title: Non-steady-state heat conduction in composite walls.
abstract: 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.
authors.affiliation: Department of Applied Mathematics , University of Washington , Seattle, WA 98195-2420, USA.
authors.forename: Bernard
authors.initials: B
authors.lastname: Deconinck
authors.affiliation: Department of Mathematics , University of Reading , Reading RG6 6AX, UK.
authors.forename: Beatrice
authors.initials: B
authors.lastname: Pelloni
authors.affiliation: Department of Applied Mathematics , University of Washington , Seattle, WA 98195-2420, USA.
authors.forename: Natalie E
authors.initials: NE
authors.lastname: Sheils
keywords: Fokas method; composite walls; heat equation; interface problem; non-steady-state heat conduction