A Model for Spinning Non‐Stretching Rolie–Poly Fluids

In this paper, we present a mathematical model for the steady, isothermal extrusion of a non‐stretching Rolie–Poly (RP) fluid fiber, relevant to the melt‐spinning of viscoelastic polymers. Starting from the averaged mass and momentum balances coupled with the RP constitutive relation, an analytical formulation is derived that relates the applied stress to the fiber velocity and cross‐sectional profile. The dimensionless form of the equations reveals the influence of the Deborah number, inertia, draw ratio, and convective constraint release (CCR) parameter on fiber dynamics. Existence and uniqueness of solutions are established, and numerical simulations demonstrate how viscoelastic effects govern the evolution of velocity, stress, and area along the spinline. The study offers a simplified yet physically consistent framework for understanding non‐Newtonian fiber spinning using the Rolie‐Poly model.