The start-up flow of a nematic rod-like polymer in an eccentric cylinder geometry is studied on the basis of the rigid rod model. The simulations neglect the polymer stress contribution in the momentum equation. The nematic configuration is obtained by integrating the diffusion equation for the orientational distribution function with a Galerkin approach. The predictions are compared with results obtained by introducing different closure approximations. Both a quadratic and a Bingham closure are considered. The comparison shows that the approximations have a qualitative impact on the results.