A numerical study of the hydrodynamics of nematic liquid crystals in cylindrical Couette geometry is presented, based on Leslie-Ericksen theory. The aim of this study is to interpret the director dynamics observed in Rheo-NMR experiments, where the sample (lyotropic cholesteric system PBLG/m-cresol 14%) is subjected to viscous, elastic and magnetic torques. When analysing the macroscopic response of the liquid crystal polymer to the azimuthal Couette flow, competing with the effect of the strong magnetic field applied perpendicular to the shear plane in the NMR set- up, we observe the existence of a steady state characterised by a distribution of director orientations neither parallel to the field nor in the shear plane. We show that this behaviour requires the occurrence of an instability, like the director analogue of Taylor cells, associated to a secondary flow. A proper modelling of the velocity profile allows us to interpret satisfactorily the main features of the experimental data.