In addition to being used as a guard insulation material, the fumed-silica board was also utilized as the specimens themselves in one set of three heating/cooling cycles. The material is non- reactive, so that the computed thermal conductivity results can be compared directly to the previously measured values.8, 9 However, an additional complication arises in this case. When the fumed-silica board is used only as guard insulation, it has a much lower thermal conductivity than the typical FRM specimens and the assumption of one-dimensional heat transfer through the thickness of the guarded square FRM specimens appears to be valid, as indicated by the results presented above. Conversely, when the fumed-silica board is used for the specimens as well, the relative heat transfer through the "guarded" areas of the sandwich configurations becomes significant. While the temperature rise of the slug is still indicative of the heat flow into the slug, the area (A in equation (7)) for this flow is no longer simply 0.152 m by 0.152 m. For the analysis presented below, it has been assumed that in this case, the total area available for heat transfer is given by the total area of specimen surrounded by the guard (0.203 m by 0.203 m) plus the area of the thin sides of one half of the slug calorimeter (two times 0.203 m by 0.00635 m plus two times 0.152 m by 0.00635 m). In addition, the mass of the "FRM" specimen was taken as the mass of the fumed-silica insulation board specimen plus the masses of all of the guard materials comprising one half of the sandwich specimen configuration.
Physically, these first order approximations seem reasonable and as shown in Figure 9, they do produce thermal conductivities for the cooling curves that are both reproducible and that agree with the previously measured data to within about 5 %. The data in Figure 9 appear much noisier than those in Figures 7 and 8, but it must be kept in mind that the scale on the y-axis in Figure 9 has been reduced by a factor of eight relative to that employed in the other two figures. One other point worth noting from Figure 9 is that once again, only the heating results for the third run, where a more gradual heating curve (extending only up to 500 ºC in this case) was employed, compare favorably to the gradual cooling results for the three runs and the previously measured data. In the first two runs that employed basically the same heating rate as that shown in Figure 6, due to the low thermal conductivity (and thermal diffusivity) of the fumed-silica board, "steady-state" conditions were apparently only approached at the very end of the heating curve (500 ºC and beyond). The reproducibility of the heating and cooling curves for the first two runs in Figure 9 does provide further support that the fumed-silica board is indeed behaving as a non-reactive material over the temperature range employed in this preliminary study. The results for run 3 with the slower heating rate indicate once again the potential for piecing together the thermal conductivity values determined from the heating and cooling curves to provide a single thermal conductivity versus temperature curve that covers a larger temperature range than either of its two component curves. Radiation effects are seen to be of much less importance in this material as the computed values of k agree well with those previously measured over the entire temperature range investigated with the slug calorimeter. Of course, the fumed-silica insulation board had been formulated specifically to minimize radiation transfer at high temperatures via the addition of an opacifier.8
The first two heating tests with the fumed-silica insulation board were terminated when the exterior of the specimens reached a temperature of about 900 ºC, quite similar to the termination point used for the testing of the two FRMs. However, in comparison to the FRMs, where the slug had achieved a temperature of about 540 ºC at this point, for the fumed-silica board, the interior slug temperature was still well below 200 ºC at this time. Naturally, this reinforces the critical importance of using a low thermal conductivity material to protect steel structures exposed to fire.
Figure 9– Computed effective thermal conductivity results for fumed-silica insulation board in comparison to previously measured NIST data (with error bars indicating ± 5 %).8,9 Note: NIST data have been corrected to values for one standard atmosphere of pressure (sea level) using the procedure provided in reference 9.