Interaction of radiation with the boundary layer - Nongray media

Conduction and radiation in a nongray absorbing and emitting planar medium and in the boundary-layer flow of a nongray fluid over a constant-temperature flat black plate are investigated analytically. Radiation is modeled using P-3 and P-1 approximations, and single-valued and two-level rectangular models are applied to evaluate the spectral dependence of the absorption coefficient. The governing equations are derived and solved by a collocation procedure or by a two-point boundary-value-problem approach; both techniques have a more straightforward computer implementation than a finite-element technique of the same order. The results are presented in tables and graphs and found to be in good agreement with exact solutions. The method is considered applicable to problems (in ablative cooling, cryodeposits, glass manufacturing, combustion chambers, rocket nozzles, and the study of shock waves) where the gray approximation is of limited utility.