# Development of Predictive Equations for Thermal Conductivity of Compost Bedding
## 3 Results and Discussion
### Thermal Properties of Composts in Different Particle Sizes  
The \(k\) of granular materials is known to be affected by the quality of contact between the particles. The particle contact quality depends on the material density, particle geometry,  
Figure 7: Response surface of moisture content (MC) and dynamic compaction (DC) on thermal conductivity (\(k\)) of bed compost materials at different depths: H1 (**a**), H2 (**b**), and H3 (**c**). and PS distribution. The effects of these factors on \(k\) are evaluated in this study using air-dried bedding materials and transient line heat source sensors. The behavior of directly observed \(k\) data in relation to PS distribution for bedding samples in compost barn plants using green sawdust, greenhouse sawdust, or a mixture of materials is shown in Figure 8. Measurements of \(k\) were not carried out on samples of thicker material whose particle size was larger than 25 mm due to the difficulty in inserting the sensor thermal probe into the sample. As can be observed in Figure 8, the values of \(k\) increase with the increase in the PS of the analyzed materials, which is the reverse of what was expected, as described by [PERSON] and [PERSON] [51] and [PERSON] et al. [15]. According to [PERSON] et al. [36], the porosity has a great influence on the thermal properties of the material due to its dependence on the PS, that is, as the PS increases, the thermal conductivity decreases, since more particles are required for the same porosity, meaning more thermal resistance between the particles. This behavior can probably be explained by the higher retention of moisture in larger particles since the compost bedding materials were air dried for the same period of time and because the materials had different PSs, so drying did not occur evenly, which probably influenced the values of the thermal properties. Considering the physical mechanism associated with conduction in general, the \(k\) of a solid is greater than that of a liquid and that of a liquid is greater than that of a gas [36]. Thus, the effect of PS on the \(k\) was more pronounced on larger PSs. However, a small increase in \(k\) for all materials was observed when PS was less than 4.75 mm. It was also observed that \(k\) increased dramatically (>85%) in materials with a PS greater than 8.00 mm (Figure 8). These changes can be explained considering the change in porosity filled with fine particles of material. For grain-like materials, for example, where the pores of the materials are filled with air, generally the \(k\) increases as the PS decreases. However, in materials with large particles, the \(k\) presents inverse results [16]. Statistical analysis of the data revealed that there was a significant difference between the values of \(k\) and the different PSs evaluated (Tukey test, \(p<0.05\)). Thus, in Figure 9, the main effect of PS on \(k\) is presented. In general, \(k\) values were higher in compost materials with a PS greater than 8.00 mm. This means that with a high PS (>8.0 mm), the impact of the MC on \(k\) became positive, in other words, depending on the MC, the \(k\) tends to increase when the PS increases. An explanation for this phenomenon may be that the increased PS created more space between the pores of the material, increasing the amount of water retention and raising the values of k. According to [PERSON] et al. [25], as with other thermal properties, the \(k\) of the material depends on the MC, but the porosity and \(k\) of the solid fraction are also strong determinants. Figure 8: Variation in thermal conductivity (W m\({}^{-1}\) K\({}^{-1}\)) with different compost particle sizes of compost materials: Green sawdust, Kiln-dried shavings or sawdust, and Mix. The average \(k\) of the bedding materials tested in the current study was 0.198 W m\({}^{-1}\) K\({}^{-1}\), varying between 0.088 and 0.608 W m\({}^{-1}\) K\({}^{-1}\) depending on particle size. Values of \(k\) found in this study agree with some previous studies. Research performed by [PERSON] et al.