## 3 Measurement and Analysis Results
The values marked as black stars depict values gathered from thermal images and refer to the highest recorded temperature on the bottom heat sink. The values marked as blue crosses refer to temperatures calculated in the point P2 in the numerical model, which is located on the bottom heat sink. The values were achieved by ambient temperature \(T_{\text{amb}}\) = 28 \({}^{\circ}\)C and zero airflows. Analyzing the data presented in Figure 6, it is obvious that the numerical model of the lamp heats up much faster and that the steady state occurs after only three hours of the simulation time, while the actual model reaches the temperature saturation only after seven hours. This is the result of many simplifications adopted in the computational model, and is related to the fact that not all elements of the lamp were modeled, but only the key parts in terms of the geometry of the top and bottom heat sinks. However, despite this difference in the transient state, the temperature in the steady state is convergent in the model, as shown exemplary for the point P2. The experimental data were interpolated using rational function \(f\)(t), which is given by Equation (13), obtaining suitable results and achieving the following fitting parameters: sum squared error (SSE) = 2.6273, root mean square error (RMSE) = 0.1824. The red line in Figure 6 depicts the approximation result. \[f(t)=\frac{p_{1}t^{2}+p_{2}t+p_{3}}{t^{3}+q_{1}t^{2}+q_{2}t+q_{3}} \tag{13}\]  
Figure 5: Temperature values measured (in blue) and calculated using the numerical model (in red) along the edge of the lamp on its surface established after 8 h of operation. Figure 6: Results of measurements (in red) and simulation using the numerical model (in blue) gathered in the transient state during the heating process. where \(t\) is time normalized by mean = 7.374e + 05 and std = 0.1264, and the coefficients (with 95% confidence bounds) are as follows: \(p_{1}\) = 512.4 (-127.8, 1153); \(p_{2}\) = 4350 (2651, 6050); \(p_{1}\) = 7557 (6397, 8717); \(q_{1}\) = 9.626 (1.703, 17.55); \(q_{2}\) = 56.96 (33.8, 80.11); \(q_{3}\) = 101.6 (85.88, 117.2). On the basis of the results presented in Figures 5 and 6, it was stated that the calculation model is positively verified, which allows for its application for further theoretical analyses. Therefore, in the next step, parametrical analysis was performed, in which the ambient temperature and the airflow velocity were changed and their influence on the temperature distributions was investigated. In Figure 7, an example of steady-state simulation results depicting temperature distribution at the lamp surface by \(T_{\text{amb}}\) = 44 \({}^{\circ}\)C and wind speed equal to \(v\) = 0.3 m/s and \(v\) = 3 m/s are depicted. From Figure 7, it may be observed that the dependence of the ambient temperature is not linear, and the influence of air cooling is different for various ambient temperatures. The cooling effect is lower at higher ambient temperatures. The temperature on the lamp surface is distributed according to the direction of the air movement. The values depend on the velocity and the ambient temperature. In Figure 8, the results of theoretical analyses for various values of T\({}_{\text{amb}}\) and \(v\) in a wide range of changes that concern the steady-state temperature values in point P2 are presented. Please note that the scale is logarithmic for wind speed. In Figure 9, the results of analyses for various wind speed changes concerning the steady-state temperature values calculated along the lamp edge by \(T_{\text{amb}}\) = 24 \({}^{\circ}\)C are presented. The influence of cooling is the lowest in the bottom heat sink and the highest in the transparent plastic part. At the highest cooling values, the differences become blurred, and so at \(v\) = 10 m/s, the temperature of the lamp surface drops to the ambient values.