Comptes Rendus
An example of entropy balance in natural convection, Part 2: the thermodynamic Boussinesq equations
Comptes Rendus. Mécanique, Volume 333 (2005) no. 2, pp. 133-138.

Numerical simulations of natural convection performed with the usual Boussinesq equations result in unbalanced irreversibility budget. The thermodynamic Boussinesq equations solve this problem, especially because they simulate production of kinetic energy within the fluid through its expansion and contraction. These fluid volume changes, without which natural convection would not occur, also induce heat transfer by piston effect. The piston effect, which appears then as an intrinsic component of buoyancy-induced natural convection, introduces the non-dimensional adiabatic temperature gradient as a control parameter of natural convection.

Les simulations numériques réalisées avec les équations de Boussinesq usuelles ne peuvent pas donner un bilan d'irréversibilité fermé. Les équations de Boussinesq thermodynamiques apportent une solution au problème, en particulier parce qu'elles incluent la production d'énergie cinétique à l'intérieur du fluide, par sa dilatation et contraction. Ces variations de volume du fluide, sans lesquelles la convection naturelle n'existerait pas, provoquent aussi un transfert de chaleur par effet piston. L'effet piston, qui apparaît alors consubstantiel à la convection naturelle, fait du gradient de température adiabatique adimensionné un des paramètres de contrôle de la convection naturelle.

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DOI: 10.1016/j.crme.2004.11.003
Keywords: Heat transfer, Fluid mechanics, Natural convection, Boussinesq, Thermodynamics, Irreversibility, Piston effect
Mot clés : Transferts thermiques, Mécanique des fluides, Convection naturelle, Boussinesq, Thermodynamique, Irréversibilités, Effet piston

Michel Pons 1; Patrick Le Quéré 1

1 Laboratoire d'informatique pour la mécanique et les sciences de l'ingénieur, CNRS-LIMSI, BP 133, bâtiment 508, campus universitaire, 91403 Orsay cedex, France
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Michel Pons; Patrick Le Quéré. An example of entropy balance in natural convection, Part 2: the thermodynamic Boussinesq equations. Comptes Rendus. Mécanique, Volume 333 (2005) no. 2, pp. 133-138. doi : 10.1016/j.crme.2004.11.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.11.003/

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