In-depth absorption of externally incident radiation in nongray media

During flame spread along a surface, the thermal radiation emitted by high-temperature combustion products supports the advancement of the flame front. To model the response of the solid to the externally incident radiation, it is necessary to consider the spectral variation of radiative properties of the solid. For highly absorbent solids, such as wood or particle board, almost all of the externally incident radiation is absorbed at or very near the surface. However, for highly semitransparent materials, such as a plastic material whose surface is not clean, the externally incident radiation is absorbed both at the surface and within the material. In this work, the objective is to study both theoretically and experimentally the importance of in-depth radiation. A transient, one-dimensional model is formulated and solved numerically. The spectral radiative properties employed in the radiation model have been obtained from separate experiments on polymethylmethacrylate (PMMA), a clear plastic. The model demonstrates the importance of in-depth absorption. Model results exhibit the same trend as those revealed in experiments for the rise in surface temperature of the sample.