One-dimensional energy transfer in radiant media

Abstract

The equations of one-dimensional radiative energy transfer are extended from their classical astrophysics form to include walls of arbitrary radiative properties. The concepts of emissivity and penetration length are examined. As an application, the case of the steady infinite flat layer is considered, with conduction and radiation present. The wall conditions are so chosen as to give a good model of a low-speed high-temperature boundary-layer. It is found that the effect of the “long-range” process of radiation is to smooth out the temperature profiles and relieve the sharp temperature gradients at the cool wall. As a result, the application of the exact method yields a lower value of both components of the total heat flux (radiation plus convection) than calculated previously by assuming a temperature profile on the basis of conduction only. Such coupling of convective and radiative fluxes is governed by the magnitude of a non-dimensional parameter, depending on the physical properties and the flow geometry of the problem.