An alternative to performing x-ray microtomography characterization of the pores in an FRM and then using the obtained three-dimensional microstructure as input for computing thermal conductivities is to directly apply equation 3 to predicting thermal conductivities for the porous FRM. Knowing the bulk and powder densities of the FRM allows for an estimation of its total porosity, p. Then, a single measured room temperature thermal conductivity value can be used to provide an estimate of the ksolid term in equation 3. The characteristic pore radius to be used in equation 2 can be estimated using optical microscopy (see Figure 1). Finally, equation 3 can be applied to predicting the thermal conductivity of the FRM as a function of temperature. Results of applying this procedure to FRMs A and B are presented in Figure 6. For the two fiber/portland cement-based FRMs, this approach is seen to provide an excellent fit to the measured values for temperatures up to 1000 ºC, as was also observed elsewhere for the gypsum-based FRM C that contains smaller pores (1). While FRM B is quite similar to FRM A from a chemical composition viewpoint, its higher porosity (lower density) and larger pores result in significantly higher thermal conductivity values at higher temperatures (> 400 ºC).
Figure 6 Measured thermal conductivities (2) and predictions (solid lines) based on theory of Russell/Loeb (7, 8) for two fiber/portland cement-based spray-applied FRMs (A and B), from ref. (1).