The radiative transfer equation with a nonhomogeneous reflectivity boundary condition coupled with the heat conduction equation

Abstract

In this paper, we make a rigorous mathematical analysis of the radiative heating of a semitransparent body made of a glass by a black radiative source surrounding it. This requires the study of the coupling between quasi‐steady radiative‐transfer boundary value problems with nonhomogeneous reflectivity boundary conditions (one for each wavelength band in the semitransparent electromagnetic spectrum of the glass) and a nonlinear heat‐conduction evolution equation with a nonlinear Robin boundary condition, which takes into account those wavelengths for which the glass behaves like an opaque body. We prove existence and uniqueness of the solution and give also uniform bounds on the solution, ie, on the absolute temperature distribution inside the body and on the radiative intensities.