Approximation errors in the heat flux integral of the discrete transfer method, part 2: participating media

The truncation error in the heat flux integral associated with the discrete transfer method (DTM) is the difference between the actual heat flux and its approximation. Estimates of this error in radiative heat transfer problems in enclosures filled with a transparent medium were presented in a companion article [1]. Here we extend the methodology to cases in volving participating media. We give expressions for the errors associated with the discretization of the heat flux integral for enclosures where the surface intensity and medium source function are known exactly and represented as piecewise constant. Excellent agreement between theoretical and computed errors was found for three illustrative test cases. The theory was also applied to one of the cases of the well-known Hsu and Farmer (1995) benchmark [9]. A good match was obtained between the error limits of the Monte Carlo and DTM solutions.