Quasi-static diffusion model of complex heat transfer with reflection and refraction conditions

Abstract In the framework of P 1 approximation, for a multicomponent domain, an analysis of the quasi-stationary model of complex (radiative-conductive) heat transfer accounting for reflection and refraction effects at the boundaries of subdomains is performed. For the nonlinear parabolic-elliptic system, a priori estimates of the solution are obtained, on the basis of which the unique solvability of the initial-boundary value problem with reflection and refraction conditions is proved. In numerical experiments, an influence of radiation effects on the temperature field and its stabilization is studied.