A numerical study of natural convection in eccentric spherical annuli

A fluid between two spheres, concentric or not, at different temperatures will flow in the presence of a constant gravitational force. Although there is no possible hydrostatic state, energy transport is dominated by diffusion if temperature difference between the spheres is small enough. By the use of a full three-dimensional thermal lattice Boltzmann model we study the transition between the conductive, the steady convective, and the unsteady convective regimes. We use the concentric case to validate the results by comparing with experiments and numerical simulations found in the literature, and then we extend our numerical experiments to the eccentric case to observe the general behavior of the different regimes. We analyze the energy transport characterized by the relation between Nusselt and Rayleigh numbers as well as the arising flow patterns.