**4. Results**

*4.1. Solution Method*

We numerically solve the system of differential Equations (36), (37), (43) and (45) using a fourth-order Runge–Kutta–Merson method to integrate them in the axial direction. To this end, we first integrate Equation (43) and iteratively solve the whole system of equations until we find a value of the tension that satisfies the condition

$$
\overline{w}\_0(\overline{\zeta} = 1) - 1 < 10^{-3}
$$

In addition, we discretize Equation (45) and the boundary conditions (46) in the radial direction using second order central difference schemes for both the first and the second derivatives.

All the relevant parameters and initial values for the different cases utilized in the numerical simulations are listed in Table 1. Although the values of the material parameters vary with the temperature, we assumed them to be constant, as their dependence on the temperature is weak. We only let the viscosity vary with the temperature, as its value changes by different orders of magnitude in the temperature range of interest. The step sizes in the axial and radial directions were chosen after a grid study to ensure that the results were trustworthy. We set <sup>Δ</sup>*<sup>ζ</sup>* = 6.25 × <sup>10</sup>−<sup>7</sup> and <sup>Δ</sup>*<sup>x</sup>* = 0.2 for the case of the slow drawing ratios DR36-1, DR54-15, and DR72-2. In the case of the high drawing ratio DR1-102, we utilized <sup>Δ</sup>*<sup>ζ</sup>* = 1.5625 × <sup>10</sup>−<sup>7</sup> and <sup>Δ</sup>*<sup>x</sup>* = 0.5.


**Table 1.** Main parameters and initial values used for the simulations. *<sup>a</sup>* Voyce et al. [22], *<sup>b</sup>* Lee and Yaluria [36], *<sup>c</sup>* Paek and runk [16], *<sup>d</sup>* Taroni et al. [24], *<sup>e</sup>* Huang et al. [47], *<sup>f</sup>* Myers [17], *<sup>g</sup>* Fitt et al. [19], *<sup>h</sup>* Luzi et al. [20].
