View Factor Calculations Between Triangular Surfaces

Year 2025, Volume: 4 Issue: 2, 49 - 59, 30.06.2025

Yanan Camaraza Medina , Abel Hernandez-guerrero , Jose L. Luviano-ortiz

Abstract

In radiative heat transfer calculations, to determine the view factor between surfaces is crucial. Currently, the available technical literature on the subject lacks an analytical expression for estimating the view factor for combinations of triangular surfaces. An analytical solution requires the summation of multiple integrals, given the changes in the integration contours, which becomes more complex in irregular contours. This work aims to develop an expression for computing the view factor between 32 triangular geometric configurations with a common edge and included angle θ. Very importantly, in modern engineering, mesh generators rarely use rectangles or squares (unless the overall geometry is a perfect cube), with triangular elements being the most commonly used elements. For comparison, 48 cases with diverse geometric relationships were calculated using the analytical solution (AS), numerical integration using Simpson's multiple 1/3 rule (MSR), the Sauer graphical solution (SGS), and Bretzhtsov cross roots (BCR). From eight basic geometries, the view factor was computed for the remaining 24 combinations using the sum rule. In all cases, identical fit values were obtained for MSR and SGS with respect to AS, while BCR showed the best correlation in all cases examined. In all the cases evaluated, the BCR showed the best fits, with an error of ±6% in more than 90% of the samples, while the MSR showed an average dispersion of ±6% in 65% of the data. Given the practical nature of the contribution and the reasonable values of the fits obtained, the current proposal constitutes a suitable tool for application in thermal engineering.

Keywords

Bretzhtsov cross roots, Radiative heat transfer, Triangular surfaces, View factor

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