Flow and heat transfer due to small torsional oscillations of a disk about a constant mean

Abstract

The paper deals with the study of flow and heat transfer in a viscous fluid from a disk performing small rotating oscillations about a constant mean. Separate solutions for low and high frequency ranges are developed. In the low frequency range the solution is obtained by Karman-Pohlhausen method. It is found that near the disk the oscillating components of radial and tangential velocities lag behind the disk oscillations. This tendency to phase lag is more than compensated as we move away from the disk. The oscillating components of the radial stress and the rate of heat transfer at the disk always lag behind, while the tangential stress has a phase lead. For very high frequencies the velocity field is of “shear-wave” type, predicting a phase lead of 45° in the tangential stress at the disk.