## 3 Results
### Model Validation  
As explained in the previous paragraphs, high temperatures can lead to thermal damage to skin tissue, causing pain due to thermal expansion. For this reason, it is necessary to control the amount of heat build-up and the thermal limits of the application spot. It mainly depends on the exposure time, the intensity of the laser radiation, and the radius of the laser beam. Figure 2 shows the results of the circumferential and axial distributions of the apparent temperatures in the layers of the skin after irradiation of the region using two wavelengths (532 and 800 nm) and two intensity values (1 and 2 W/mm\({}^{2}\)). On the one hand, it is obvious that an increase in the intensity of the laser radiation causes an increase in temperatures of no less than 20% in both distributions. On the other hand, the temperatures in the diagonal direction seem more stable, with a decrease of no more than 4% between the beginning and the end of the studied section. On the other hand, it is clear from the distribution of temperatures in the axial direction that the laser radiation was more focused on the irradiated focus and that the heat dissipation towards the depth occurs more clearly, as a 30% difference is observed between the center of the application area and the end of the section. Figure 3 shows the distribution of heat and equivalent stresses at the mentioned wavelengths and intensities (1 and 2 W/mm\({}^{2}\)) and an exposure time of 30 s. The maximum temperature readings on the skin's exterior are observed when utilizing a 532 nm \begin{table}
\begin{tabular}{l c c} \hline \hline
**Variables** & **Lower Level (\(-\)1)** & **Upper Level (\(+\)1)** \\ \hline I = Intensity (W/mm\({}^{2}\)) & 1 & 5 \\ S = Size (mm) & 0.5 & 3 \\ T = Time (s) & 30 & 600 \\ W = Wavelength (nm) & 532 & 800 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The lower and upper levels of the studied variables. Figure 2: The circumferential and axial thermal diffusion caused by the laser radiation at the laser radiation application center (r = 0, z = 0). wavelength due to the skin's greater absorption coefficient at this wavelength compared to 800 nm. Upon exposure to laser radiation, the absorbed energy is transformed into heat energy, leading to a rise in temperature. On the other hand, when the exposure time is increased to 600 s, a transfer of the maximum temperature is noticed, corresponding to the wavelength of 800 nanometers, to deeper levels within the skin. This is attributed to the conductive role of the skin tissue, which allows the absorbed laser energy to spread to deeper layers (Figure 4). The temperature changes with time are studied to accurately track the effect of exposure time. Figure 5 shows the temperature change with time, which allows the evaluation of exposure time. It is noticed that the temperature increases exponentially with time to reach a steady state after approximately 300 s. On the other hand, the increase in intensity by 1 W/nm\({}^{2}\) caused the temperature to increase by 27%. Figure 6 shows the effects of laser beam radius and laser intensity, where a three-dimensional representation of the equivalent temperatures and stresses is shown at 600 s exposure time and 532 nm wavelength. Increasing beam radius seems to cause a slight increase in maximum temperature values (1%) while the positions of maximum values were varied. On the other hand, it seems clear that increasing the intensity of the laser beam leads to a noticeable increase in the site of the maximum temperature, which is located on the upper layer of the skin.