A high-order method for heat transfer in a fluid between concentric rotating spheres

A numerical method for describing the hydrodynamic and thermal fields between concentric rotating spheres is presented. The thermodynamic field is presented in terms of stream and vorticity functions, whereas the thermal field is described in terms of isotherms for a wide range of characteristic parameters such as Re, Pr, geometric size factor, and a kinematic factor describing the relative motion of the inner and outer spheres. The results show that the method is capable of producing accurate results not generally obtainable for large values of Re. Results obtained for large Re are in good agreement with other published results for the hydrodynamic field. The behavior of isotherms was found to fit into the classical convective and conductive heat transfer arguments. It is suggested that the method is applicable in numerical analysis, fluid dyanmics, the study of gyroscopes and centrifuges, geophysics, and spherical geometry.