Double Diffusive Natural Convection in Non-Darcy Porous Media with Non-Uniform Porosity


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Abstract


We studied in this paper the phenomena of double-diffusive convection in a cylindrical enclosure filled with a porous medium saturated with a Newtonian fluid. The porosity of the porous media is variable from the walls to the bulk and follows an exponential law. The enclosure is heated from below and two mass concentrations C0, C1 are applied respectively to the surfaces (bottom, top) of the cylinder. The vertical walls are rigid, impermeable and adiabatic. An extended law of Brinkman-Forchheimer (EBFD) describes the fluid flow occurring in the porous layers by using the Boussinesq approximation. The mass concentration follows the basic Fick law, and the model chosen to describe the heat transfer is based on the approximation of one temperature. The heat and mass flow are controlled by the dimensionless numbers such as Rayleigh, Lewis, Darcy, Prandtl number that appear by dimensionless of the system of equations. The finites differences method is used to solve numerically the problem. The study focused on the effect of the dimensionless numbers on the concentrations and on the rate of heat transfers profiles in the overall Nusselt number, while considering the porosity uniform or non-uniform. The numerical code developed can be used for various industrial processes involving the phenomenon of natural convection
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Keywords


Natural Convection; Porous Media; Variable Porosity; Cylindrical Cavity; Extended Darcy Law

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References


M.Kaviany « Principles of Heat Transfert in Porous Media » Second Edition, New York, 1995, USA

Donald A. Nield, Adrian Bejan, « Convection in Porous Media» Third Edition, New York, USA , 2006.
http://dx.doi.org/10.1007/978-1-4757-2175-1

Zoltán E. Heinemann, « Fluid Flow in Porous Media » Leoben, October 2005.

Marcelo J.S. de Lemos « Turbulence in Porous Media Modeling and Applications » First Edition, Great Britain, 2006.
http://dx.doi.org/10.1016/b978-0-08-098241-0.00016-4

Kambiz Vafai , « HandBook of Porous Media » second Edition, United States of America , 2005.
http://dx.doi.org/10.1201/9780415876384

Derek B.Ingham & Ioan Pop « Transport Phenomena in Porous Media » First Edition, Netherlands, 2002.
http://dx.doi.org/10.1016/b978-008042843-7/50000-3

C. Béghin, F. Haghighat et F. Allard, Numerical study of double-diffusive natural convection in a square cavity, Int. J. Heat Mass Transfer, 35 (1992), 833-846.
http://dx.doi.org/10.1016/0017-9310(92)90251-m

H. Han et T. H. Kuehn, Double Diffusive Natural Convection in a Vertical Rectangular Enclosure, I. Experimental Study, Int. J. Heat Mass Transfer, 34-2 (1991), 449-459.
http://dx.doi.org/10.1016/0017-9310(91)90264-f

J. Kramer, Boundary domain integral method for the study of double diffusive natural convection in porous media, Engineering Analysis with Boundary Elements, 31 (2007) 897–905
http://dx.doi.org/10.1016/j.enganabound.2007.04.001

S. Sivasanka and all, Double diffusive convection of anomalous density fluids in a porous cavity, Transp Porous Med (2008) 71:133–145
http://dx.doi.org/10.1007/s11242-007-9114-7

Luzia A. and all, Double-diffusive turbulent natural convection in a porous square cavity with opposing temperature and concentration gradients, Int. Communications in Heat and Mass Transfer 36 (2009) 991–995
http://dx.doi.org/10.1016/j.icheatmasstransfer.2009.06.018

Shohel Mahmud and all, Mixed convection in a square vented enclosure filled with a porous medium, International Journal of Heat and Mass Transfer 49 (2006) 2190–2206
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2005.11.022

Ching-Yang Cheng, Natural convection heat and mass transfer from a vertical truncated cone in a porous medium saturated with a non-Newtonian fluid with variable wall temperature and concentration, International Communications in Heat and Mass Transfer 36 (2009) 585–589
http://dx.doi.org/10.1016/j.icheatmasstransfer.2009.03.011

D. Gobin, B. Goyeau and J. P. Songbe, Double diffusive naturel convection in a composite fluid-porous layer, Trans. ASME, J. of Heat Transfer, 120 (1998), 234-242.
http://dx.doi.org/10.1115/1.2830047

S.V. Patankar « Numerical Heat Transfer and Fluid Flow» , Hemisphere, New York, 1980.
http://dx.doi.org/10.1002/cite.330530323

Driouich, M., Gueraoui, K., Haddad, Y.M., Sammouda, M., El Hammoumi, A., Kerroum, M., Taibi, M., Fassi Fehri, O., Numerical and theoretical modelling of unsteady flows for incompressible fluid in rigid conducts. Application to molten polymers flow, (2010) International Review on Modelling and Simulations (IREMOS), 3 (6), pp. 1317-1323.

Driouich, M., Gueraoui, K., Haddad, Y.M., Hammoumi, A.E., Kerroum, M., Fehri, O.F., Mathematical modeling of non permanent flows of molten polymers, (2010) International Review of Mechanical Engineering (IREME), 4 (6), pp. 689-694.

K. Gueraoui and all « Modélisation théorique d'écoulements pulsés de fluides non newtoniens en conduites viscoélastiques poreuses et anisotropes » C. r. Acad. sci. Ser. 2. Fasc. b. 1998. 326, N 9, pp. 561-568.
http://dx.doi.org/10.1016/s1251-8069(98)80021-5

Kamal Gueraoui, Bennasser Bahrar, Gamal Zeggwagh, The Shape and the Motion of the Barchan Dunes in the Field of Laayoune, (2009) International Review on Modelling and Simulations (IREMOS), 2 (5), pp. 588-594.

Sammouda, M., Gueraoui, K., Driouich, M., El Hammoumi, A., Brahim, A.I., The variable porosity effect on the natural convection in a non-darcy porous media, (2011) International Review on Modelling and Simulations (IREMOS), 4 (5), pp. 2701-2707.

A .Mrabti, simulation numérique d’écoulement de convection naturelle dans une géométrie cylindrique a axe verticale soumise a l’effet d’un champ magnétique ou d’un gradient solutal, Thèse, Faculté des Sciences Rabat, Agdal, Maroc 1999.


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