Heat equation on a network using the Fokas method. (29th July 2015)

• Record Type: Journal Article
• Authors: Sheils, N E; Smith, D A
• Is Part Of: Journal of physics. Volume 48:Number 33(2015)
• Publication Date: 2015-07-29
• Subjects: unified transform method -- interface problem -- partial differential equation -- diffusion equation -- Fokas method; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/48/33/335001
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: The problem of heat conduction on networks of multiply connected rods is solved by providing an explicit solution of the one-dimensional heat equation in each domain. The size and connectivity of the rods is known, but neither temperature nor heat flux are prescribed at the interface. Instead, the physical assumptions of continuity at the interfaces are the only conditions imposed. This work generalizes that of Deconinck et al ( Proc. R. Soc. A 470 22) for heat conduction on a series of one-dimensional rods connected end-to-end to the case of general configurations.