## 2 Materials and Methods  
### The Object under Study  
The article considers experimental and theoretical works aimed at determining the distribution of heat emitted by an obstacle lighting lamp. The object under study has two heat sources, one of which is LEDs emitting light, and the other consists of stabilizers and other elements of the lamp power supply system. For the purpose of experimental tasks, the lamp was installed in the front part of a rectangular tunnel made of chipboard, with dimensions \(\mathrm{W}\times\mathrm{H}\times\mathrm{L}=(1\times 2\times 8.8)\) m. For the measurement of heat emitted by the lamp, a thermal imaging camera type VIGOcam v5 from VIGO System S.A. was applied. This device is equipped with a bolometric matrix of a resolution \(384\times 288\) px, where pixel size equals \(25\times 25\) m; the registered spectral range is 8-14 m. The applied lens has a diameter of 35 mm with a spatial resolution of \(0.7\times 10^{-3}\) rad. The emissivity was corrected to value relevant for red paint and equals 0.96. The camera was located in the tunnel at 1.75 m distance from the lamp at its hight, using a tripod rack. The measurement conditions were controlled in such a manner that the tunnel was closed, no forced airflow was present, and the ambient temperature was stable at 28 \({}^{\circ}\)C.  
For the purpose of theoretical analysis, a simplified model of the lamp and the tunnel was implemented. The CAD (computer-aided design) drawing of the computational domain depicting the rectangular tunnel with the lamp and an enlarged view of the lamps is depicted in Figure 1, where also the coarse location of the thermal imaging camera is marked. The lamp has a cylindrical shape of a maximal radius equal to 54.47 mm. The simplified numerical model of the lamp consists of two heat sinks made of aluminum covered with paint (see Figure 2a) and a transparent, light-transmittable cylinder made of acrylic plastic (plexiglass) of 5 mm width (see Figure 2b). The LEDs emitting light are installed on a printed circuit board at the surface of the bottom heat sink, while the stabilizers and other elements of the power supply system are mounted inside the top heat sink. The theoretical model assumes that the heat produced by the LEDs and stabilizers is evenly distributed over the area directly adjacent to the heat sink; therefore, we define a surface heat source for the LEDs and stabilizer, as depicted in Figure 2c. For the outer edge of the computational domain, we assume a constant ambient temperature, while the tunnel floor is assumed to be thermally insulated (see Figure 2d). Figure 1: A CAD drawing of the computational domain depicting the rectangular tunnel with the lamp and the lamps enlarged view (to the right). Figure 2: _Cont._  
In the first step, measurements of the heat emitted by the lamp in the tunnel were registered from the moment the lamp was switched on until the temperature was stabilized, which under laboratory conditions lasted about 7 h. Based on the gathered results, the numerical model was verified in order to adjust all the model parameters, which are described in the next section. After the experimental verification process, theoretical analyses of heat emission under various meteorological conditions were carried out. Simulations in both the transient and stationary state were performed, while the value of ambient temperature and airflow velocity were changed; then, the influence of these parameters on the temperature distribution on the surface of the lamp was determined. For theoretical calculations, we applied a PC computer featuring an Intel(R) Xeon(R) CPU E5-1650 v4 @ 3.60 GHz with 12 cores. For the computational problem, which was connected with solving large linear equation systems resulting from discretized partial differential equations, as described in Section 2.3, we applied an efficient Geometric Multigrid Solver [13], which applies hierarchical algorithms.