# Development of Predictive Equations for Thermal Conductivity of Compost Bedding
## 3 Results and Discussion
### Prediction of Bed Compost Thermal Conductivity  
Figure 12 shows a comparison of the predicted \(k\) from Equations (2)-(4) and the experimental data when applying SC for each depth evaluated (H1, H2, and H3). Figure 11: Thermal conductivity (\(k\), \(W\) m\({}^{-1}\) K\({}^{-1}\)) as a function of dynamic compaction (DC) and depth (H1, H2, and H3) at different moisture contents: (**a**) 30%, (**b**) 45%, (**c**) 60%, and (**d**) interaction between average values of DC and MC at different depths. Values followed by different letters are significantly different (\(p\) < 0.05; Tukey). Through a preliminary statistical analysis, it was found that there is no statistically significant difference between the estimated thermal conductivity (\(k_{\rm est}\)) and (\(k_{\rm mea}\)) measured (\(t\) test, \(p>0.05\)). The adjusted expressions are statistically significant (F test, \(p<0.0001\)), providing mean errors of 0.065, 0.077, and 0.077, respectively (Figure 12). When comparing the \(k\) of bed compost materials applying SC values \(k_{\rm est}\) with the \(k_{\rm mea}\) values by Equations (2)-(4), the proposed models were found to be precise in predicting the \(k\) (Figure 12). The adjustment equations between the models and the data for each depth (H1, H2, and H3) were:  
\[k_{\rm est\,H1} =0.9444\cdot k_{\rm mea\,H1}+0.0199,\,{\rm R}^{2}=0.87 \tag{8}\] \[k_{\rm est\,H2} =0.9604\cdot k_{\rm mea\,H2}+0.0072,\,{\rm R}^{2}=0.89\] (9) \[k_{\rm est\,H3} =0.9936\cdot k_{\rm mea\,H2}+0.0032,\,{\rm R}^{2}=0.94 \tag{10}\]  
According to [PERSON] et al. [55], the coefficient of determination (R\({}^{2}\)) is an indicator of the goodness-of-fit between the model and the data. Comparing R\({}^{2}\) values of the three test models showed that the third model (Figure 12c) outperformed the others (0.879, 0.895, and 0.940, respectively). These results indicate that the \(k\) values predicted by the models (Equations (2)-(4)) were similar to values experimentally observed (Equations (8)-(10)) [56]. Figure 13 shows a comparison of the predicted thermal conductivities (\(k_{\rm est}\), W m\({}^{-1}\) K\({}^{-1}\)) from Equations (5)-(7) and the experimental data (\(k_{\rm mea}\), W m\({}^{-1}\) K\({}^{-1}\)) when applying dynamic pressure (DC) for each depth evaluated (H1, H2, and H3). The adjustment equations between the models and the data for each depth (H1, H2, and H3) were:  
\[k_{\rm est\,H1} =0.8715\cdot k_{\rm mea\,H1}+0.0101,\,{\rm R}^{2}=0.79 \tag{11}\] \[k_{\rm est\,H2} =0.9684\cdot k_{\rm mea\,H2}+0.0013,\,{\rm R}^{2}=0.83\] (12) \[k_{\rm est\,H3} =0.9475\cdot k_{\rm mea\,H3}+0.0072,\,{\rm R}^{2}=0.86 \tag{13}\]  
Based on Figure 13a-c, it is possible to observe that the estimated thermal conductivity of bed compost materials when applying DC for each depth evaluated in comparison with the observed values showed good results too. The adjusted expressions are statistically significant (F test, \(p<0.0001\)), showing an R\({}^{2}\) of 0.794, 0.831, and 0.867, respectively, where the linear and angular coefficients are significant (\(t\) test, \(p>0.05\)). The average and standard deviations of the simulated and observed \(k\) at the three depths tested were 0.210 \(\pm\) 0.08, 0.214 \(\pm\) 0.09, and 0.209 \(\pm\) 0.09, respectively, resulting in an average absolute deviation of 0.072, 0.078, and 0.074, respectively, and an average error of 0.037, 0.037, and 0.036, respectively. The model to predict the \(k\) for H3 showed better results in comparison with H1 and H2. Figure 12: Estimated thermal conductivity (\(k_{\rm est}\), W m\({}^{-1}\) K\({}^{-1}\)) of bed compost materials versus measured (\(k_{\rm mea}\), W m\({}^{-1}\) K\({}^{-1}\)) values when applying static compaction (SC) for each depth evaluated: (**a**) H1, (**b**) H2, and (**c**) H3. In spite of the good R\({}^{2}\) values presented by Figure 13, these results indicate that the models to predict \(k\) values applying SC (Figure 12) showed better adjustment with better R\({}^{2}\) values than the models to predict \(k\) applying DC (Figure 13).