## 3 Numerical Strategy
### Overall Solution Strategy
These are presented in the Appendix A and plotted in Figure 7. Figure 7 also shows the viscosity-temperature dependency of the pure PP in [12]. Although the evolution of the viscosity is proposed for our case, we do not have a sufficient amount of information regarding the variation of the other parameters. However, in recent works, constant values have been used [6; 7; 9; 12; 14; 15; 16; 17] in absence of better information. This is supported by the studies based on simulation results conducted by [PERSON] et al. [35], who concluded that parameters such as density, thermal conductivity, and heat capacity are of little importance to the burning behaviors of polymers in comparison with other parameters affecting combustion. ```
1 if(T > 453.15 and T <= 515.88):
2 mu = 1.25 \(\times\) 10\({}^{4}\)\(\times\) e\({}^{(-3.4\times 10^{-3}\times\)T)}\)
3 else if(T > 515.88 and T <= 533.15):
4 mu = 1.10 \(\times\) 10\({}^{-25}\)\(\times\) e\({}^{(1.26\times 10^{-1}\times\)T)}\)
```
**Algorithm 2**Definition of the experimental viscosity curve. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Polymer** & **Air** \\ \hline Density & 905 [kg/m\({}^{3}\)] & see Section 2 \\ Viscosity & \(\tilde{\text{(T)}}\) & \(1\times 10^{-5}\) [m\({}^{2}\)/s] \\ Specific heat capacity & 1900.0 [J/KgK] & 1310.0 [J/KgK] \\ Thermal conductivity & 0.16 [W/mK] & 0.0131 [W/mK] \\ Emissivity & 1.0 & – \\ absorption coefficient & – & 1000 [m\({}^{-1}\)] \\ Stefan–Boltzmann & & \\ constant & – & \(5.67\times 10^{-8}\) [W/m\({}^{2}\)K\({}^{4}\)] \\ Arrhenius coefficient & \(1.63\times 10^{14}\) [min\({}^{-1}\)] & – \\ Activation energy & 181.9 [K]/mol & – \\ Enthalpy of vaporization & \(8\times 10^{5}\) [W/m\({}^{2}\)K] [12] & – \\ B\({}_{\text{c}}\) & – & \(5.96\times 10^{9}\) [m\({}^{3}\)/Kgs] \\ T\({}_{\text{a}}\) & – & 10,700 [K] \\ C & – & \(2.601\times 10^{4}\) [K]/Kg] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Input parameters for the PFEM and Eulerian solvers. Figure 6: Temperature evolution for sensors 1, 2, and 3. Figure 7: Viscosity curve. ### Numerical Results

Figures 8-10 compare the experimental versus numerical results corresponding to the proposed curves. In these figures, the initial length of the specimen is indicated by a continuous line. Note that the polymer specimen (main body) loses mass due to two mechanisms: (i) gasification and (ii) melting and dripping. Both phenomena are strongly interrelated due to the fact that the dripping modifies the temperature of the surface and, therefore, the mass loss rate due to gasification. Figure 11a shows the volume loss curves for the three curves. A quick inspection of the figures reveals good agreement in the shapes between the experimental and numerical results for all of the curves up to 20 s. This is due to the fact that the three cases have the same viscosity until 723.15 K. As time progresses, the difference between the three cases becomes more evident. For instance, case 1 begins to reduce its volume due to melting and dripping before the experiment does. On the other hand, case 3 shows behavior dominated more by melting than by dripping. In fact, the length and width of the model are larger than those of the experimental model until 60 s (Figure 11b). Finally, case 2, whose curve is between case 1 and 3, shows better agreement with the experimental results in terms of shapes of the specimen than that of the other cases. However, none of these cases is able to capture the thread of molten material that appears after 70 s. This behavior is probably linked to the surface tension effects, which are not considered in this work. Moreover, a higher temperature at the edges due to the edge effect was observed [36; 37]. In addition, according to Figures 8-10, the sample did not stop the fire from spreading as in the case of the UL 94 test. The results shown in Figure 12a present the computed temperature distribution across four horizontal cut planes at different heights of the air domain for curve 2.