Kinematic regimes of convection at high Prandtl number in a shallow cavity

Jean-Marc Flesselles; Franck Pigeonneau

doi:10.1016/j.crme.2004.06.003

Kinematic regimes of convection at high Prandtl number in a shallow cavity

Presented by: Patrick Huerre

Jean-Marc Flesselles ¹ ; Franck Pigeonneau ¹

¹ Saint-Gobain Recherche, 39, quai Lucien Lefranc, 93303 Aubervilliers, France

Comptes Rendus. Mécanique, Volume 332 (2004) no. 10, pp. 783-788.

Abstract
Résumé

We consider free convection in a horizontal shallow cavity with different end temperatures, filled with a high Prandtl number fluid. From scaling analysis, we find two kinematic regimes resulting from the competition of heat transfer by conduction and by convection. Numerical simulations realized for a large range of Rayleigh number and aspect ratio confirm the phenomenological analysis and provide the threshold between the two regimes. The conductive and convective regimes occur at $Ra A^{2}$ smaller and larger than 443 respectively, where Ra is the Rayleigh number and A is the aspect ratio. In the convective regime, the characteristic velocity is independent of depth of the cavity.

Nous traitons de la convection naturelle dans une cavité horizontale allongée différentiellement chauffée selon les parois verticales, emplie d'un fluide à grand nombre de Prandtl. L'analyse d'échelles fait apparaître deux régimes cinématiques résultant de la compétition entre transfert de la chaleur par conduction et par convection. Des simulations numériques faites dans une large gamme de nombre de Rayleigh et de facteur de forme confirment l'analyse phénoménologique. Le régime conductif (resp. convectif) apparaît pour $Ra A^{2}$ inférieur (resp. supérieur) à 443, où Ra est le nombre de Rayleigh et A le facteur de forme. La loi d'échelle du régime convectif donne une vitesse caractéristique indépendante de la hauteur de la cavité.

Received: 2004-06-21
Published online: 2004-08-10

DOI: 10.1016/j.crme.2004.06.003

Keywords: Fluid mechanics, Natural convection, High Prandtl number
Mots-clés : Mécanique des fluides, Convection naturelle, Haut nombre de Prandtl

Author's affiliations:

Jean-Marc Flesselles ¹; Franck Pigeonneau ¹

¹ Saint-Gobain Recherche, 39, quai Lucien Lefranc, 93303 Aubervilliers, France

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     author = {Jean-Marc Flesselles and Franck Pigeonneau},
     title = {Kinematic regimes of convection at high {Prandtl} number in a shallow cavity},
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     year = {2004},
     doi = {10.1016/j.crme.2004.06.003},
     language = {en},
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Jean-Marc Flesselles; Franck Pigeonneau. Kinematic regimes of convection at high Prandtl number in a shallow cavity. Comptes Rendus. Mécanique, Volume 332 (2004) no. 10, pp. 783-788. doi : 10.1016/j.crme.2004.06.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.06.003/

References
Cited by

[1] G.K. Batchelor Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures, Q. Appl. Math., Volume 12 (1954), pp. 209-233

[2] B. Boehrer Convection in a long cavity with differentially heated end walls, Int. J. Heat Mass Transfer, Volume 40 (1997), pp. 4105-4114

[3] A. Bejan Convection Heat Transfer, Wiley, New York, 1995

[4] P. Germain Méthodes asymptotiques en mécanique des fluides, Fluid Dynamics, Gordon and Breach, London, 1977, pp. 1-147

[5] R.K. Zeytounian Modélisation asymptotique en mécanique des fluides newtoniens, Springer-Verlag, 1994

[6] D.E. Cormack; L.G. Leal; J. Imberger Natural convection in a shallow cavity with differentially heated end walls. Part 1. Asymptotic theory, J. Fluid Mech., Volume 65 (1974), pp. 209-229

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