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Li, Conway; Fowkes, Neville; Florio, Brendan; Matthews, Miccal

Near-exact radiating fins via boundary tracing. (English) Zbl 1497.35160

SIAM J. Appl. Math. 82, No. 4, 1356-1368 (2022).
Summary: 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.

MSC:

35J25 Boundary value problems for second-order elliptic equations
35J60 Nonlinear elliptic equations
35J65 Nonlinear boundary value problems for linear elliptic equations

Keywords:

boundary tracing; flux boundary condition; nonlinearity; thermal radiation

Software:

DLMF
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Full Text: DOI

References:

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