## 3 Numerical Strategy
### Overall Solution Strategy
The numerical results reveal that a well-adjusted viscosity of the material is crucial to achieving good agreement in the evolution of the temperature measurements given by the three thermocouples positioned inside the polymer as well as in the evolution of the shape of the polymer. Thus, the effect of MDH on the viscosity curve of pure PP and its important role in PP's behavior in fire situations were examined. This allowed for us to improve our understanding of the complex behavior of polymeric materials during fires. To further improve the model, examination of polymer material properties as a function of temperature and a better characterization of the chemical reaction in the air are needed. However, the inclusion of temperature-dependent parameters is trivial in our model. Therefore, in the case of obtaining these dependencies from the experiments, they can be immediately integrated into the model. J.M. : software, validation, visualization, and writing--original draft. J.d.I.V. : formal analysis, investigation, and writing--original draft. D.-Y.W. : supervision, methodology, and writing--review and editing. E.O. : writing--review and editing. All authors have read and agreed to the published version of the manuscript. This document is the results of the research project funded by the COMETAD project of the National RTD Plan (ref. MAT2014-60435-C2-1-R) from the _Ministerio de Economia y Competitividad_ of Spain. The authors [PERSON] and [PERSON] acknowledges financial support from the Ministerio de Ciencia, Innovacion e Universidades of Spain via the Severo Ochoa Programme for Centres of Excellence in RD (referece: CEX2018-000797-S)

Not applicable. The authors declare no conflict of interest. ## Appendix A The viscosity curves corresponding to the images in Figure 7 are as follows
```
1 If(T <= 373.0):
2 mu=\(5.72\times 10^{6}\times e^{(-6\times 10^{-3}\times T)}\) else if(T > 373.0 and T <= 453.15):
3 mu = \(1.95\times 10^{16}\times e^{(-6.48\times 10^{-2}\times T)}\) else if(T > 453.15 and T <= 515.88):
4 mu = \(1.25\times 10^{4}\times e^{(-3.4\times 10^{-3}\times T)}\) else if(T > 515.88 and T <= 533.15):
5 mu = \(1.10\times 10^{-25}\times e^{(1.26\times 10^{-1}\times T)}\) else if(T > 533.15000001 and T <= 724.0):
6 mu = 20000.0 else
7 mu = \(1.83\times 10^{16}\times e^{(-4.98\times 10^{-2}\times T)}\)
```
**Algorithm A1**Definition of the curve 1. ```
1 if(T <= 533.15):
2 Definition Curve 1 else if(T > 533.15000001 and T <= 723.0):
3 mu = 20000.0 else if(T > 723.0 and T <= 762.49):
4 mu = \(1.38\times 10^{15}\times e^{(-0.035\times T)}\) else if(T > 762.49 and T <= 769.5):
5 mu = \(1.70\times 10^{266}\times e^{(-7.94\times 10^{-0.001}\times T)}\) else if(T > 769.5 and T <= 791.5):
6 mu = \(1.49\times 10^{25}\times e^{(-7.30\times 10^{-2}\times T)}\) else if(T > 791.5 and T <= 819.0):
7 mu = \(2.99\times 10^{22}\times e^{(-6.52\times 10^{-2}\times T)}\) else if(T > 819.0 and T <= 850.0):
8 mu = \(1.75\times 10^{4}\times e^{(-1.39\times 10^{-2}\times T)}\) else if(T = 0.13)
```

**Algorithm A2**Definition of the curve 2. ## References

* [PERSON] (1973) [PERSON] Molecular Basis of Flame Inhibition. _J. Res. Natl. Bur. Stand. Sect. A Phys. Chem._**1973**, _77_, 733-754. [CrossRef]
* [PERSON] _et al._ (2009) [PERSON]; [PERSON] _Fire Retardancy of Polymeric Materials_, 2 nd ed. ; CRC Press: Boca Raton, FL, USA 2009. * [PERSON] (1986) [PERSON]; [PERSON] Mechanism of Intumescence in Fire Retardant Polymers. _Rev. Inorg. Chem._**1986**, \(8\), 69. [CrossRef]
* [PERSON] _et al._ (2015) [PERSON]; [PERSON]; [PERSON]; [PERSON] Influence of Flame Retardants on the Melt Dripping Behaviour of Thermoplastic Polymers. _Materials_**2015**, \(8\), 5621-5646. [CrossRef]
* ASTM D3801-10. _Standard Test Method for Measuring the Comparative Burning Characteristics of Solid Plastics in a Vertical Position;_ ASTM International: West Conshohocken, PA, USA, 2010.