An example of entropy balance in natural convection, Part 2: the <i>thermodynamic</i> Boussinesq equations

Michel Pons; Patrick Le Quéré

doi:10.1016/j.crme.2004.11.003

An example of entropy balance in natural convection, Part 2: the thermodynamic 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. 133-138.

Abstract
Résumé

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.

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

DOI: 10.1016/j.crme.2004.11.003

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

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} 2: the \protect\emph{thermodynamic} {Boussinesq} equations},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {133--138},
     publisher = {Elsevier},
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     number = {2},
     year = {2005},
     doi = {10.1016/j.crme.2004.11.003},
     language = {en},
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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/

References
Cited by

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

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

[3] 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

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

[5] J.A. Dutton; G.H. Fichtl Approximate equations of motion for gases and liquid, J. Atmos. Sci., Volume 26 (1969) no. 2, pp. 241-254

[6] J. Fröhlich; P. Laure; R. Peyret Large departures from Boussinesq approximation in the Rayleigh–Bénard problem, Phys. Fluids A, Volume 4 (1992) no. 7, pp. 1355-1372

[7] J. Vierendeels; B. Merci; E. Dick Numerical study of natural convective heat transfer with large temperature differences, Int. J. Numer. Methods Heat Fluid Flow, Volume 11 (2001) no. 4, pp. 329-341

[8] B. Gebhart; Y. Jaluria; R.L. Mahajan; B. Sammakia Buoyancy-Induced Flows and Transport, Hemisphere, New York, 1988

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

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

[11] B. Zappoli Near-critical fluid hydrodynamics, C. R. Mecanique, Volume 331 (2003) no. 10, pp. 713-726

[12] Y. Masuda; T. Aizawa; M. Kanakubo; N. Saito; Y. Ikushima Numerical simulation of two-dimensional piston effect and natural convection in a square cavity heated from one side, Int. Commun. Heat Mass Transfer, Volume 31 (2004) no. 2, pp. 151-160

[13] M. Gitterman Hydrodynamics of fluids near a critical point, Rev. Mod. Phys., Volume 50 (1978) no. 1, pp. 85-106 (Part I)

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