Natural convection in eccentric spherical annuli

Abstract

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. In this conductive regime the average Nusselt number remains approximately constant for all Rayleigh numbers below some critical value. Above the critical Rayleigh number, plumes appear and thermal convection takes place. We study this phenomenon, in particular the case where the inner sphere is displaced from the centre, using a two-component thermal lattice Boltzmann method to characterize the convective instability, the evolution of the flow patterns and the dependence of the Nusselt number on the Rayleigh number beyond the transition.