ANALYTIC SOLUTION OF THE TRANSIENT-BEHAVIOR OF RADIATION-BACKSCATTERING HEAT SHIELDS

An analytic solution of the material response to combined radiative and convective heating is presented. The solution includes the equations of radiative transfer (within the material), coupled to a transient energy equation that contains both radiative and convective terms. The analysis allows for unlimited spectral detail, but assumes that within the range of applicability, the various material properties do not vary significantly with temperature. To facilitate development of the analytic solution, it is also assumed that scattering within the material dominates absorption, and that the exposed surface of the material does not ablate. The exposed surface boundary condition includes convective heating and spectral radiation, some of which is absorbed by the surface and some of which penetrates the surface.