Upper bounds on the torque in cylindrical Couette flow

Abstract

Upper bounds on the torque are derived for a fluid that is contained between two concentric rotating cylinders. Absolute upper bounds are obtained by requiring that the fluid satisfy the boundary conditions and the dissipation integral. Improved bounds are then found by requiring that the fluid satisfy continuity conditions. These bounds are in qualitative agreement with the data in that they reflect the asymptotic parameter dependence in the range of experimental data.