## 4 Results and Discussion
### Flux from the Door  
As mentioned, one aspect of this analysis is the heat flux from the vertical openings, which in this case is the doorway of the dwelling. Heat flux data measured 30 cm from the top of the doorway clearly show the growth, steady-state, and decay phases in each experiment--examples are given in Figure 12. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{3}{*}{Case Name} & \multicolumn{3}{c}{**Average Temperature for Top TCs**} & \multicolumn{3}{c}{**Area under the Heat Flux Curve**} \\  & \multicolumn{3}{c}{**over the Steady-State Period**} & \multicolumn{3}{c}{**(Total Radiative Energy)**} \\  & \multicolumn{3}{c}{**(\({}^{\circ}\)C)**} & \multicolumn{3}{c}{**(kJ/m\({}^{2}\))**} \\ \cline{2-7}  & **RB\_5** & **LB\_5** & **RF\_5** & **LF\_5** & **30 cm from the Door** & **15 cm from the Side** \\ \hline \multicolumn{7}{c}{**Central Openings with Polycarbonate**} \\ \hline
**S\_016\_Open\_1** & 294 & 291 & 274 & 275 & 1587 & 1170 \\ \hline
**S\_016\_Open\_2** & 330 (13\%) & 320 (10\%) & 286 (4\%) & 290 (5\%) & 1526 (\(-\)4\%) & 1160 (\(-\)1\%) \\ \hline \multicolumn{7}{c}{**Corner Openings without Polycarbonate**} \\ \hline
**C\_016\_Open\_1** & 324 & 304 & 318 & 305 & 1572 & 1161 \\ \hline
**C\_016\_Open\_2** & 360 (10\%) & 336 (11\%) & 351 (10\%) & 343 (11\%) & 1466 (\(-\)7\%) & 1215 (5\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Repeatability check for two cases. The potential for ignition of materials in the vicinity of a burning dwelling will be determined largely by three aspects of heat flux: magnitude, duration, and variability. All three are implicitly recognised within a calculation method called the Flux-Time Product (FTP) method [36; 37]. The theory is that any given material has an FTP threshold value that reflects its thermal properties and will ignite once this threshold is exceeded when subject to a known input flux-time curve:  
\[ \begin{array}{l}FTP=\sum\limits_{i=1}^{m}\left(\dot{q}_{inc}^{\prime\prime}- \dot{q}_{cr}^{\prime\prime}\right)^{n}\Delta t_{i}\\ for\ all\ t_{i}\ when\ \dot{q}_{inc}^{\prime\prime}>\dot{q}_{cr}^{\prime\prime}\end{array}  \tag{3}\]  
In simple terms, this calculation tracks the margin between incident flux (\(\dot{q}_{inc}^{\prime\prime}\)) and critical heat flux (\(\dot{q}_{cr}^{\prime\prime}\)) over the time of exposure to heating. However, the intention of this experiment was not to determine if certain materials would ignite adjacent to the small-scale dwelling, given the magnitudes of heat flux will be much larger for full scale dwellings, and thus no direct FTP calculations are made here. Instead, the cumulative flux over the steady-state phase, shown in Figure 13, is a simpler metric that implicitly quantifies the magnitude and duration of heat flux, and thus the risk of ignition in general. Figure 11: Time to flashover of compartments with different horizontal opening areas. Figure 12: Heat flux at 30 cm from the door for cases: CL, C_004_Poly, and C_016_Poly_2. The key features of these curves are the overall magnitude and the gradient, which is simply the average steady state heat flux. The closed roof case clearly produces the highest cumulative flux, or to be specific, exposed the receiver to the greatest quantity of thermal energy. This is due to the combination of a steep gradient and long duration of the steady-state phase. However, from the FTP method it is clear that the magnitude by which the Critical Heat Flux (CHF) of a material is exceeded consistently over time is key for establishing time to ignition. Therefore, whilst the 0.01 and 0.04 m\({}^{2}\) corner opening cases expose the receiver to less cumulative energy over the full course of the steady-state phase, they may actually decrease the time to ignition of certain materials given they exceed the gradient--implicitly, the margin by which the CHF is exceeded--produced by the closed case.