Unstructured finite-volume method for radiative heat transfer in a complex two-dimensional geometry with obstacles

The radiative heat transfer in a complex two-dimentional enclosure with obstacles with participating medium is very important in practical engineering applications. In order to deal with this problem, in this study the finite-volume method (FVM) for radiation has been derived using the unstructured grid system. A general discretization equation was formulated by introducing the directional weight and the step scheme for spatial differencing. For its comparison and validation, two test eases, an equilateral triangular enclosure and a square enclosure with baffle, were chosen. Then more complex and practical cases, such as a semicircular enclosure with cylinder hole, a square enclosure with finned internal cylinder, and a furnace with embedded cooling pipes, were investigated. All the results obtained by the unstructured FVM agreed very well with the exact solutions as well as the results obtained by the zone method Furthermore, the wiggling behavior occurring in the blocked-off FVM ns not produced by the unstructured FVM. Three types of manipulation of control angle overlap were also examined here. It was found that the solutions depended on the type of manipulation of control angle overlap, especially when the number of control angles was small, Usually, both the pixelation method and tract treatment introduced here yielded between solutions than the hold approximation.