# Development of Predictive Equations for Thermal Conductivity of Compost Bedding
## 3 Results and Discussion  
### Thermal Properties of Composts in Different Moisture Contents and Static Compaction Degrees  
The values of \(k\), recorded during the study, are presented graphically as a function of each percentage (30, 45, and 60%) of the MC evaluated and as a function of the different SCs (0.0, 0.1, 0.2, 0.3, and 0.4 MPa) of the bedding materials in Figures 4a and 4b, respectively. These results indicate that the values of \(k\) increased as MC and SC increased, likely due to a reduction in the volumetric fraction of air within the bedding material (Stein  
The analysis of variance showed that for the three depths, there was a significant interaction between SC and MC, regarding its effect on \(k\) (\(p\) < 0.001). Thus, it is verified that the levels of SC and MC are not independent to explain the values of \(k\). Then, after descriptive analysis of the data, through the dispersion graph, it was found that the behavior of the variable MC (30%, 45%, and 60%) is of a linear line, while the behavior of the variable SC (0.0, 0.1, 0.2, 0.3, and 0.4 MPa) is a quadratic model. The values found for \(k\), in the different compost bedding materials, in relation to the levels of MC (30, 45, and 60%) and SC (0.0, 0.1, 0.2, 0.3, and 0.4 MPa) tested for each one of the three depths evaluated (H1, H2, and H3) ranged from 0.0141 to 0.768 W m\({}^{-1}\) K\({}^{-1}\). The regression analysis for compost materials showed a polynomial relationship between the variable of \(k\) and the dependent variables MC and SC for each depth evaluated in this way:  
\[k_{\text{H1}}=0.0022\cdot\text{MC}+0.1838\cdot\text{SC}\ -1.1601\cdot\text{SC}^{2}+0.0154 \cdot\text{MC}\cdot\text{SC},\,R^{2}=0.92 \tag{2}\]  
\[k_{\text{H2}}=0.0028\cdot\text{MC}+0.6711\cdot\text{SC}^{2}+0.0140\cdot\text{ MC}\cdot\text{SC},\,R^{2}=0.92 \tag{3}\]  
\[k_{\text{H3}}=0.0027\cdot\text{MC}+0.4251\cdot\text{SC}^{2}+0.0111\cdot\text{ MC}\cdot\text{SC},\,R^{2}=0.91 \tag{4}\]  
A significant effect was observed when observing the MC and SC separately and also when observing the significant influence of the MC \(\times\) SC interaction, since methodologically it is already known that the \(k\) value of water is greater than that of air (0.06 W m\({}^{-1}\) K\({}^{-1}\) > 0.026 W m\({}^{-1}\) K\({}^{-1}\); [PERSON] et al. [22]). The thermal conductivity of air is about 25 times less than that of water; hence, if air is replaced by water in the pores of a material (i.e., if the water content increases), the bulk thermal conductivity increases [38]. Therefore, increasing the moisture content, the pores of the bed material were filled with water, which increased the values of \(k\). In addition, \(k\) also increased with the increased degree of SC due to a reduction in empty space. Generally, the thermal properties of composite materials show specific tendencies related to water content, apparent density, and particle size [15, 35, 39, 40]. If water content increases, the volume fraction of air decreases, and the volume fraction of solid increases. Consequently, the bulk thermal conductivity increases [38]. In other words, if SC and MC increase, solid particles move closer to one another, and the thermal contact resistance between bed particles decreases, thus raising the \(k\) values. The highest values of \(k\) were observed at depth H1 (0.153 \(\pm\) 0.047 W m\({}^{-1}\) K\({}^{-1}\)), followed by H2 (0.142 \(\pm\) 0.045 W m\({}^{-1}\) K\({}^{-1}\)) and H3 (0.136 \(\pm\) 0.041 W m\({}^{-1}\) K\({}^{-1}\)), respectively. Values of \(k\) in several other studies have varied depending on the type of material, com  
Figure 4: Variation in thermal conductivity (\(k\)) at different degrees of moisture content (**a**) and (**b**) static compaction degree of compost bedding materials. Values followed by different letters are significantly different (\(p\) < 0.05; Tukey). posting time, moisture content, and physical and chemical characteristics, among other factors.