Equilibrium Temperatures in a Boundary-Layer Flow Over a Flat Plate of Absorbing-Emitting Gas

The effect of radiation on the equilibrium temperature for a flow of emitting-absorbing gas over a flat plate is studied. Three methods of solution are formulated: An approximate solution for a thin boundary layer, a similarity solution for the limiting case when the boundary layer is optically thick, and an exact solution. Emphasis is put on the study of the recovery or adiabatic wall case, where conduction to the wall is balanced by the net radiation away from the wall. Results are reported for the limiting cases of a black plate and completely reflective plate and for a unit Prandtl number. The exact solution reflects very favorably on the use of the approximate methods and points out clearly the conditions for which the approximate solutions are applicable. Results are also reported for the equilibrium wall temperature for the case of constant heat flux and for the recovery factor in the case of blowing and suction; both for optically thin boundary layers. Special attention is put on the interaction mechanism and the role of the emitting-absorbing coefficient on this process. It is shown that, for small absorption coefficient, high wall emissivity, and Mach number, the results approach the case where the gas is transparent.