## 3 Results and Discussion
### Assessment of Temperature-Corrected Shear Viscosity  
The effects of viscous heating (or temperature thinning) on experimentally measured shear viscosity are investigated for three types of thermoplastic melts, including amorphous polymers (HIPS, GPPS, and ABS), a crystalline polymer (PP), and a filled polymer (PA66). We began the nonisothermal capillary flow simulations with the viscous Cross-WLF model for the orifice die depicted in Figure 1a (\(L/D=0.2\)), based on the shear viscosities with and without temperature correction. It is known that the contraction flow has an elongational character along the centerline [35; 37; 46] and that a purely viscous model has a much lower elongational viscosity than a viscoelastic model, therefore it is not surprising to see that the viscous Cross-WLF model severely underpredicted the entrance pressure drop \(\Delta P_{\rm ent}\)[35; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57]. This is illustrated for GPPS in Figure 6a, where \(\Delta P_{\rm ent}\) were measured using the 0.2-mm-long orifice die. As expected, \(\Delta P_{\rm ent}\) increases significantly with increasing \(\dot{\gamma}_{\rm a}\), and its value is higher at lower measurement temperature. For the 30-mm-long die (depicted in Figure 1b), however, we see in Figure 6b that \(\Delta P_{\rm ent}\) is not a small portion of the total; \(\Delta P_{\rm ent}\) / \(\Delta P_{\rm total}\) can be as large as 0.1-0.2 at \(\dot{\gamma}_{\rm a}=5000\) s\({}^{-1}\). Considering that viscous heating occurs mainly along the capillary die, and that the measured \(\Delta P_{\rm ent}\) are available for all the test samples, in the following discussion, we concerned ourselves primarily with the pressure drop over the length of the capillary \(\Delta P_{\rm cap}\) (\(\approx\Delta P_{\rm total}-\Delta P_{\rm ent}\)). The purpose of this analysis is two-fold: First, viscous heating contribution to \(\Delta P_{\rm cap}\) can be better quantified without being influenced by the contraction flow. Second, the GNF is expected to hold well for the shear-dominated capillary flow. Figure 6: (**a**) Measured entrance pressure drop \(\Delta P_{\rm ent}\) (symbols, \(L/D=0.2\)) vs. viscous Cross-WLF model prediction based on \(\eta\) (\(\dot{\gamma}\)) with and without temperature correction (lines) as a function of \(\dot{\gamma}_{\rm a}\) for GPPS. (**b**) Fraction of the entrance pressure drop \(\Delta P_{\rm ent}\) for GPPS. To evaluate the role of viscous heating in pressure loss, it is instructive now to consider the purely viscous Cross-WLF model and neglect viscous heating correction of shear viscosity (i.e., using the uncorrected viscosity). For all the samples studied, the experimental \(\Delta P_{\text{cap}}\) are compared with the Cross-WLF model predictions (dashed lines) in Figure 7a-e. Whereas the viscous model describes the measured pressure drops very well at low shear rates, it begins to underpredict the experimental data above a critical apparent shear rate (200 or 500 s\({}^{-1}\)). As discussed later, the Nahme number (Na) can be used to delineate the flow regimes. In Figure 7a-e the trend in the observed deviation is universal for all the melts investigated and is reminiscent of the comparison made earlier in Figure 2d, where the likely underestimate of experimental \(\Delta P_{\text{cap}}\) is, to a large extent, ascribed to neglecting the effect of the fluid temperature rise on shear viscosity. Moreover, it can be seen in Figure 7c,e that, due to their large shear stresses and sensitivity of viscosity to temperature (i.e., large \(\alpha_{\eta}\)), the extent of disagreement is comparatively large for ABS and filled PA66. Figure 7: _Cont._  
To show the viscous heating contribution to \(\Delta P_{\rm cap}\), we next used the temperature-corrected shear viscosity in the nonisothermal capillary flow simulation; the corrected flow curves have been presented earlier in Figure 4 for all the samples studied.