Combined radiation and conduction heat transfer through various high-temperature, high-porosity, unbonded (loose) fibrous insulations was modeled based on first principles. The diffusion approximation was used for modeling the radiation component of heat transfer in the optically thick insulations. The relevant parameters needed for the heat transfer model were derived from experimental data. Semi-empirical formulations were used to model the solid conduction contribution of heat transfer in fibrous insulations with the relevant parameters inferred from thermal conductivity measurements at cryogenic temperatures in a vacuum. The specific extinction coefficient for radiation heat transfer was obtained from high-temperature steady-state thermal measurements with large temperature gradients maintained across the sample thickness in a vacuum. Standard gas conduction modeling was used in the heat transfer formulation. This heat transfer modeling methodology was applied to silica, two types of alumina, and a zirconia-based fibrous insulation, and to a variation of opacified fibrous insulation (OFI). OFI is a class of insulations manufactured by embedding efficient ceramic opacifiers in various unbonded fibrous insulations to significantly attenuate the radiation component of heat transfer. The heat transfer modeling methodology was validated by comparison with more rigorous analytical solutions and with standard thermal conductivity measurements. The validated heat transfer model is applicable to various densities of these high-porosity insulations as long as the fiber properties are the same (index of refraction, size distribution, orientation, and length). Furthermore, the heat transfer data for these insulations can be obtained at any static pressure in any working gas environment without the need to perform tests in various gases at various pressures.

Combined radiation and conduction heat transfer through a high-temperature, highporosity, rigid multiple-fiber fibrous insulation was modeled using a thermal model previously used to model heat transfer in flexible single-fiber fibrous insulation. The rigid insulation studied was alumina enhanced thermal barrier (AETB) at densities between 130 and 260 kg/m 3 . The model consists of using the diffusion approximation for radiation heat transfer, a semi-empirical solid conduction model, and a standard gas conduction model.

Heat transfer in rigid reusable surface insulations was investigated. Steady-state thermal conductivity measurements in a vacuum were used to determine the combined contribution of radiation and solid conduction components of heat transfer. Thermal conductivity measurements at higher pressures were then used to estimate the effective insulation characteristic length for gas conduction modeling. The thermal conductivity of the insulation can then be estimated at any temperature and pressure in any gaseous media. The methodology was validated by comparing estimated thermal conductivities with published data on a rigid high-temperature silica reusable surface insulation tile. The methodology was also applied to the alumina enhanced thermal barrier tiles. Thermal contact resistance for thermal conductivity measurements on rigid tiles was also investigated. A technique was developed to effectively eliminate thermal contact resistance on the rigid tile's cold-side surface for the thermal conductivity measurements.

Combined radiation and conduction heat transfer through a high-temperature, highporosity, rigid multiple-fiber fibrous insulation was modeled using a thermal model previously used to model heat transfer in flexible single-fiber fibrous insulation. The rigid insulation studied was alumina enhanced thermal barrier (AETB) at densities between 130 and 260 kg/m 3 . The model consists of using the diffusion approximation for radiation heat transfer, a semi-empirical solid conduction model, and a standard gas conduction model.

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