Radiation transfer in absorbing, emitting two-dimensional media bounded by reflecting walls

Radiation transfer in absorbing, emitting, two-dimensional rectangular media bounded by diffusely reflecting walls is analyzed. The analysis of the considered problem is based on utilizing the integral form of the integro- differential equation of radiative transfer, which is represented by a system of four coupled Fredholm type integral equations. To solve in a highly accurate manner for the unknown functions, power series expansions are employed. A collocation strategy based on the zeroes of the Chebyshev polynomials is subsequently applied to generate a system of linear algebraic equations for the unknown expansion coefficients. A comprehensive parametric study is performed in order to examine the importance of the reflecting walls, as opposed to assuming black bounding walls.