Analysis of sublimation-cooled coated mirrors in convective and radiative environments.

Analytical solutions were obtained for the thermal response of a transpiration- or sublimation-cooled spherical mirror coating exposed to convective and radiative heating. The solutions allow unlimited spectral detail to be accounted for. Results indicate that transpiration-cooled thick coatings (1 cm) may withstand up to 10 kW/sq cm on a steady basis without excessive temperature rise for quartzlike materials with an internal absorption coefficient of 0.01 per cm. On a transient basis, fluxes up to 20 kW/sq cm can be accommodated for a second (cW laser exposure time), 4 kW/sq cm for 5 sec (planetary entry heating time), and of the order of MW/sq cm for millisecond times (short-duration laser bursts) without transpiration cooling for a material with an absorption coefficient of 0.1 per cm. Proportionately higher fluxes can be accommodated with lower absorption coefficients. Thermal stresses produced by the heat pulse are found to be high but within the strength of the materials. The regime in which meaningful solutions may be obtained is mapped in detail.