@article{c4e62868a3744c9b8dbcccb8cec3f842,
title = "Near-Exact Radiating Fins via Boundary Tracing",
abstract = "In contexts such as space travel, thermal radiation is the primary mode of heat transfer. The Stefan-Boltzmann law gives rise to a boundary flux which is quartic in temperature, and this nonlinearity renders even the simplest of conduction-radiation problems analytically insurmountable in more than one dimension. An unconventional approach known as boundary tracing allows for analytical inroads into flux boundary value problems that would otherwise require numerical study. In this paper, the method of boundary tracing is used to generate near-exact results for an infinite family of conduction-radiation domains representing radiating fins; realistic lengths and temperatures can be realized.",
keywords = "boundary tracing, flux boundary condition, nonlinearity, thermal radiation",
author = "Conway Li and Neville Fowkes and Brendan Florio and Miccal Matthews",
note = "Funding Information: \ast Received by the editors February 7, 2022; accepted for publication (in revised form) May 19, 2022; published electronically July 26, 2022. This article is an abridged version of the first author's thesis [9, mostly section 3.1]. https://doi.org/10.1137/22M1476228 Funding: The work of the first author was supported by an Australian Government Research Training Program (RTP) Scholarship and a Bruce and Betty Green Postgraduate Research Top-Up Scholarship. \dagger Corresponding author. Current address: RGB Assurance, Level 3, 150 St Georges Terrace, Perth, WA 6000, Australia (
[email protected]). \ddagger Department of Mathematics and Statistics, The University of Western Australia, Perth, WA 6009, Australia (
[email protected],
[email protected]). \S Current address: Department of Education (Western Australia), Perth, Australia (brendan.
[email protected]). 1i.e., a wavelength-and direction-independent emitter. Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics.",
year = "2022",
doi = "10.1137/22M1476228",
language = "English",
volume = "82",
pages = "1356--1368",
journal = "SIAM Journal on Applied Mathematics",
issn = "0036-1399",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",
}