Non-steady-state heat conduction in composite walls

The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but neither temperature nor heat flux is prescribed there. Instead,...

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Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2014-05, Vol.470 (2165), p.1-22
Main Authors: Deconinck, Bernard, Pelloni, Beatrice, Sheils, Natalie E.
Format: Article
Language:English
Subjects:
Applied mathematics
Boundary conditions
Conductive heat transfer
Contour lines
Fourier transformations
Heat equation
Heat flux
Heat transfer
Integrands
Real lines
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Summary:The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but neither temperature nor heat flux is prescribed there. Instead, the physical assumptions of their continuity at the interfaces are the only conditions imposed. The problem of two semi-infinite domains and that of two finite-sized domains are examined in detail. We indicate also how to extend the solution method to the setting of one finite-sized domain surrounded on both sides by semi-infinite domains, and on that of three finite-sized domains.
ISSN:1364-5021