Free convection above a uniformly heated horizontal circular disk (Q1058938)

The free convection boundary layer above a uniformly heated horizontal disk is considered. The equations of motion are solved numerically and by a series expansion valid near the circumference. It is shown that near the edge of the disk the flow is basically the same as on a plate, with the importance of the curvature effects increasing as the centre is approached. It is also shown that near the centre, the boundary-layer thickness increases very rapidly and that the solution splits up into two distinct regions. There is a thin viscous region next to the disk of thickness \(O(r^{2/3})\), where r measures distance from the centre, and a very much thicker inviscid region of thickness \(O(r^{-2/3})\).