Radiative heat transfer in a 2D semi-transparent gray medium with a centered inner square cavity

Abstract

Exact semi-analytical expressions of the incident radiation and radiative flux fields are developped, inside a two-dimensional semi-transparent medium and followed by numerical simulations. A rectangular cavity is filled-in with a gray absorbing-emitting, but non-scattering semi-transparent medium at radiative equilibrium. An opaque inner centered cavity with black and imposed temperatures surfaces is set as a non-participating medium, nevertheless its external boudary surfaces participate to radiative transfer. An exact method based on ray tracing and specific functions is performed to evaluate the incident radiation and radiative flux fields. Spatial and angular discretization are ensured with a Gauss quadrature by Numerical issue. Temperature field is computed with an iterative process until convergence. Verification of results is done both for simple and complex geometries, and remains in good agreement with literature. Hence, the other one results of radiative quantities are tabulated as benchmark solutions and simulated for several sizes of the inner square cavity for different ranges of optical thickness.