Near-Exact Radiating Fins via Boundary Tracing

Conway Li, Neville Fowkes, Brendan Florio, Miccal Matthews

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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.

Original languageEnglish
Pages (from-to)1356-1368
Number of pages13
JournalSIAM Journal on Applied Mathematics
Issue number4
Publication statusPublished - 2022


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