The conventional discrete ordinate method using the radiative transfer equation was reformulated into equations of second order differentiation. This gives two advantages over the conventional discrete ordinate method. They are; (ⅰ) the number of unknowns(or equations) is reduced to half and (ⅱ) the popular elliptic solvers of flow and transport can be directly employed with minor changes to solve this problem.
Two sample problems were solved to verify the applicability of the second order discrete ordinate method. The first problem is a square enclosure containing gray absorbing-emitting medium of uniform heat source with cold black walls. Very realistic results were obtained as compared with the results using conventional first order discrete ordinate method and zone method. The second problem by substituting one of the wall with hot wall of uniform temperature and removing heat source from the first problem was solved to give partly unrealistic results. Some numerical aspects were discussed to improve ray effect.
