"Second-Order Finite Difference Solutions for the Flow Between Rotating Concentric
Spheres"
by
David H. Schultz,
Steve Schwengels, and Gunol Kocamustafaogullari
The steady motion of a viscous fluid contained between two concentric spheres
which rotate about a common axis with different angular velocities is
considered. A second-order method which was introduced previously by the
authors to obtain numerical solutions of a class of Navier-Stokes problem
coupled with a superimposed thermal field is successfully extended here
to investigate the influence of the internal generation of heat by viscous
dissipation on the thermal field. The resulting thermal field solutions are
presented for various values of the Eckert number and the rotation ratio.
It is shown that the inclusion of heat generation by viscous dissipation
significantly alters the thermal field behavior, while the relative rates
of rotation of the two spheres do not change the general character of the
thermal field.