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Mathematical issues concerning the Boussinesq approximation for thermally coupled viscous flows
Author(s) -
Díaz J. Ildefonso,
Rakotoson JeanMichel,
Schmidt Paul G.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700471
Subject(s) - dissipative system , boussinesq approximation (buoyancy) , buoyancy , energy–momentum relation , momentum (technical analysis) , conservation law , energy balance , flow (mathematics) , classical mechanics , conservation of energy , mechanics , physics , mathematics , heat transfer , thermodynamics , mathematical analysis , economics , natural convection , finance , rayleigh number
The flow of a viscous fluid driven by buoyancy forces is governed by balance equations for momentum, mass, and internal energy. Frequently, the Boussinesq approximation is employed to simplify the system, even in situations where dissipative heating cannot be neglected. The resulting equations violate the principle of conservation of total energy, which causes significant mathematical problems. We discuss these problems and possible remedies. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)