Improved calculations for the steady flow over a heated sphere at high Grashof number

A numerical approach is described which has been used to obtain solutions to the free convective steady flow, at high Grashof number, over a heated sphere. The gross singularity is extracted before attempting a numerical solution of the governing partial differential equations. As a result, the range of calculations is extended to within an angular distance of 0.002 pi from the upper pole of the sphere. The weak singularity still present in the sphere prevents the pole from being reached. The overall features of the flow obtained elsewhere are confirmed, in particular the convergence of the flow onto, and eruption from, the upper pole. It is demonstrated that the analytical structure close to the upper pole derived by Brown and Simpson (1982) is consistent with the numerical solution.