In order to analyze the evolution of the concentration profile experimentally observed by MacDonald and Muller under shear-induced polymer migration in a rotating cone-and-plate device, we use a constitutive equation for the diffusion flux, where the gradient of a generalized non-equilibrium chemical potential appears instead of the concentration gradient. From this model of coupling between diffusion and viscous pressure, together with the mass balance equation, we derive some general features of the concentration profile, the temporal behavior of the polymer concentration near the apex of the cone and some relevant trends of the dynamical process of polymer migration.