Approximate analysis of influence of surface emissivity on combined heat radiation and conduction in aspect of the flat sample thickness effect on heat conduction of semitransparent media

This paper is a continuation of considerations concerning analytical and numerical analysis of the problem of the "thickness effect curve" in active optical media presented in papers [1] and [2]. As before, the method of division of the thermal conductivity thickness dependence k(l) into three parts of different width has been used, [1] and the limited value of the sample thickness lgr, which corresponds to an initial region of the actual thermal conductivity k(l), as a function of absorption coefficient κ and sample thickness l was presented [2]. The novelty in present work is that a more realistic situation than before has been studied. Instead of black surface, the grey and diffuse reflecting ones have been considered. To validate the proposed method the results of analytical calculations which were made to include the influence of surface emissivity on the sample "thickness effect curve" and on the steady-state heat transfer have been compared with the numerical solution of the 1-D coupled radiation and conduction heat transfer model in emitting and absorbing medium limited by grey walls [5].