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Incorporating boundary conditions in the heat conduction model

โœ Scribed by V. Bertola; E. Cafaro

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
140 KB
Volume
52
Category
Article
ISSN
0017-9310

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โœฆ Synopsis

This note introduces a mathematical derivation of the heat conduction model that incorporates boundary conditions. In particular, in the present approach boundary conditions are derived in parallel to the heat equation, while in the standard approach to heat conduction modelling they are appended at a later stage. Because of its peculiar mathematical formulation, this method allows modelling heat sources or sinks placed on the boundary. Furthermore, it is shown that when such heat sources depend linearly on the surface temperature and the heat flux, each of their points can be described as a point source emitting a heat wave directed into an infinitesimal volume in the neighbourhood of the surface.

๐Ÿ“œ SIMILAR VOLUMES

Heat conduction with radiating boundary
Heat conduction with radiating boundary conditions
โœ R.B. Guenther; J.W. Lee ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 279 KB

Existence of positive solutions is established for a class of nonlinear boundary value problems that include steadystate heat conduction problems with radiation at the boundary according to the fourth power radiation law. Existence is established using topological methods and a priori bounds.