SCALING OF THE LAMINAR NATURAL-CONVECTION FLOW IN A HEATED SQUARE CAVITY

The steady laminar natural-convection flow of air and water in a squar e heated cavity is calculated for increasingly large Rayleigh number. The flow is calculated by solving both the Navier-Stokes equations and the boundary-layer equations. The results are used to determine the p roper scalings of the flow in the different asymptotic flow regions: v ertical boundary layers, core region, comer region and horizontal boun dary layers. In particular the scalings according to the Navier-Stokes equations agree with the asymptotic model for the core and vertical b oundary layers as proposed by Gill [J. Fluid Mech. 26, 515-536 (1966)] .