Symmetry Criteria for the Equality of Interior and Exterior Shape Factors With Exact Solutions
Name
McKee Symmetry for interior-exterior shape factors JHMT 2024.pdf
Description
Published version
Size
3.33 MB
Format
Adobe PDF
Checksum (MD5)
74353d773b8815743a6e661fcf9dcfd5
Author(s)
McKee, Kyle I.
Lienhard, John H
Date Issued
July 4, 2024
Journal
ASME Journal of Heat and Mass Transfer
Publisher
ASME International
Citation
McKee, K. I., and Lienhard, J. H. (July 4, 2024). "Symmetry Criteria for the Equality of Interior and Exterior Shape Factors With Exact Solutions." ASME. J. Heat Mass Transfer. November 2024; 146(11): 111401.
Version
Final published version
Abstract
Lienhard (2019, “Exterior Shape Factors From Interior Shape Factors,” ASME J. Heat Mass Transfer-Trans. ASME, 141(6), p. 061301) reported that the shape factor of the interior of a simply-connected region (Ω) is equal to that of its exterior (ℝ2\Ω) under the same boundary conditions. In that study, numerical examples supported the claim in particular cases; for example, it was shown that for certain boundary conditions on circles and squares, the conjecture holds. In this paper, we show that the conjecture is not generally true, unless some additional condition is met. We proceed by elucidating why the conjecture does in fact hold in all of the examples analyzed by Lienhard. We thus deduce a simple criterion which, when satisfied, ensures the equality of interior and exterior shape factors in general. Our criterion notably relies on a beautiful and little-known symmetry method due to Hersch which we introduce in a tutorial manner. In addition, we derive a new formula for the shape factor of objects meeting our N-fold symmetry criterion, encompassing exact solutions for regular polygons and more complex shapes.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Department of Mechanical Engineering
Rohsenow Kendall Heat Transfer Laboratory (Massachusetts Institute of Technology)
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Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1115/1.4065741
