Application of the Second Order Discrete Ordinates Method to a Radiation Problem in a Square Geometry

Abstract

Radiative heat transfer in a two dimensional square enclosure containing gray absorbing/emitting and nonscattering medium was investigated using the second order discrete ordinates method which had been reformulated from the conventional discrete ordinates method. Discretizaton equations were obtained using a Taylor series expansion method and using an exponential scheme with cubic interpolation method, and the results were compared with the conventional discrete ordinates solutions and with the zonal computations. Two sample problems were solved: in the first, the medium has known heat source and the walls are cold, and in the second, the medium has no heat source and one of the walls is hot while the others are cold. The walls are black and diffuse in both problems. Very promising results of the two schemes were obtained and especially the result of the exponential scheme agrees faifly well with those of the conventional discrete ordinates method and the zonal computations.