## 3 Results and Discussion
### Temperature and Velocity Simulations  
Temperature and air flow velocity distributions have been analyzed during normal breathing conditions while wearing the six different masks. For this study, a maximum breathing flow rate of 0.5 L/s was considered the initial inlet condition based on previous studies [43; 44]. The breathing cycle is described by a time-dependent, unsteady flow rate profile. The governing equation for unsteady and incompressible turbulent flow was used (the RNG k-\(\epsilon\) turbulence model) to simulate the breathing cycle, as used by other scientists [43; 44; 45; 46; 47; 48]. The no-slip boundary condition was set at the mouth, nose, and forehead of the face mask wearer. The external/ambient temperature was set to 23 \({}^{\circ}\)C. The initial temperature inside the mask was set at 31.2 \({}^{\circ}\)C based on the average data obtained from the 12 volunteers (Table 3). The pore size of the masks was measured and used based on our previous study [36] to simulate the air flow resistance. The material properties were selected from the engineering database available on Solidworks. The velocity inlet follows the velocity profile shown in Figure 7, with a direction normal to the boundary and a turbulent intensity of 1%. The turbulent kinetic energy was set to \(10^{-5}\) m\({}^{2}\)/s\({}^{2}\), and the turbulent dissipation rate was set to \(10^{-6}\) m\({}^{2}\)/s\({}^{3}\) in order to conduct the equation within the software and simulate the air flow through the mask to demonstrate the air flow and temperature distributions [49; 50]. A duration of five respiratory cycles was used to simulate with a time step of 0.1 s. The largest velocity during exhalation and inhalation was observed at 2.4 m/s and 1.35 m/s, respectively. The velocities outside the masks were relatively small compared to the velocities at the forehead and nose. The flow velocities became larger during exhalation and inhalation under the nostrils, which can be due to the small distances between the nostril and the upper part and between the upper and lower parts of the mask. The air flow velocity distribution results inside the face mask wearer during the inhalation peak (t\({}_{2}\) = 3 s) and the exhalation peak (t\({}_{1}\) = 1 s) are shown in Figure 7. Overall, air flow velocities were higher inside the mask compared to outside for both inhalation and exhalation. During the inhalation phase (Figure 7a,c,e,g,i,k), all six face masks showed a low air velocity distribution (\(\sim\)0.8-1.4 m/s) inside the mask (within the nose and mouth). The _Silk_ and _Antiviral_ masks had a higher air flow velocity (2.3 m/s) around the mouth. However, during the exhalation phase, the air flow velocity was distributed evenly inside the _FFP3_, _FFP2_, and _Surgical_ masks (Figure 7b,d,f)), whereas the air flow velocity was higher for the _silk_ (Figure 7j) and antiviral (Figure 7l) face masks. Moreover, it can be observed that during the exhalation phase, more air passes through the _Silk_ and the _Antiviral_ masks (blue areas in Figure 7j,l)). These results correlate with the high pore size and low filtration efficiencies measured for the _Silk_ and _Antiviral_ face masks [33]. Figure 8 shows the simulation results for the temperature distribution inside the face mask while wearing it at the inhalation peak (t2 = 3 s) and the exhalation peak (t1 = 1 s) during the breathing cycle. As the temperature of the exhaled air is high, this can increase the temperature inside the mask, whereas during the inhalation phase, the temperature inside the mask remains almost the same. However, different face masks exhibit different behaviors. For instance, the simulations show low temperature fluctuations for the _FFP3_ (Figure 8a,b) and _FFP2_ (Figure 8c,d) during the inhalation (29 \({}^{\circ}\)C) and exhalation (32 \({}^{\circ}\)C) peaks. However, the temperature near the nose and the mouth regions inside the mask increases (red area, 31-33 \({}^{\circ}\)C).