This paper discusses the development of boundary layers in the flow of a Newtonian fluid between two parallel, infinite disks. One of the disks is rotating at a constant angular velocity while the other remains stationary. An analytical series approximation and a numerical solution method are used to describe the velocity profiles of the flow. Both methods rely on the commonly used similarity transformation first proposed by Von Kármán [T. von Kármán, ZAMM 1, 233 (1921)]10.1002/zamm.19210010401. For Reh <18, the power series analytically describe the complete velocity profile. With the numerical model a Batchelor type of flow was observed for Reh > 300, with two boundary layers near the disks and a non-viscous core in the middle. A remarkable conclusion of the current work is the coincidence of the power series’ radius of convergence, a somewhat abstract mathematical notion, with the physically tangible concept of the boundary layer thickness. The coincidence shows a small deviation of only 2% to 4%.
Eeten, van, K. M. P., Schaaf, van der, J., Schouten, J. C., & Heijst, van, G. J. F. (2012). Boundary layer development in the flow field between a rotating and a stationary disk. Physics of Fluids, 24(3), 033601-1/18. . https://doi.org/10.1063/1.3698406