The particular problem under study is that of the flow of a viscous incompressible fluid, with heat transfer, between concentric rotating spheres. This involves the solution of four PDEs. The application of a new technique to the rotating spheres problem is appropriate for several reasons. First reaseachers in numerical analysis and fluid dynamics are always interested in numerical techniques that are accurate and stable for a wide range of parameters. Secondly, fluid motion inside rotating containers has a wide variety of applications in engineering, such as the study of gyroscopes and centrifuges.
Applications also arise in geophysics, where atmospheric and oceanic circulations are studied.
Many papers have been written on the numerical solution of steady, viscious, imcompressible flow between two rotating spheres. However, these papers have either been based only on first-order methods or have produced results only for small Reynolds number. In this paper we will present a second-order method which converges for both large and small Reynolds numbers and Prandtl numbers. This technique allows us to generate more accurate solutions with larger Reynolds numbers than has been possible with other methods. This problem, with heat transfer, has been studied in only one other paper, and only for very small Reynolds numbers.