Method of spherical triangle-division for solving view factors in built environment and its application for non-uniform thermal radiation environments

Radiative heat transfer is the focus of many studies on heat transfer issues in the built environment, and the view factor (VF) between the surfaces of built objects in space is a crucial parameter for quantitative analysis of radiative heat transfer. In the built environment, not only the types of space are diverse, but also the forms of the objects of interest are often different from each other. Studying the thermal radiation heat transfer in complex space usually requires to simplify the calculation of VF between the surfaces, based on specific studied problems. In this paper, the method of Spherical Triangle-division is constructed by mathematical derivation through spatial analytic geometry and surface integral. The analytical formula is then developed to calculate VF from the surface element to the surface of the polygonal plane, with arbitrary orientation in space. Using the geometric transformation in terms of planar projection and polygonal intersection, the method can also be used to solve the VF in occlusion conditions, and it is proven to be more accurate. Finally, the application of the method is discussed, which aims at providing novel ideas and tools for the quantitative analysis of non-uniform thermal radiation issues in the built environment.