Incorporating boundary conditions in the heat conduction model

V. Bertola, E. Cafaro

Research output: Contribution to journalArticlepeer-review


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. (C) 2008 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)644-646
Number of pages3
JournalInternational journal of heat and mass transfer
Issue number3-4
Publication statusPublished - 31 Jan 2009


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