A numerical study of thermal convection in a rotating spherical annulus with axial gravitational field by using parametric spline function approximation

Abstract

A parametric spline function approximation is used to study the steady combined convection of a Boussinesq fluid contained between two concentric rotating spheres. A spline function which depends on a parameter p > 0 is used for approximation. This approximation gives second order accuracy. The spheres which form the flow region are maintained at uniform but different temperatures and are allowed to rotate about a common vertical axis with different angular velocities. A uniform gravitational field acts in the direction parallel to that of the axis of rotation. The resulting flow patterns, temperature distributions, total heat flux and torque characteristics are presented for various cases considered and it is found that these results are in good agreement with the results of Dallman and Douglass in 1980.