John Lienhard’s Post

More fun with classical heat conduction! In our paper – just out – Kyle McKee and I have shown that heat conduction shape factors inside and outside planar objects are equal when the objects have a particular N-fold symmetry. Examples of these shapes are regular polygons, gears, snowflakes, and even a Compass Rose.   And we have found an analytical expression for the shape factor of ANY such object!   We exploited a lovely method in complex analysis due to Hersch (1982). Our findings also limit my 2019 conjecture on interior/exterior equality. While the result is very general, it is not universal: N-fold symmetry is required.   The paper is here (and OPEN ACCESS): https://lnkd.in/ezUyQU2N   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.