Heat conduction on the ring: Interface problems with periodic boundary conditions

Natalie E. Sheils; Bernard Deconinck

doi:10.1016/j.aml.2014.06.006

Heat conduction on the ring: Interface problems with periodic boundary conditions

Natalie E. Sheils, Bernard Deconinck

School of Mathematics

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19 Scopus citations

Abstract

The classical problem of heat conduction in one dimension on a composite ring is examined. The problem is formulated using the heat equation with periodic boundary conditions. We provide an explicit solution of this problem using the Method of Fokas. The location of the interfaces is known, but neither temperature nor heat flux are prescribed there. Instead, the physical assumption of continuity at the interface is imposed.

Original language	English (US)
Pages (from-to)	107-111
Number of pages	5
Journal	Applied Mathematics Letters
Volume	37
DOIs	https://doi.org/10.1016/j.aml.2014.06.006
State	Published - Nov 2014

Bibliographical note

Funding Information:
The authors thank Peter Olver for useful discussions. This work was generously supported by the National Science Foundation under grant NSF-DMS-1008001 (B.D.). N.E.S. acknowledges support from the National Science Foundation under grant number NSF-DGE-0718124 . Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding sources.

Keywords

Heat equation
Interface
Method of Fokas
Periodic boundary conditions

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10.1016/j.aml.2014.06.006

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title = "Heat conduction on the ring: Interface problems with periodic boundary conditions",

abstract = "The classical problem of heat conduction in one dimension on a composite ring is examined. The problem is formulated using the heat equation with periodic boundary conditions. We provide an explicit solution of this problem using the Method of Fokas. The location of the interfaces is known, but neither temperature nor heat flux are prescribed there. Instead, the physical assumption of continuity at the interface is imposed.",

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author = "Sheils, {Natalie E.} and Bernard Deconinck",

note = "Funding Information: The authors thank Peter Olver for useful discussions. This work was generously supported by the National Science Foundation under grant NSF-DMS-1008001 (B.D.). N.E.S. acknowledges support from the National Science Foundation under grant number NSF-DGE-0718124 . Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding sources.",

year = "2014",

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doi = "10.1016/j.aml.2014.06.006",

language = "English (US)",

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T1 - Heat conduction on the ring

T2 - Interface problems with periodic boundary conditions

AU - Sheils, Natalie E.

AU - Deconinck, Bernard

N1 - Funding Information: The authors thank Peter Olver for useful discussions. This work was generously supported by the National Science Foundation under grant NSF-DMS-1008001 (B.D.). N.E.S. acknowledges support from the National Science Foundation under grant number NSF-DGE-0718124 . Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding sources.

PY - 2014/11

Y1 - 2014/11

N2 - The classical problem of heat conduction in one dimension on a composite ring is examined. The problem is formulated using the heat equation with periodic boundary conditions. We provide an explicit solution of this problem using the Method of Fokas. The location of the interfaces is known, but neither temperature nor heat flux are prescribed there. Instead, the physical assumption of continuity at the interface is imposed.

AB - The classical problem of heat conduction in one dimension on a composite ring is examined. The problem is formulated using the heat equation with periodic boundary conditions. We provide an explicit solution of this problem using the Method of Fokas. The location of the interfaces is known, but neither temperature nor heat flux are prescribed there. Instead, the physical assumption of continuity at the interface is imposed.

KW - Heat equation

KW - Interface

KW - Method of Fokas

KW - Periodic boundary conditions

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VL - 37

SP - 107

EP - 111

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

Heat conduction on the ring: Interface problems with periodic boundary conditions

Abstract

Bibliographical note

Keywords

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