The purpose of this paper is the presentation of a second order method to obtain the solutions of the flow of a viscous incompressible fluid, with heat transfer, between concentric rotating spheres. The application of a second order method to the rotating spheres problem is appropriate for several reasons. First, researchers are always interested in numerical methods that are accurate and stable for a wide range of parameters. Secondly, fluid motion inside rotating containers has a wide variety of applications, such as the study of gyroscopes and centrifuges.
Applications also arise in geophysics, where atmospheric and oceanic circulation are studied.
This problem was chosen because of its applications and because it represents a good benchmark for numerical techniques. This problem, with heat transfer, has been studied in only one other paper and only for very small Reynolds numbers. We present results for both large and small Reynolds numbers and Prandtl numbers, as well as various rotating parameters and distances between spheres.