Free convection boundary layers over humps and indentations

Attention is given to the way in which a free convection boundary layer on a vertical surface negotiates a small hump or indentation on the surface. The hump/indentation is taken to have a streamwise spread of O(G-sub-r to the -3/14), G-sub-r being the Grashof number of the oncoming flow, and a transverse spread of O(G-sub-r to the -9/28); in this way, the interaction can be described by means of a double-deck structure. For very small humps/indentations, the lower-deck equations can be linearized, and the resulting equations are solved by Fourier transforms. In general, the equations must be solved numerically, and results are given for the boundary shape Y = h-sub-0 exp(-k-squared X-squared) for a range of h-sub-0 and k; h-sub-0 and k are constants giving the height and spread of the hump (or indentation), respectively, in the lower-deck scalings. It is found that for sufficiently large values of the absolute value of h-sub-0, a region of reversed flow exists; this region is downstream of X = 0 for humps and centers on X = 0 for indentations.