Improved calculations for the steady flow over a heated sphere at high Grashof number
Abstract
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.
 Publication:

Journal of Mathematical and Physical Sciences
 Pub Date:
 1984
 Bibcode:
 1984JMPS...18..115A
 Keywords:

 Boundary Layer Equations;
 Computational Fluid Dynamics;
 Grashof Number;
 Steady Flow;
 Thermal Boundary Layer;
 Convective Flow;
 Equations Of Motion;
 Free Convection;
 Spheres;
 Fluid Mechanics and Heat Transfer