Numerical method for calculating view factor between two surfaces

Long-wave radiation heat transfer is calculated using a geometrical factor the so-called view factor, which is normally estimated in a simplified way by building simulation programs, especially when there is no information in the literature due to the complexities to solve the double integral which defines the view factor between two surfaces. Analytical solutions are only available in the literature for a restricted number of simple configurations. This simplification on the process may implicate several errors on the evaluation of the internal surface temperatures which can cause discrepancies on the prediction of thermal comfort level and energy consumption, mainly when surfaces present complex geometries, openings (windows and doors) and when there are obstructions between them. In this way, the objective of this work is to present a computational method to determine the view factor between two surfaces considering simple or complex geometries with openings and obstructions, using an algorithm to generate a finiteelement mesh onto surfaces to distinguish viewed/shaded surface areas. The algorithm is fast,   memory-efficient, robust and uses constrained and unconstrained Delaunay triangulations. The mesh quality is guaranteed by the use of the Rupert’s Delaunay refinement algorithm that avoids undesirable small triangle angles. A comparison with literature data available only for the case of simple configurations (without openings and obstructions) shows the excellent accuracy of the proposed computational method. For those cases, a sensitivity analysis consisting in varying the mesh refinement and the distance between the two surfaces has been performed. The results obtained for some geometries considering openings and obstructions are also presented.