On the radiative heat transfer in a semi-transparent medium enclosed in a cylindrical annulus of infinite length with specularly reflecting lateral surfaces

In this paper, we present analytical and numerical investigations in order to determine the incident radiation and radiative flux in a semi-transparent medium at radiative equilibrium and enclosed in a cylindrical annulus with two specularly reflecting surfaces. As for the case of a purely diffuse reflexion, we show that the incident radiation and radiative flux can be completely defined by some weighting coefficients whose closed-form analytical expressions are detailed. The specular part of the weighting coefficients is computed with a Gauss quadrature, and a numerical validation is performed by comparing the numerical results to optically thin approximation analytical solutions. Finally some examples show that the results for temperature and radiative flux fields may strongly be different from the ones obtained in the case of a purely diffuse reflexion.