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 fluid contained between two concentric spheres, maintained at different temperatures and rotating about a common axis with different angular velocities, is considered numerically, when the angular velocities are arbitrary functions of time. The resulting flow pattern, temperature distribution and heat transfer characteristics are presented for the various cases, including exponential and sinusoidal angular velocities. An interesting effect, of long delays in the heat transfer of a large portion of the fluid in the annulus, is observed, because of the angular velocities of the corresponding spheres.