Mathematical issues concerning the Boussinesq approximation for thermally coupled viscous flows |
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| Authors: | J Ildefonso Díaz Jean-Michel Rakotoson Paul G Schmidt |
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| Institution: | 1. Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain;2. Laboratoire de Mathématiques et Applications, Université de Poitiers, 86962 Futuroscope Chasseneuil cedex, France;3. Department of Mathematics and Statistics, Auburn University, AL 36849-5310, USA |
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| Abstract: | 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) |
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