On spreading resistance for an isothermal source on a compound flux channel
On spreading resistance for an isothermal source on a compound flux channel
Recently, Jain [ASME J. Heat Mass Transfer, 220 (2024)] provided spreading-resistance formulas for an isothermal source on compound, orthotropic, semi-infinite, two-dimensional (axisymmetric) flux channels (tubes). The boundary condition (BC) in the source plane was a discontinuous convection (Robin) one. Along the source, a sufficiently large heat transfer coefficient was imposed to approximate an isothermal condition; elsewhere, it was set to zero, imposing an adiabatic BC. An eigenfunction expansion resolved the problem. Distinctly, we impose, precisely, a mixed isothermal-adiabatic BC in the source plane and use conformal maps to resolve the spreading resistance for the limiting case of a compound, isotropic flux channel. Our complimentary approach requires more time to compute the spreading resistance. However, it converges uniformly rather than pointwise, converges to the exact spreading resistance rather than one with an error, eliminates the Gibbs phenomenon at the edges of the source and fully resolves the square-root singularities in heat flux as the discontinuity in the BC is approached.
Miyoshi, Hiroyuki
5166135b-8fab-4c16-a310-b5b11eed680d
Kirk, Toby L.
7bad334e-c216-4f4a-b6b3-cca90324b37c
Hodes, Marc
31732b12-8b18-4b0e-9bc8-6dc690229ae9
12 June 2025
Miyoshi, Hiroyuki
5166135b-8fab-4c16-a310-b5b11eed680d
Kirk, Toby L.
7bad334e-c216-4f4a-b6b3-cca90324b37c
Hodes, Marc
31732b12-8b18-4b0e-9bc8-6dc690229ae9
Miyoshi, Hiroyuki, Kirk, Toby L. and Hodes, Marc
(2025)
On spreading resistance for an isothermal source on a compound flux channel.
ASME Journal of Heat and Mass Transfer, 147 (9), [091403].
(doi:10.1115/1.4068640).
Abstract
Recently, Jain [ASME J. Heat Mass Transfer, 220 (2024)] provided spreading-resistance formulas for an isothermal source on compound, orthotropic, semi-infinite, two-dimensional (axisymmetric) flux channels (tubes). The boundary condition (BC) in the source plane was a discontinuous convection (Robin) one. Along the source, a sufficiently large heat transfer coefficient was imposed to approximate an isothermal condition; elsewhere, it was set to zero, imposing an adiabatic BC. An eigenfunction expansion resolved the problem. Distinctly, we impose, precisely, a mixed isothermal-adiabatic BC in the source plane and use conformal maps to resolve the spreading resistance for the limiting case of a compound, isotropic flux channel. Our complimentary approach requires more time to compute the spreading resistance. However, it converges uniformly rather than pointwise, converges to the exact spreading resistance rather than one with an error, eliminates the Gibbs phenomenon at the edges of the source and fully resolves the square-root singularities in heat flux as the discontinuity in the BC is approached.
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Miyoshi_et_al_2025_JHMT_author_accepted
- Accepted Manuscript
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Accepted/In Press date: 29 April 2025
Published date: 12 June 2025
Identifiers
Local EPrints ID: 504149
URI: http://eprints.soton.ac.uk/id/eprint/504149
ISSN: 2832-8450
PURE UUID: ec4a4c28-6d62-4c5f-a471-228cf0a83340
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Date deposited: 28 Aug 2025 16:30
Last modified: 29 Aug 2025 02:18
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Author:
Hiroyuki Miyoshi
Author:
Toby L. Kirk
Author:
Marc Hodes
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