## 1 Introduction  
Once a fire starts in the living area of a residential building, mattresses and upholstered furniture made of polymeric materials are often the first items to enhance its growth. Many of these materials tend to liquefy, flow, and drip, forming flammable pools, which then crucially spread the fire to objects that were originally non-adjacent. This burning behavior influences the onset of the fire, and the flames spread within it. In order to considerably reduce the risk of these accidents, the introduction of fire retardants (FRs) in the polymer matrix was a key step in inhibiting combustion and smoke generation. This is due to the fact that they affect the fire and material properties in numerous ways [1, 2, 3, 4], e.g., heat absorption and melt viscosity. To assess the flammability of \"new materials\", there exists a set of small-scale reaction-to-fire tests. One of these is the vertical UL 94 test [5]. In this test, a small-sized specimen is exposed to a flame for 10 s, thereby forcing its ignition. After this period of time, the flame is removed and the burning becomes free. Apart from fire tests, numerical simulation is another way to assess flammability. In [6], the authors investigate the effect of FRs on the fire behavior of a polycarbonate/acrylonitrile butadiene styrene (PC/ABS) specimen using a Lagrangian finite element model known as the particle finite element method (PFEM). The computational solution procedure of the UL 94 test using PFEM consists of a non-linear loop, where at each step, the Navier-Stokes equations are solved in conjunction with the temperature equation. Furthermore, the authors of [7] simulate the burning of a polypropylene (PP) with other FRs to understand the complex burning behavior introduced by them. Although in both papers the PFEM was able to simulate the melt flow and dripping, facilitating an understanding of the complex behavior of polymeric materials during fire, none of the works modeled the effect of the surrounding air, and, therefore, a strongly simplified combustion model was used. Furthermore, there was no comparison between the experimental and numerical results in terms of evolution of the free surface of the polymer, temperature inside the polymer, etc. On the other hand, recently, researchers have developed a numerical strategy [8] that can reproduce the UL 94 test much more accurately than other cited models can [6; 7; 9]. The main difference between the new approach and the previous one is that the new one combines the PFEM for the polymer with an Eulerian formulation for the surrounding air. The coupling is performed using an embedded Dirichlet-Neumann scheme [8]. Although the numerical tool was observed to be a promising methodology for predicting behavior, as the numerical results agree well with the experimental ones corresponding to pure PP, the tool requires reliable input parameters for modelling the behavior of the material in fire situations. The work proposed in the current study focuses on using the numerical tool developed by the authors to assess the behavior of an FR polymer in the UL 94 set-up. It should be noted that the tool has not previously been used for FRs. Traditionally halogenated FRs are highly effective in the flame retardancy of polymers [10]. However, the application of halogenated FRs has caused an increasing number of environmental problems due to their toxicity and/or bioaccumulation. Therefore, the development and use of halogen-free FRs on polymers has aroused a considerable amount of interest in this field. Amongst the halogen-free FRs, magnesium hydroxide (MDH, Mg(OH)2) is one of the widest applied on polymers due to its low cost and environmental friendliness. In the fire condition, MDH decomposes to magnesium oxide and releases water, which is a typical endothermic reaction [11]. The endothermic decomposition of MDH absorbs some of the heat during the combustion process, delaying both the ignition and the combustion of the polymer.