A new method for calculating the view factor from a wall to a spheroidal canopy

Abstract

The view factor (VF) is an essential parameter for calculating the thermal radiation exchange between ground objects and exterior building surfaces. However, the VF between the spheroidal tree canopy and the adjacent wall has yet to be obtained systematically, preventing further quantitative research on how the tree canopy influences the adjacent buildings. This article proposes a theoretical method for calculating the view factor from a wall to the adjacent spheroidal tree canopy (TVF). The integral equation of the TVF is derived following the VF equivalence principle and the contour integral method. The interpolation method and corresponding equations are then proposed to enhance practical applications. As demonstrated by two specific calculation examples, the integral equation is consistent with previous research. Meanwhile, the interpolation equation is shown to be quicker and more accurate. The proposed TVF calculation algorithm is neither geographically nor climatically constrained. The differential elements on the wall with the same TVF are distributed on an ellipse. TVF is positively correlated with e and negatively correlated with xp. Compared to the ENVI-met simulation under the same meteorological conditions, the equations for calculating thermal radiation exchange based on the VF are accurate. Therefore, the impact of plants on the outdoor thermal environment, sectors involving building energy consumption, and building carbon emissions can be investigated further, leaving positive scientific significance for the promotion of theoretical research and evaluation in these fields.