## 2 Modelling and Methods
### Heat Transfer Analysis, Fire Load, Assumptions, and Conventions
#### 2.2.3 Modeling Heat Transfer Assumptions and Conventions  
An element that required special attention was the behaviour of EPS when exposed to significantly high temperatures. The material is a combustible thermoplastic that remains stable when exposed to temperatures up to 100 \({}^{\circ}\)C. Its thermal properties start to rapidly degrade shortly after that, while temperatures upwards of 160 \({}^{\circ}\)C lead to the complete loss of the inflated bead structure and the liquefaction of the insulation boards. Approaching temperatures of 278 \({}^{\circ}\)C leads to the gasification of the material [30]. Provided that the wall samples were subject to temperatures significantly higher than 100 \({}^{\circ}\)C, the above behaviour had to be stimulated.  
Conventionally, and accepting that no material can be removed from the finite element analysis model once the analysis has commenced, a temperature-dependent variable was utilised to reproduce the reduced performance and ultimate collapse of EPS. The thermal conductivity coefficient (\(\lambda_{\text{EPS}}\)) of the insulating material was artificially increased when temperatures beyond 150 \({}^{\circ}\)C were encountered. That allowed for the unhindered transfer of heat through the melting EPS boards, resembling the gradual removal of the physical barrier. The coefficient was linearly increased from a value of \(\lambda_{\text{EPS}}=0.035\text{ W/(m\cdot K)}\) at 150 \({}^{\circ}\)C to \(\lambda_{\text{EPS}}=20\text{ W/(m\cdot K)}\) at 200 \({}^{\circ}\)C (practically no heat transfer resistance). Similarly, its density (\(\rho_{\text{EPS}}\)) and special heat capacity (\(\text{CP}_{\text{EPS}}\)) were reduced to negligible figures. Figure 5 demonstrates the steep material property changes for the melting EPS layer.  
It is worth highlighting that the failure of the EPS material would naturally result in the detachment and collapse of the attached render. To ensure the removal of the render's beneficial insulating function, a similar approach was adopted, wherein all associated thermophysical properties were altered to reproduce its collapse. To ensure the change was introduced in a timely manner, an exploratory analysis was performed to identify the time for the interface between render and EPS to reach the critical temperature of 150 \({}^{\circ}\)C. This threshold temperature was achieved at t = 240 sec. The thermal conductivity coefficient (\(\lambda_{\text{render}}\)) was increased from \(\lambda_{\text{render}}=1.40\text{ W/(m\cdot K)}\) to \(\lambda_{\text{render}}=2000\text{ W/(m\cdot K)}\), while its density (\(\rho_{\text{render}}\)) and specific heat capacity (\(\text{CP}_{\text{render}}\)) were reduced to negligible values.  
Figure 4: Typical fire curve (ISO 834) applied to finite element analysis models as seen in EN1991-1-2.  
Although the same process would normally apply to both faces of the wall (exposed to fire and non-exposed), only the properties of the exposed insulation and render were altered within the scope of the present study. Similarly, no allowance has been made for the ignition of EPS volatiles.