## 3 Numerical Strategy
### Overall Solution Strategy  
To this end, all the components of the strategy are specified. The problem to be solved can be formulated as: \"given the nodal position, the velocity, the pressure, and temperature in both domains and exclusively in the air domain, the mass fraction of fuel Y\({}_{F}\) and the oxygen Y\({}_{O}\) as well as the incident radiation G at time \(t^{n}\) find these variables at \(t^{n+1}\). The overall solution strategy is summarized in Algorithm 1. ```
1:Initialization \(\mathbf{M}\), \(\mathbf{T}\), \(\mathbf
```
1 for\(t=t^{n+1}\)do in the air domain * Fix on the interface the velocity and temperature (Equation (2)) following [19]; * Solve: - RTE eq. (Equation (16)); - Energy eq. (Equation (17)); - Navier-Stokes eq. (Equations (19) and (20)); in the polymer domain * Prescribe the normal heat flux \(q_{R}\) provided by the air at the surface; * Solve: - Energy eq. (Equation (15)); - Navier-Stokes eq. (Equations (13) and (14)). ```
**Algorithm 1**Solution algorithm for the simulation of the UL 94 test. ### Materials, Experimental Methods, and Input Parameters

#### 4.1.1 Material

The mixing of MDH (Sigma Aldrich) at 30 wt.% and polypropylene (ISPLEN PP-045 G1E-PP YPF, \(\rho\) = 905 kg/m\({}^{3}\), C = 1.8-2.0 kJ/Kg \({}^{\circ}\)C, \(\kappa\) = 0.1-0.22 Wm\({}^{-1}\)K\({}^{-1}\)) was conducted by first melt-blending in a high-torque microcompounder (Xplore MC 15) at 100 rpm, 190 \({}^{\circ}\)C for 3 min in each batch. Afterwards, the compounding material was heat molded using a platen hot-press (LabPro 400, Fontijne Presses). All of the samples were pressed at 2 MPa for 10 min at 190 \({}^{\circ}\)C.

#### 4.1.2 Thermogravimetric Analysis

In order to estimate the kinetics parameters (Ea and A, activation energy and Arrhenius coefficient, respectively), the pyrolysis process was carried out in a thermogravimetric analyzer (TGA Q50, TA Instruments) under nitrogen atmosphere. For further details on the procedure, the reader is referred to [29; 30]. There exist two main groups that can be used in the analysis of the kinetics in non-isothermal and solid-state mode obtained from the TGA (fitting and free models) [31]. Free models are more often implemented than free ones, as the latter possess more inherent complications with regard to the selection of the kinetic model [32] than those of the former. Free models estimate activation energy and the Arrhenius coefficient by using different heating rates and obtaining a range of activation energy as a function of different conversion values. Flynn-Wall-Ozawa and Kissinger methods are the non-isothermal free models selected to calculate both kinetic parameters. In the case of the Kissinger model, the values calculated are 181.9 kJ/mol and 1.63 \(\times\) 1014 min\({}^{-1}\) for activation energy and the Arrhenius coefficient, respectively, while for the FWO method, they are 84.75 kJ/mol and 28,883.43 min\({}^{-1}\) for activation energy and the Arrhenius coefficient, respectively. #### 4.1.3 Rheological Behavior

To obtain experimental values of viscosity MDH30/PP samples, a rheometer (AR200 EX, TA Instruments) was used. The dimensions of the samples were 25 mm in diameter and 0.5 mm in thickness. The experiments were conducted according to the evolution of the viscosity of the material in the dynamic temperature step mode ranging from 453.15 to 533.15 K. A low value of shear rate (0.1 rad/s) was chosen for the experimental tests since the process of dripping occurs when this value is low [6]. Figure 2 exhibits the values of viscosity depending on the temperature. #### 4.1.4 UL 94 Test

The UL 94 test [33] was performed in a burning chamber (UL 94, FTT, UK) Technology, United Kingdom). The dimensions of the specimens were 127 \(\times\) 12.7 \(\times\) 3.2 mm\({}^{3}\), and each of them was equipped with three type-K thermocouples (Inconel 600, diam. 0.75 mm, long. 250 mm, Tmax = 800 \({}^{\circ}\)C) located in different sections of the specimens (Figure 3).