Calculation of view factors for complex geometries using Stokes’ theorem

Abstract

This paper presents an algorithm that calculates the radiative view factors based on Stokes' theorem. The authors propose a formulation where the original surfaces are divided into a grid of elementary areas and Stokes' theorem is applied for the determination of the view factors between these elementary areas. With this approach, the account of the shading effect of obstructions is significantly improved. The capabilities of the proposed formulation were tested with the calculation of radiative view factors between flat and curved surfaces. The results obtained showed a good agreement with the corresponding analytical solutions, with relative errors (REs) lower than 2%. The proposed methodology was also compared with the application of the double integral area formulation and a better agreement was found, between RE and the CPU, using the present formulation. IntroductionIn engineering applications, it is important to accurately determine the net radiative heat transfer between surfaces. There are several applications that ask for this detailed calculations, such as industrial equipment studies (Boulet et al. A parameter commonly used to quantify the heat exchange by radiation is the view factor concept, also known as configuration factors or shape factors, and defined as the radiative fraction that leaves a surface i and directly reaches surface j. The scientific literature presents graphs and tables with values and expressions to calculate the view factors of many geometric configurations, obtained from analytical solutions or numerical methods (Sparrow and Cess 1978;Çengel 2003). However, despite being extremely useful, this information is inappropriate to generic geometries and computational procedures, to incorporate into computer fluid dynamic (CFD) programs, or, for

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