## 4 Results and Discussion
### Thermal Conductivity with Change in Porosity and Fine Particle Contents  
Figure 6 shows the variation in thermal conductivity of the baseline and mixed specimens with changes in porosity. The variation in initial porosities results from the particle shape, grain size distribution, and chemical composition of the surfaces, even under the same compaction energy. In general, the thermal conductivity increases with a decrease in porosity for all samples, which is consistent with previously published data [14; 16; 29]. When the initial porosity is high, the coordination number has a greater influence on the decrease in porosity than the contact area [30]. However, at a low initial porosity, the change in contact area is more significant, affecting the thermal conductivity more [30]. This implies that the increased effective stress results in a larger coordination number and contact area, which causes a decrease in porosity and an increase in thermal conductivity. Figure 5: Thermal conductivity with respect to one-dimensional load. Figure 6: \(Cont\). For the A-B mixed specimens in Figure 5(a), the thermal conductivity of specimens containing 10% to 100% of fine particles B is higher than that of the 100% sample A. However, the effect of the fine particle contents on thermal conductivity of the 20% to 80% B specimens does not seem straightforward. The fine particles B may fill the pore body of the baseline A for fine contents of up to 10%. But for fine contents of 20% or more, the fine particles B may replace particles of the baseline A instead of filling the voids (because the size of fine particles B (\(D_{50}\) = 0.33 mm) is not much smaller than the size of the pore body of specimen A). Note that the expected pore body size of sample A is 0.348 mm. On the other hand, the A-C mixed specimens show a clear trend, and the thermal conductivity of the mixed specimens increases with an increase in fine particles C. The relatively smaller fine particles C (\(D_{50}\) = 0.16 mm, as shown in Figure 1) seem to fill better the pore body of baseline A. The decrease in pores (by adding fine particles C) causes the thermal conductivity to rise. An attempt was made to relate the thermal conductivity of a mixed specimen to the properties representing the size and packing of the particles. Various properties such as porosity, coefficient of uniformity, and coefficient of curvature were investigated, but porosity showed better correlation than the other properties. The results of the trials are not presented herein. Figure 7 shows contours of thermal conductivity as a function of porosity and a proportion of B or C fine particles. The label of the contour indicates the thermal conductivity of the mixed specimens. From the plots, the effects of the porosity and proportion of fine particles can individually be investigated. The results indicate the following. First, the thermal conductivity tends to increase under the lower porosity and higher proportion of fine granular materials (i.e., fine particles B or C), and vice versa. Second, compared to the A-B mixed specimens, the thermal conductivity of the A-C mixed specimens show a clearer trend of increasing thermal conductivity, with increasing proportion of fine particles C (Figure 6(b)). The sizes of the fine particles C are much smaller than the theoretical pore body size of sample A (\(D_{50}\) of sample C is 0.16 mm, and the expected pore body size of sample A is equal to 0.348 mm, based on Figure 3(a)). The fine particles C (which are smaller than particles B) may effectively fill the pore space in sample A, elevating the coordination. The heating energy can transfer better with the heightened coordination number; the increase in fine particles C results in larger thermal conductivity. Figure 6: Thermal conductivity with respect to porosity. However, the size of fine particles B (\(D_{50}\) = 0.33 mm) is similar to the theoretical estimate of the size of the pore body of sample A.