The natural convection in a spherical shell

We have calculated the critical Rayleigh numbers for natural convection und er a central force field in the gap between two spherical surfaces as a fun ction of radius ratio eta. The investigation of the natural convection unde r a central force field shows important and interesting applications in geo physics. For example, for the radius ratio eta = R-1/R-2 = 0.54 we consider the convection in the Earth's mantle, for eta = R-1/R-2 = 0.34 we consider the convection in the outer Earth's core. The investigation of the natural convection under the axial force field has important applications to heat exchangers and spherical fluid pump systems.