## 3 Results
### Temperature Profiles of Average Collision Cross Sections  
In this part, the dependence of the average electron-neutral collision cross section (\(\overline{Q}\)) on the electron temperature (\(T_{e}\)) for each of the six covered gaseous species is visualized for the range of \(T_{e}\) from 2000 K to 3000 K. For each species, a figure is provided where four curves representing the obtained \(\overline{Q}\) profiles using the four methods discussed earlier are displayed. This not only helps contrast the predictions using the different methods but also helps reveal the general trend of \(\overline{Q}\) as \(T_{e}\) increases from the lower temperature limit of 2000 K (typical of air-fuel combustion) to the upper temperature limit of 3000 K (typical of oxy-fuel combustion). For the third method (integration-based weighted average), the published discrete values are plotted as scattered markers, while a dotted straight line is added near them that represents the regression model derived here for these data points. Figure 7 is used to contrast the four predicted curves of the average electron-neutral collision cross sections for carbon monoxide (CO). All four methods agree about the increase in \(\overline{Q}_{\rm CO}\) as \(T_{e}\) increases. Based on the arithmetic mean profile (not shown); it passes through the points representing the arithmetic mean, also called the simple average, of the four \(\overline{Q}\) values using the four methods at each temperature, the mean rate of change in \(\overline{Q}_{\rm CO}\) is 0.0019515 A\({}^{2}\)/K. This is the average change in \(\overline{Q}_{\rm CO}\) as \(T_{e}\) increases by 1 K. Methods 1 (\(\overline{u}_{e}=1.5\bar{T}_{e}\)), 2 (linear), and 4 (quadratic) have similar values of \(\overline{Q}_{\rm CO}\), which together deviate remarkably from the results of method 3 (integration). Method 3 gives a larger \(\overline{Q}_{\rm CO}\) for the entire examined range of \(T_{e}\). Although method 1 involves the use of a nonlinear function for \(\overline{Q}_{\rm CO}(T_{e})\), the nonlinearity in the temperature range of interest here is too weak to be noticeable. Method 4 proposes a linear (not a quadratic) modeling function for \(\overline{Q}_{\rm CO}(T_{e})\); thus, the displayed perfectly straight line obtained via this method is expected. Figure 8 is used to contrast the four predicted curves of the average electron-neutral collision cross sections for carbon dioxide (CO2). All four methods agree about the decrease in \(\overline{Q}_{\rm CO2}\) as \(T_{e}\) increases (opposite behavior to \(\overline{Q}_{\rm CO}\)). Based on the arithmetic mean profile of the four individual profiles, the mean rate of change in \(\overline{Q}_{\rm CO2}\) is \(-0.0080654\) A\({}^{2}\)/K. The predictions of methods 1 (\(\overline{u}_{e}=1.5\bar{T}_{e}\)) and 3 (integration) have similar values of \(\overline{Q}_{\rm CO2}\), which together are noticeably smaller than those predicted using methods 2 (linear) and 4 (quadratic). The ratio of the largest \(\overline{Q}_{\rm CO2}\), obtained using method 4, to the smallest \(\overline{Q}_{\rm CO2}\), obtained using method 3, is 2.4385 at 2000 K, and 2.4280 at 3000 K. The values of \(\overline{Q}_{\rm CO2}\) are nearly twice those of \(\overline{Q}_{\rm CO}\); thus, carbon dioxide has a stronger interaction with electrons  
Figure 6: Profiles of the monoenergetic electron–neutral collision cross section and the corresponding weight function for molecular oxygen (O\({}_{2}\)). The \((x-u_{e})\) mapping and the \((x-v_{e})\) mapping correspond to an absolute electron temperature of 3000 K.  
than carbon monoxide, causing less electron mobility and more suppression of the plasma electric conductivity. Despite the nonlinear expression for \(\overline{Q}_{\text{CO2}}(T_{e})\) in methods 1 and 4, the actual predictions in the temperature range of interest here resemble a linear decline when the electron temperature increases, and thus, the nonlinearity is not strongly manifested.