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View factor for radiative heat transfer calculations between triangular geometries with common edge

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Abstract

In radiation heat transfer calculations, the view factor between surfaces is an element of vital importance. Currently, the available technical literature does not have an analytical expression that allows the view factor to be directly computed for combinations of triangular surfaces. An analytical view factor solution requires the addition of multiple integrals, given the changes in the integration contours, which makes it a complex task to obtain solutions for various configurations. This work aims to analytically develop the view factor expression for radiative heat transfer of 30 triangular geometries with common edge and included angle \(\theta \). To establish comparisons, twelve examples with several aspect ratios were calculated for each geometry, using the analytical solution (AS), the numerical solution of the quadruple integral using multiple Simpson’s 1/3 rule with five intervals (MSR), the graphical solution given by Sauer (GS) and the view factors calculated using Bretzhtsov cross-roots. From the eight basic geometries, the view factor for another 22 triangular geometries is obtained, by means of the Summation Rule. In all cases, identical fit values of MSR and GS were obtained with respect to AS, while Bretzhtsov cross-root showed the best fit in all cases examined. Given the practical nature of the contribution and the reasonable values of adjustments obtained, the proposal is a suitable tool for application in thermal engineering and related practices that require thermal radiation calculations.

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Acknowledgements

The authors are very grateful for the help and recommendations provided by Professor Dr. John R. Howell, from the Department of Mechanical Engineering, University of Texas-Austin, USA.

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Authors and Affiliations

  1. Technical Sciences Faculty, Universidad de Matanzas, Matanzas, Cuba

    Yanan Camaraza-Medina

  2. Department of Mechanical Engineering, University of Guanajuato, Guanajuato, Mexico

    Abel Hernandez-Guerrero & J. Luis Luviano-Ortiz

Authors
  1. Yanan Camaraza-Medina
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  2. Abel Hernandez-Guerrero
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  3. J. Luis Luviano-Ortiz
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Contributions

YC-M contributed to methodology, formal analysis, data curation, writing–original draft, review and editing. AH-G contributed to review and editing, resources, data curation. J. LL-O contributed to review and editing, resources, data curation.

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Correspondence to Yanan Camaraza-Medina.

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Camaraza-Medina, Y., Hernandez-Guerrero, A. & Luviano-Ortiz, J.L. View factor for radiative heat transfer calculations between triangular geometries with common edge. J Therm Anal Calorim 148, 4523–4539 (2023). https://doi.org/10.1007/s10973-023-11975-y

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  • DOI: https://doi.org/10.1007/s10973-023-11975-y

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