## 2 Materials and Methods  
### Thermoplastic Polymers and Rheological Characterization  
We carried out a series of capillary flow experiments on five injection molding grade thermoplastic melts, which were chosen because of their very different sensitivity of viscosity to temperature at the high stress levels encountered in capillary rheometry (see their respective values of the temperature coefficient of viscosity \(\alpha_{\eta}\) in Table 1). The polymer samples include a high impact grade polystyrene (HIPS, POLYREX PH-60, Chi Mei Corp., Tainan County, Taiwan), a general purpose polystyrene (GPPS, POLYREX PG-33, Chi Mei Corp.), an acrylonitrile butadiene styrene (ABS, POLYLAC PA-757, Chi Mei Corp.), a crystalline polypropylene homopolymer (PP, Globalene 6331, LCY Corp., Taipei, Taiwan), and a carbon-fiber reinforced polyamide 66 (PA66, LUVOCOM 1/XCF/25, LEHVOSS Group, Hamburg, Germany). Prior to the measurements, the pellets were dried under vacuum conditions overnight at temperatures suggested by the manufacturers. Steady shear flow measurements at low shear rates were performed using a rheometer (MCR 301, [PERSON], Graz, Austria) equipped with a 25 mm diameter parallel-plate fixture (disposable aluminum substrate). A high pressure capillary rheometer (RG25, [PERSON], Buchen, Germany) was operated in the controlled speed mode to consecutively measure shear viscosities in the apparent shear rate range \(\dot{\gamma}_{\mathrm{a}}=\) 50-5000 s\({}^{-1}\). All the capillary measurements were repeated twice to ensure data reproducibility. Three circular dies of diameter \(D=1\) mm and different lengths \(L=10,\ 20,\ \mathrm{and}\ 30\) mm were used to determine the entrance pressure drop (Bagley correction) and, hence, the true shear stress [34; 35]. We found that the extrapolation method resulted in practically the same end corrections as those measured using a tapered orifice die (\(D=1\) mm and \(L=0.2\) mm). The Weissenberg-Rabinowitsch correction was performed to obtain the true wall shear rates [36; 37]. Since the temperature dependences of the density \(\rho\), specific heat capacity \(\hat{C}_{p}\), and thermal conductivity \(k\) were taken into account in the nonisothermal flow simulation, the fluid properties (\(\rho,\hat{C}_{p},\ k\)) were measured, respectively, using a PVT-6000 apparatus (Gotech), DSC 8500 (PerkinElmer), and RG25 accessory (Gottfert). Pressure-volume-temperature (PVT) diagrams for the molten materials were obtained under isobaric conditions (30, 60, 90, and 120 MPa) at a cooling rate of 5 \({}^{\circ}\)C/min. For the differential scanning calorimetry (DSC) measurements, each sample was heated to 250 or 300 \({}^{\circ}\)C at a temperature ramp rate of 10 \({}^{\circ}\)C/min in a nitrogen environment. The thermal conductivity measurements were performed under stationary conditions in a temperature range up to 250 or 300 \({}^{\circ}\)C. The measured values at an intermediate measurement temperature are compiled in Table 1 for reference, along with the melt flow index (MFI), the longest polymer relaxation time \(\lambda\), and the temperature coefficient of viscosity \(\alpha_{\eta}\) (\(=-\partial\eta/\eta\partial T\)) numerically evaluated at \(\dot{\gamma}_{\mathrm{a}}=500\) s\({}^{-1}\) from the temperature-corrected shear viscosity [1; 25].