An example of entropy balance in natural convection, Part 1: the <i>usual</i> Boussinesq equations

Michel Pons; Patrick Le Quéré

doi:10.1016/j.crme.2004.11.011

An example of entropy balance in natural convection, Part 1: the usual Boussinesq equations

Presented by: Sébastien Candel

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

Comptes Rendus. Mécanique, Volume 333 (2005) no. 2, pp. 127-132.

Abstract
Résumé

Numerical simulations of natural convection in cavities performed with the usual Boussinesq equations result in an unbalanced irreversibility budget. Thermodynamic analysis shows that these equations represent a system that exchanges with the surroundings, not only two heat fluxes, but also two fluxes of mechanical energy: an input, that generates the fluid motion, and an output, due to viscous friction. After this analysis, the thermodynamic discrepancies can be explained.

. Les simulations numériques réalisées avec les équations de Boussinesq usuelles ne peuvent pas donner un bilan d'irréversibilités fermé. L'analyse thermodynamique démontre que ces équations représentent un système qui échange avec l'extérieur, en plus des deux flux de chaleur, deux flux d'énergie mécanique : un flux entrant, qui est la source du mouvement du fluide, un flux sortant, qui est dû à la friction visqueuse. Grâce à cette analyse, les incohérences thermodynamiques trouvent une explication.

Received: 2004-04-06
Accepted: 2004-10-28
Published online: 2005-01-08

DOI: 10.1016/j.crme.2004.11.011

Keywords: Heat transfer, Fluid mechanics, Natural convection, Boussinesq, Thermodynamics, Irreversibility
Mots-clés : Transferts thermiques, Mécanique des fluides, Convection naturelle, Boussinesq, Thermodynamique, Irréversibilités

Author's affiliations:

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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     author = {Michel Pons and Patrick Le Qu\'er\'e},
     title = {An example of entropy balance in natural convection, {Part} 1: the \protect\emph{usual} {Boussinesq} equations},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {127--132},
     publisher = {Elsevier},
     volume = {333},
     number = {2},
     year = {2005},
     doi = {10.1016/j.crme.2004.11.011},
     language = {en},
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Michel Pons; Patrick Le Quéré. An example of entropy balance in natural convection, Part 1: the usual Boussinesq equations. Comptes Rendus. Mécanique, Volume 333 (2005) no. 2, pp. 127-132. doi : 10.1016/j.crme.2004.11.011. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.11.011/

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