## 3 Numerical Strategy
### Overall Solution Strategy
As time progresses, the heat zone develops in the air domain, providing heat feedback to the specimen. As a consequence, thee temperature in the polymer evolves, leading to a reduction in the viscosity value corresponding to curve 2. Due to this viscosity change, the polymer starts to melt and drip. The aforementioned phenomena together with the gasification are responsible for the volume reduction in the sa

Figure 8: Comparison between experimental versus PFEM results for curve 1: blue and red correspond to 298 and 1000 K, respectively. in Figure 12b, the maximum concentration of fuel appears in the polymer-air interface when the polymer reaches the gasification temperature due surface exposure to a heat flux. Finally, this fuel mixes with the oxygen and reacts, thereby producing the combustion. Figure 10: Comparison between experimental versus PFEM results for curve 3: blue and red correspond to 298 and 1000 K, respectively. Figure 9: Comparison between experimental versus PFEM results for curve 2: blue and red correspond to 298 and 1000 K, respectively. Figure 6 compares the experimental and numerical temperatures at different times for thermocouples 1, 2, and 3. The latter corresponds to the finite element, where the thermocouple can be observed, as the size of the mesh coincides with the diameter of the thermocouple. In all cases, the numerical strategy captures considerably well the rising branch of the curve, which corresponds to when the thermocouples are inside the polymer. Note that its extension depends on the evolution of the shape of the polymer, which is governed by the melting and dripping of the material. Moreover, we note that as we move from sensor 1 in the direction of sensor 3, the discrepancies between the experimental and the numerical values are more evident. This difference could originate due to the result of some complex phenomena not considered in this work, such as bubbling, micro-explosions, char formation, and complex time-dependent decomposition. Figure 11: Evolution of the length and volume simulated with PFEM. Figure 12: Evolution of the temperature and fuel distribution in the air domain at 10, 20, 30, 40, 50, and 60 s.

Subsequently, the remaining curve represents the measurements of the temperature corresponding to the flame or melted material passing through the thermocouples. It is important to remark that all of the thermocouples for an unknown reason move away from their original positions. Note that this is evident for thermocouple 1, where the recorded temperatures decrease. In order to consider this effect, an approximated trajectory was taken from the images. Although this procedure is limited by the quality of images, the numerical results corresponding to the trajectory of the thermocouples follow the same trend as that observed in the experimental results. In particular, the results corresponding to curve 2 are those that best fit the experimental results. One can conclude that knowing the change in viscosity of PP due to the addition of MDH is crucial to achieving good agreement between the numerical results and the evolution of the temperature measurements given by the three thermocouples positioned inside the polymer. Accounting for the viscosity change is also crucial to the prediction of the evolution of the polymer shape. Although the correlation observed is not perfect, given the complexity of the set-up, we consider the agreement between the experiments and the simulation results satisfactory. ## 5 Conclusions

In this paper, the numerical tool developed by the authors was applied for modelling the dripping and melting behavior of a blend of polypropylene mixed with a commercial halogen-free fire retardant (30 wt.% MDH, magnesium hydroxide) in a UL 94 fire scenario set-up coupled with temperature monitoring. The input parameters required for the model were obtained from different literature sources/diverse manufacturers and previously performed experimental studies.