Experimental

Four inorganic FRMs were investigated, two each from two different manufacturers. Two (here denoted as A and B) are gypsum-based with different lightweight extenders (fillers) and two (denoted as C and D) are calcium silicate-based. The measured room temperature densities of the four materials are provided in Table 1.

Specimens were nominally 152.4 mm x 152.4 mm x 25.4 mm, although the exact thickness of each specimen was assessed using a micrometer and averaging the measurements obtained from eight points (two coming in from each of the four edges). Following the physical characterization of the mass and dimensions of each specimen, thermal measurements were performed using either a Hot Disk^l Thermal Constants Analyzer for the transient plane source method or a recently constructed slug calorimeter. For the transient plane source method, a nickel wire spiral probe with a radius of 14.67 mm was sandwiched between twin specimens of the FRM being evaluated, with a power input of 0.08 W for 320 s. The raw data was collected by the Hot Disk software analysis package and evaluated to provide estimates of the room temperature thermal conductivity and volumetric heat capacity of the FRM being evaluated. At least five separate room temperature measurements were made on each set of "twin" specimens and the average values are reported here. The average measured volumetric heat capacities were then converted to mass-based heat capacities [units of J/(kg·K)] using the measured room temperature average densities of the FRMs from Table 1. Hot Disk reports reproducibilities of ± 2 % for thermal conductivity and ± 7 % for heat capacity (specific heat per unit volume).

Separate (pairs of) specimens of each FRM were also evaluated in a high temperature electrical furnace using a simple slug calorimeter that has been described in detail [7] Its underlying principles are similar to those in the apparatus originally described by Fitch [8] that is still utilized for estimating the thermal conductivity of leather in the ASTM Standard Test Method for Estimating the Thermal Conductivity of Leather with the Cenco-Fitch Apparatus (D 2214) [3] The metal slug consists of an American Iron and Steel Institute (AISI) Type 304 stainless steel plate 152 mm x 152 mm x 12.7 mm containing three holes at the top for the insertion of high temperature Type N thermocouples [7] The steel plate has a mass, M_x, of 2340 g, and the heat capacity as a function of temperature values for 304 stainless steel were taken from the literature [9]. With these thermophysical properties and the measured temperature of the steel slug as a function of time, the heat flow into the slug during heating (or from the slug during cooling) can be readily computed. Knowing the total heat flow (including the contribution to raising the temperature of the FRM specimens) and the temperature difference across the FRM, an effective thermal conductivity can be easily computed as outlined in [7] and using the following equation:

where k is the effective thermal conductivity [in W/(m·K)], F is the temperature increase (or decrease) rate (in K/s), l is the FRM specimen thickness (in m), M is mass (in kg), c_p is heat capacity [in J/(kg·K)], A is the FRM specimen area (152 mm x 152 mm), and ΔT is the temperature difference across the FRM specimen(s) (in K).  In this paper, the FRM heat capacity needed for the slug calorimeter analysis in equation (1) will be supplied by the room temperature Hot Disk measurements and is assumed to be constant with temperature.  While measurements conducted by a private laboratory have indicated that the heat capacity of FRM A, for example, varies from 1046 J/(kg·K) to 1400 J/(kg·K) as temperature is increased from 50 ºC to 600 ºC, using the single value of 1220 J/(kg·K) from Table 1 resulted in little visible difference in the calculated effective thermal conductivity curves, as the value of the M_Sc_p^S term in equation (1) is generally 5 to 6 times larger than that of the M_FRMc_p^FRM term for the experimental setup employed in this study.  Due to the heterogeneous microstructure of many FRMs it is often difficult to obtain a representative volume sample to determine their heat capacities using more conventional techniques such as the ASTM Standard Test Method for Determining Specific Heat Capacity by Differential Scanning Calorimetry (E 1269) [3]. Furthermore, for this study, the masses M_FRM of the FRM specimens were measured before and after the heating/cooling exposures in the furnace and the measured mass losses (values provided in Table 1) were distributed uniformly over the specimen temperature rise experienced during the first heating cycle.

A schematic and a photograph of the slug calorimeter experimental setup are provided in Figure 1. While more information on the mathematical analysis and the expected uncertainties accompanying the slug calorimeter measurements can be found in [7], the most significant contributor to the expanded uncertainty is the uncertainty in the temperature measurement.  For example, assuming an uncertainty of 1 º C for the thermocouple readings and a 5 min sampling interval, the estimated uncertainty in the effective thermal conductivity would be about 5 % for values computed in the temperature range of 400 ºC to 700 ºC during heating [7].

¹Hot Disk, Uppsala, Sweden. Certain commercial products are identified in this paper to specify the materials used and procedures employed. In no case does such identification imply endorsement by the National Institute of Standards and Technology, nor does it indicate that the products are necessarily the best available for the purpose.