Abstract

CAMARAZA-MEDINA, Yanan. POLYNOMIAL CROSS-ROOTS APPLICATION FOR THE EXCHANGE OF RADIANT ENERGY BETWEEN TWO TRIANGULAR GEOMETRIES. Ingenius [online]. 2023, n.30, pp.29-41. ISSN 1390-860X.  https://doi.org/10.17163/ings.n30.2023.03.

The view factor between surfaces is essential in heat transfer by radiation. Currently, there are no analytical solutions available to evaluate the view factors between triangular geometries with common edges and angle ( , due to the high mathematical complexity associated with their development. For these configurations, the literature only has Sauer’s graphic solutions, the use of which generates mean errors of 12 %. In this work an approximate method is developed that does not give a high mathematical complexity and that guarantees an adjustment of less than 12 %. For this purpose, 32 different geometric configurations (8 basic and 24 derived) were studied, obtaining the solutions for each of the evaluated cases. For the validation of the models obtained, 42 different aspect ratios of leaving and reaching surfaces were used, the view factors being computed in each case by means of the analytical solution (AS), the numerical solution obtained with Simpson’s multiple rule 1/3 (SMR) with five intervals and using Bretzhtsov’s crossed root (BCR), finally comparing the results obtained in each of the eight basic cases. 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 SMR showed an average dispersion of ±6 % in 65 % of the data. The practical nature of the contribution and the reasonable adjustment values obtained establish the proposal as a suitable tool for use in thermal engineering.

Keywords : Triangular surfaces; Bretzhtsov crossroot; view factor.

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