Steady laminar natural convection of a Boussinesq fluid contained within a spherical annul us is investigated by the method of partial spectral expansions. The fluid generates heat uniformly. The natural convection is established due to the uniform gravitational field and the thermal gradients in the fluid. The inner sphere is insulated and the outer surface is an isotherm. From the dimensionless equations for the stream-function and temperature, three dimensionless parameters are seen to govern the flow field: the Grashof (Gr) and Prandtl (Pr) numbers and the radius ratio. Results are presented for a radius ratio of 0.5, 5 × 103 ≤ Gr ≤ 107, and 0.1 ≤ Pr ≤ 2. In all cases, the shape of the streamfunction is essentially unaltered, but its magnitude increases as Gr increases and Pr decreases. The isotherms show a large dependence on both Gr and Pr as does the local heat flux along the outer surface.