Infinite Reflections Method for Calculation of Radiation Exchange between Grey-Diffuse Surfaces : UP to four surface interactions (Part 1)

Abstract

Unlike black surfaces, calculation of radiation exchange for grey-diffuse surfaces is generally considered too complex. This is because a grey surface is not a perfect absorber as for a black surface. As radiation leaves a surface, it travels to the other surfaces whereby it is absorbed partially and is then reflected many times in between with partial absorption at each contact with a surface. Therefore, a proper analysis of the problem must take into account of these multiple reflections. The existing methods of analysis can be classified into two categories; those which do not take into account of the multiple reflections for more than two surfaces, and those which account for these multiple reflections but they are only applicable for enclosures and are not fully reliable in implementation. This first part of the paper presents a method of analysis for the exact calculation of radiant heat transfer between two grey-diffuse surfaces due to the interaction of up to four surfaces whereby multiple reflections of radiation are accounted for. This is based upon two concepts; the arborescent diagrams and the infinite series algebra. Complementary work for the understanding of this part is presented in the second part of the paper.