Unsteady natural convection phenomena of air in a sphere heated suddenly from the outer surface were studied numerically for the axisymmetric cases. Boussinesq approximation was applied to the equations of motion which described the buoyant circulation of air in the sphere, and the solution method was based on the stream function-vorticity approach. Numerical simulation of the unsteady convection was accomplished and presented by using the mixed finite difference schemes which proved efficient for the spherical coordinate systems as well.