# Numerical Analysis of a Moderate Fire inside a Segment of a Subway Station
## 3 Transient Simulation of Non-Stationary Heat Conduction
### Piecewise Uniform Prescription of Three Specific Temperature Histories  
The results of the preceding section suggested that the right column was exposed to higher surface temperatures compared to the near-surface-measurements at the top slab and the right wall. In order to improve the agreement between simulation results and experimental measurements, the inner surface of the analyzed structure was subdivided into three sub-regions. In each of them, a specific temperature history was prescribed at the inner surface in a spatially-uniform fashion. This was done such that the symmetry of the simulated heat conduction problem was preserved. 1. The top and bottom slabs were subjected to the temperature history, measured at the midspan of the left cell of the top slab, at a depth of 2 mm from the heated surface. 2. Both walls were subjected to the temperature history, measured at the center of the right wall, at a depth of 2 mm from the heated surface. 3. Both columns were subjected to the temperature history imposed on the top and bottom slabs, amplified by a fitting-factor. This was done, noting that the temperature was not measured near the surface of the columns and that, because of their position and their larger exposed-surface-to-volume ratio, the columns were expected to heat up faster than the slabs and the walls. This was confirmed by the results from the previous section. Furthermore, since the same source that heated the slabs also heated the columns, similar qualitative temperature evolutions were assumed to occur at both positions. Setting the amplifying factor equal to 3.2 provided satisfactory agreement between the simulated and the measured temperature evolutions. The three different prescribed temperature histories are shown as blue dotted graphs, labeled \"BC\", in Figure 14.  
The simulated and measured temperatures agree well at the positions where near-surface-measurements are available, provided that the temperature history measured at a depth of 2 mm is prescribed as the boundary condition at the surface; see Figure 14a,d. At these positions, the maximum difference between the simulated and the measured temperatures amounts to 3.6 \({}^{\circ}\)C and 1.4 \({}^{\circ}\)C, respectively. This underlines the fact that the heat transfer was predominantly one-dimensional at these positions and took place in the direction orthogonal to the heated surface. The simulated and measured temperatures also agree well at the middle cell of the bottom slab. Here, the maximum difference between the simulated and the measured temperatures is 2.5 \({}^{\circ}\)C. This suggests that the two surfaces at the midspan positions of the right cell of the top slab and of the middle cell of the bottom slab were exposed to very similar temperature histories; see Figure 14a,e. The updated simulation (Figure 15) suggests that the temperature increase at the surface of the right column was significantly larger than the available near-surface-measurements at the top slab and  
Figure 13: Temperature distribution obtained by prescribing a uniform surface temperature history, 30 min after the start of the thermal loading: detail showing the central cross-section of the right column. the right wall. In the updated simulation, the maximum surface temperature of the columns amounts to 284 \({}^{\circ}\)C, and the difference between the simulated and the measured temperatures amounts to 3.1 \({}^{\circ}\)C. In this context, it is emphasized that the updated simulation was simply based on constant thermal properties of concrete (Table 4). As for the top slab, at the midspan positions both in the middle and the left cell, also the updated simulation does not deliver satisfactory results; see Figure 14b,c. This underlines the fact that the thermal loading of the top slab was characterized by significant gradients of the surface temperature across the three cells.