Comptes Rendus
no. 7
On the thermal anisotropy affecting transfers in a multilayer porous medium
[Sur l'effet de l'anisotropie thermique sur les transferts dans un milieu poreux multicouches]

Présenté par : René Moreau

Rachid Bennacer1  ; Mohammed El Ganaoui2  ; Pierre Fauchais2
1 LEEE-EEVAM, 5, mail Gay Lussac, Neuville sur Oise, 95031, Cergy-Pontoise, France
2 Faculté des sciences et techniques de Limoges, SPCTS UMR 6638 CNRS, 123, Albert Thomas, 87000 Limoges, France
Comptes Rendus. Mécanique, Volume 332 (2004) no. 7, pp. 539-546.

Un modèle analytique est développé pour l'étude de la convection double diffusive dans un milieu poreux multicouche thermiquement anisotrope et comparé à un modèle de simulation numérique directe. Le domaine composé de deux couches poreuses horizontales est soumis à un flux thermique horizontal et à un flux massique vertical, la couche inférieure est thermiquement anisotrope. L'hypothèse d'un écoulement parallèle est validée et l'effet de l'anisotropie sur les transitions dynamiques est qualifié.

An analytical model for studying double-diffusive natural convection within a multilayer anisotropic porous medium is developed and validated with respect to a direct numerical silmulation. The studied domain is composed of two horizontal porous layers where the lower one is thermally anisotropic and is submitted to a uniform horizontal heat flux and a vertical mass flux. The assumption of parallel flow is validated and the effect of anisotropy on dynamic transitions is investigated.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2004.03.002
Keywords: Fluid mechanics, Multilayer porous media, Instability and transition
Mot clés : Mécanique des fluides, Milieu poreux multicouches, Instabilité et transition
Rachid Bennacer 1 ; Mohammed El Ganaoui 2 ; Pierre Fauchais 2

1 LEEE-EEVAM, 5, mail Gay Lussac, Neuville sur Oise, 95031, Cergy-Pontoise, France
2 Faculté des sciences et techniques de Limoges, SPCTS UMR 6638 CNRS, 123, Albert Thomas, 87000 Limoges, France 
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Rachid Bennacer; Mohammed El Ganaoui; Pierre Fauchais. On the thermal anisotropy affecting transfers in a multilayer porous medium. Comptes Rendus. Mécanique, Volume 332 (2004) no. 7, pp. 539-546. doi : 10.1016/j.crme.2004.03.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.03.002/

[1] D.A. Nield; A. Bejan Convection in Porous Media, Springer-Verlag, 1999

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[3] F. Alavyoon; Y. Masuda; S. Kimura On natural convection in vertical porous enclosures due to opposing fluxes of heat and mass prescribed at the vertical walls, Int. J. Heat Mass Transfer, Volume 37 (1994), pp. 195-206

[4] R. Bennacer; H. Beji; R. Duval; P. Vasseur The Brinkman model for thermosolutal convection in a vertical annular porous layer, Int. Commun. Heat Mass Transfer, Volume 27 (2000) no. 1, pp. 69-80

[5] M. Mamou; P. Vasseur; E. Bilgen Double-diffusive convection instability in a vertical porous enclosure, J. Fluid Mech., Volume 368 (1998), pp. 263-289

[6] R. Bennacer; A. Tobbal; H. Beji; P. Vasseur Double diffusive convection in a vertical enclosure filled with anisotropic porous media, Int. J. Thermal Sci., Volume 40 (2001), pp. 30-42

[7] R. Bennacer, M. El Ganaoui, P. Fauchais, Double diffusive convection within a multilayer anisotropic horizontal porous layer submitted to cross gradients, in: R. Bennacer, A. Mohamad (Eds.), First International Conference Applications of Porous Media, Djerba, 4–8 Juin, 2002, CD-ROM (6 p.)

[8] R. Bennacer; H. Beji; F. Oueslati; A. Belghith Multiple natural convection solution in porous media under cross temperature and concentration gradients, Numer. Heat Transfer Part A, Volume 39 (2001), pp. 553-567

[9] L. Kalla; P. Vasseur; R. Bennacer; H. Beji; R. Duval Double diffusive convection in a horizontal porous layer salted from the bottom and heated horizontally, Int. Commun. Heat Mass Transfer, Volume 28 (2001), pp. 1-10

[10] S.V. Patankar Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, DC, 1980

[11] A. Tobbal; R. Bennacer Heat and mass transfer in anisotropic porous layer research trend heat, Mass and Momentum Transfer, Volume 3 (1998), pp. 129-137

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