Spatial discretization errors in the heat flux integral of the discrete transfer method

The discrete transfer method (DTM) is a widely used algorithm for the computation of radiative heat transfer in enclosures. The truncation error in the heat flux integral associated with the method is the difference between the actual heat flux and its DTM approximation. Estimates were presented by Verstzeg et al. [1, 2] of the error associated with the discretization of the hemisphere around irradiated points in enclosures filled with transparent and nonscattering participating media. In this article we quantify the errors due to the spatial discretisation of the enclosures with nonhomogeneous absorbing/emitting media with nonuniform surface intensity based on Hsu and Farmer's benchmark case E1 [3]. Our error estimates are found to be in excellent agreement with the actual DTM errors and have been used successfully to predict the convergence rates of the DTM as the control-volume mesh is refined.