The problem of radiation heat transfer in a system of large numbers of surface elements was considered. A numerical-mathematical model detailing the radiative exchange between surfaces in a generalised multiple-surface shape model was constructed, developed, and tested to a satisfactory degree of complexity, at which point it was incorporated into a general-purpose computer program. Predictions by the model were compared to selected results from pilot-scale DC arc furnace tests run at Mintek, to evaluate the significance of radiation heat transfer to the overall energy loss from the freeboard regions of such furnaces. Finally, the model was used to examine a range of process and design variables, and scale-up issues. Several interesting aspects and phenomena come out of the exhaustive modelling work, to hopefully aid the designer of DC arc furnace freeboards in the future on both the pilot and full industrial scale. (C) 2002 Elsevier Science Ltd. All rights reserved.