### Density dependence in *k*-values

Figure 3 shows the relationships between mat density and *k*-values of the two types of mats. The data are plotted separately according to heat flow direction. For CF mats, a statistically significant correlation (*P* < 0.01) was found for both heat flow directions, and the following regression equations were obtained for upward and downward heat flux, respectively.

$$ y = { 1}. 8 1 \times 10^{ - 4} x + \, 0.0 2 60\;(R^{ 2} = \, 0. 4 8 6) $$

(5)

$$ y = { 1}. 6 4 \times 10^{ - 4} x + \, 0.0 2 6 3\;\; (R^{ 2} = \, 0. 5 3 7) $$

(6)

Statistical analysis of the difference between two regression equations showed that there was no significant difference between Eqs. (5) and (6). This indicates that the *k*-value of CF mats is not affected by heat flow direction, according to the best possible measurement accuracy in this experiment. In contrast, WS mats showed poor correlation between density and *k*-value. There was a statistically significant correlation (*P* < 0.05) in the downward heat flow (Eq. 7), but not in the upward heat flow.

$$ y = { 5}. 3 5 \times 10^{ - 5} x + \, 0.0 4 2 { }\; (R^{ 2} = \, 0. 1 1 8) $$

(7)

A detailed examination of the significance of the differences between the average *k*-values for the two heat flow directions was conducted for two ranges of mat density: the lower half (60–80 kg/m^{3}) and the upper half (80–100 kg/m^{3}). The results revealed that there was no significant difference in the lower half of mat density, but there was a small difference of 2 % (upward < downward) in the upper half.

Based on these results, mat density dependence in *k*-values can be discussed without considering heat flow directions. Equations (8) and (9) show the regression equations obtained when ignoring heat flow direction for CF mats and WS mats, respectively.

$$ y = { 1}. 7 3 \times 10^{ - 4} x + \, 0.0 2 6 2\;\;(R^{ 2} = \, 0. 50 2) $$

(8)

$$ y = { 4}. 5 5 \times 10^{ - 5} x + \, 0.0 4 2 8\; (R^{ 2} = \, 0.0 9 5) $$

(9)

From Eq. (8), the *k*-value of the CF mat was found to increase by approximately 5 % with every 10 kg/m^{3} increase in mat density. This suggests that the number of heat bridges (which facilitate heat transfer by conduction) formed by fibers increase with increasing mat density. Closer examination of Fig. 3, however, reveals for densities of more than 50 kg/m^{3}, the *k*-value tended to level off. Further examination of this issue will require more experimental data with a greater range of mat densities.

Although a significant correlation (*P* < 0.01) was also found for the WS mats, the coefficient of correlation was very low. The density dependence of the *k*-values of WS mats is therefore much lower than that of CF mats; in fact the slope of the regression equation is approximately four times greater for CF mats. This can be explained by the size distribution of coarse pores in WS mats, since lower density mats tend to have larger coarse pores in which greater convective heat transfer may occur, resulting in higher *k*-values.

### Difference in *k*-values between CF and WS mats

In this experiment, we examined both CF and WS mats with a density of 60 kg/m^{3}. Figure 4 compares the appearance of the two kinds of mat at that density. The *k*-values obtained from the regression equations for CF and WS mats with a density of 60 kg/m^{3} are 0.0364 and 0.0456 W/(mK), respectively. Thus the *k*-value of the WS mat was 1.25 times higher than that of the CF mat. Assuming that the CF and WS materials themselves have the same solid *k*-value, and therefore that heat transfer via solid conduction occurs to the same degree when mat density is equal, the above difference in *k*-values is presumably caused by the difference in heat transfer through coarse pores.