Polynomial cross-roots application for the exchange of radiant energy between two triangular geometries

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Yanan Camaraza-Medina https://orcid.org/0000-0003-2287-7519


The view factor between surfaces is a vital element in the radiative heat transfer. Currently, the technical literature does not have an analytical method that allows directly calculating the view factors for the exchange of radiant energy between triangular surfaces. Developing an analytical model for triangular geometries requires the addition of multiple integrals, due to the change in the integration contours of the surfaces, which makes it a complex task to obtain the solution of various configurations. In this work, the analytical development of an expression of the view factor for the exchange of radiative energy between 32 triangular geometric configurations with common edges and included angle theta is intended. To establish comparisons, 42 examples with different shape configurations were calculated for each geometry using the analytic solution (AS), the numerical solution of the quadruple integral using Simpson's multiple rule 1/3 with five intervals (SMR) and the view factor computed using Bretzhtsov's crossed roots (BCR). From eight basic geometries, the view factor for another 24 triangular geometries is obtained using the summation rule. In all the cases evaluated, the BCR showed the best fits. The practical nature of the contribution and the reasonable adjustment of the values obtained, establish the proposal as a suitable tool for its application in thermal engineering.