equations.