A widely used technique for the coating of magnet wires is passing them through enameling dies, from which they exit with a defined layer of enamel deposited on their surface. The generalized Couette flow, which emerges inside the converging annular gap between the moving wire and the stationary wall of the die, is computationally analyzed using the lubrication theory approximation. Non-Newtonian flow behavior and heat transfer are considered as well. The obtained results give a detailed insight into the effects of shear thinning/thickening on the velocity field and the wall shear stress along the wire. Despite the intense generation of viscous heat in the highly sheared region, the still moderate increase in temperature of the enamel does not pose any possible cooling problem. The influence of the die geometry on the drag force on the wire is examined by varying the axial contraction of the die, whose shape is assumed to follow a cosine-type function. The applied changes in the die geometry produce the same trends in the resulting drag force for all considered rheologies. The targeted reduction in the drag force could be achieved with the same die shape regardless of the Row behavior of the fluid. The predictions obtained from the lubrication theory based analytical model were validated against numerical results from computationally much costlier CFD simulations. This assessment proved the analytical model as a computationally efficient and reliable approach to describe the flow inside the die also for the fairly complex case of a shear thinning non-Newtonian fluid with temperature dependent viscosity. (C) 2015 Elsevier Ltd. All rights reserved.