Numerical simulation of natural convection between two concentric isothermal spheres at moderate Rayleigh number

The numerical Simulation of natural convection within an incompressible Newtonian fluid confined between two isothermal and concentric spheres is carried out. The phenomenon considered is two-dimensional, axisymmetric and permanent, with an annular space ratio of A = 2, filled with air Pr = 0.7, at moderate Rayleigh number Ra between 103 and 106. Simultaneous resolution of the continuity equations, of Navier-Stokes and energy, is carried out by the combination of the implicit method of alternate directions (ADI) with the method of convergence acceleration by successive replacement (SAR), in the Vorticity - Stream function formulation. The isovalues of temperature T and the steam function Ψ obtained, as well as the Average Nusselt number, are in a good agreement with previous studies, and gives new Nusselt number correlation Nu = f(Ra).