## 2 Methods  
### Experimental Study  
As part of this study, an aerodynamic test bench was designed and built, which is a physical model of an inclined working (bremsberg or slope) connected to ventilation and haulage drifts (see Figure 1b). Figure 1a schematically represents the system of mine workings in the case of mining a flat mineral deposit characterized by an angle of incidence \(\alpha\). The slope and bremsberg, which serve as prototypes of the laboratory model of a mine working, are marked with fire indicators. Depending on the mining pattern, both upward and downward air flows may occur in these mine workings. Figure 1: Schematic diagrams of the mine (**a**) and aerodynamic test bench (**b**). The test bench consists of a steel channel with a rectangular cross-section measuring 300 mm by 500 mm along almost its entire length, representing a scaled-down model of a mine working. In contrast, the cross-sectional area of mine workings in modern mines is usually significantly larger. A constant cross-section is maintained everywhere except for a small area near the heating source (in the central area of the bench) and near the fan (in the upper part of the bench), where the cross-section transitions from a circular profile at the fan outlet to a rectangular profile of 300 mm by 500 mm. Photos of the assembled test bench are shown in Figure 2.  
Figure 2: Photographs of the test bench: general view of the bench tilted at the maximum angle (**a**), local expansion of the flow area near the heater (**b**), general view of the bench in a horizontal position (**c**), and the area near the opening no. 1 (**d**). Air movement in the channel is ensured by a duct fan, which allows for the regulation of performance. In this case, the average air flow velocity in the channel can vary from 0.5 to 3 m/s. The fan power is 187 W. The head-flow characteristic of the fan is shown in Figure 3.  
The bench also provides the ability to change the angle of inclination of the channel in the range from \(-15^{\circ}\) to \(15^{\circ}\), which approximately corresponds to the possible range of inclination angles of real mine workings, with some margin. This paper, however, describes the results of experimental measurements and comparative analysis with model data only at angles of \(0^{\circ}\) and \(-13^{\circ}\). A heating source was installed in the central part of the channel. It is a ducted electric heater with a maximum HRR of 22 kW. The HRR from the heating source allows for stepwise regulation with a minimum step of 2.4 kW. At the location where the heating source is installed, the cross-section of the channel changes locally due to the design features of the heaters. The release of harmful impurities in the experimental bench has not yet been considered. Thus, the subject of the study was only the thermal effect of the fire. The bench has two ventilation openings, one located in the upper part and the other in the lower part. The openings are equipped with valves that allow for manual adjustment. For the purposes of the study described in this paper, the valve of opening No. 2 was hermetically sealed, while the valve of opening No. 1 was examined in both the closed and open positions. In addition to the openings, the channel had two more aerodynamic connections with the external atmosphere: the inlet section in its upper part and the outlet section in its lower part. The outlet section of the bench is also equipped with a valve, which can be in an open or partially closed state. The range of air flow velocities and HRR values at the bench were determined to comply with the conditions of similarity of heat and mass transfer processes between the test bench and real conditions in mines. The scaling of air velocity and heat flow was carried out using the Froude scaling method described in [9]:  
\[\frac{V_{b}}{V_{m}}=\left(\frac{L_{b}}{L_{m}}\right)^{1/2} \tag{2}\]  
\[\frac{W_{b}}{W_{m}}=\left(\frac{L_{b}}{L_{m}}\right)^{5/2} \tag{3}\]  
Figure 3: The head-flow characteristic of the fan.