Turning moment of rotating inner cylinder in the entry region of concentric annuli

This paper is concerned with calculating the tangential shear stress and the torque required to turn the inner shaft of concentric annuli having a laminar flow with simultaneously developing tangential and axial boundary layers. The nondimensional governing equations have been numerically solved over a wide range of the annulus radius ratio (N = 0.5 - 0.95) and the ratio of the square of Reynolds number to Taylor number (Re²/Ta=0.3 - 10). The results clarify the effect of these two controlling parameters (N and Re²/Ta) on the torque and show that the assumption of whole-channel fully developed flow leads to a considerable underestimation of the values of the torque.