The stream function‐vorticity formulation is used for the numerical solution of a fundamental problem of fluid mechanics. In this way we overcome the limit, which the primitive variable formulation of Navier‐Stokes equations sets, and consists of the compatibility condition known as the inf‐sup condition or LBB condition. A modeling procedure is developed for natural convection heat transfer from an isothermal heated sphere located at the center of an isothermal, cooled, spherical‐shaped enclosure. The fluid is consider as viscous, Newtonian and incompressible and the flow as unsteady and axisymmetric about the vertical axis of rotation. The equations of motion and energy are solved numerically, developing and applying an efficient numerical technique based on finite differences scheme. Our numerical computations are compared with available results and experimental measurements and very good agreement is found in all cases.