Comptes Rendus
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.

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:
Accepted:
Published online:
DOI: 10.1016/j.crme.2004.11.011
Keywords: Heat transfer, Fluid mechanics, Natural convection, Boussinesq, Thermodynamics, Irreversibility
Mot clés : Transferts thermiques, Mécanique des fluides, Convection naturelle, Boussinesq, Thermodynamique, Irréversibilités

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
@article{CRMECA_2005__333_2_127_0,
     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},
}
TY  - JOUR
AU  - Michel Pons
AU  - Patrick Le Quéré
TI  - An example of entropy balance in natural convection, Part 1: the usual Boussinesq equations
JO  - Comptes Rendus. Mécanique
PY  - 2005
SP  - 127
EP  - 132
VL  - 333
IS  - 2
PB  - Elsevier
DO  - 10.1016/j.crme.2004.11.011
LA  - en
ID  - CRMECA_2005__333_2_127_0
ER  - 
%0 Journal Article
%A Michel Pons
%A Patrick Le Quéré
%T An example of entropy balance in natural convection, Part 1: the usual Boussinesq equations
%J Comptes Rendus. Mécanique
%D 2005
%P 127-132
%V 333
%N 2
%I Elsevier
%R 10.1016/j.crme.2004.11.011
%G en
%F CRMECA_2005__333_2_127_0
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/

[1] M. Pons; P. Le Quéré An example of entropy balance in natural convection, Part 2: the thermodynamic Boussinesq equations, C. R. Mecanique 333 (2005) (in this issue) | DOI

[2] A. Oberbeck Über die Wärmeleitung der Flüssigkeiten bei Berücksichtigung der Strömungen infloge von Temperatur Differenzen, Ann. Phys. Chem., Volume 7 (1879), pp. 271-292

[3] J. Boussinesq Théorie analytique de la chaleur, Gauthier-Villars, Paris, 1903

[4] B. Gebhart; Y. Jaluria; R.L. Mahajan; B. Sammakia Buoyancy-induced flows and transport, Hemisphere, New York, 1988

[5] A. Bejan Convection Heat Transfer, Wiley, New York, 1984

[6] D.J. Tritton Physical Fluid Dynamics, Oxford University Press, Oxford, 1988

[7] E.A. Spiegel; G. Veronis On the Boussinesq approximation for a compressible fluid, Astrophys. J., Volume 131 (1960), pp. 442-447

[8] G. Veronis The magnitude of the dissipation terms in the Boussinesq approximation, Astrophys. J., Volume 135 (1962), pp. 655-656

[9] D.D. Gray; A. Giorgini The validity of the Boussinesq approximation for liquids and gases, Int. J. Heat Mass Transfer, Volume 19 (1976) no. 5, pp. 545-551

[10] A. Bejan Entropy Generation Through Heat and Fluid Flow, Wiley, New York, 1982

[11] D. Jou; J. Casas-Vázquez; G. Lebon Extended Irreversible Thermodynamics, Springer-Verlag, Berlin, 1996

[12] G. De Vahl Davis Natural convection of air in a square cavity: a bench mark numerical solution, Int. J. Numer. Methods Fluids, Volume 3 (1983), pp. 249-264

[13] P. Le Quéré Accurate solutions to the square thermally driven cavity at high Rayleigh number, Comput. Fluids, Volume 20 (1991) no. 1, pp. 29-41

[14] E. Gadoin; P. Le Quéré; O. Daube A general methodology for investigating flow instabilities in complex geometries: application to natural convection in enclosures, Int. J. Numer. Methods Fluids, Volume 37 (2001) no. 2, pp. 175-208

Cited by Sources:

Comments - Policy