A Numerical Study of Flow and Heat Transfer Between Two Concentric Rotating Spheres with Time-Dependent Angular Velocities

The transient motion and heat transfer of a viscous incompressible uid contained between two concentric spheres, maintained at di erent temperatures and rotating about a common axis with di erent angular velocities, is considered numerically, when the angular velocities are arbitrary functions of time. The resulting ow pattern, temperature distribution and heat transfer characteristics are presented for the various cases, including exponential and sinusoidal angular velocities. An interesting e ect, of long delays in the heat transfer of a large portion of the uid in the annulus, is observed, because of the angular velocities of the corresponding spheres. Keywords: Flow and heat transfer; Concentric rotating spheres; Time-dependent angular velocities; Numerical solution.