Double Diffusive Convection in a Partially Porous Cavity under Suction/Injection Effects

Double-diffusive steady convection in a partially porous cavity with partially permeable walls and under the combined buoyancy effects of thermal and mass diffusion was analysed numerically using finite volume method. The top wall is well insulated and impermeable while the bottom surface is partially well insulated and impermeable and partially submitted to constant temperature T1 and concentration C1. Constant equal temperature T2 and concentration C2 are imposed along the vertical surfaces of the enclosure. Mass suction/injection and injection/suction are respectively considered at the bottom of the porous centred partition and at one of the vertical walls. Heat and mass transfer characteristics as streamlines and average Nusselt numbers and Sherwood numbers were discussed for different values of buoyancy ratio, Rayleigh number, and injection/suction coefficient. It is especially noted that increasing the injection factor disadvantages the exchanges in the case of the injection while the transfer is augmented in case of suction. On the other hand, a critical value of the buoyancy ratio was highlighted for which heat and mass transfers are minimized.

Authors:

• Y. Outaleb
• K. Bouhadef
• O. Rahli

Keywords:

• Double diffusive convection
• Injection/Extraction
• Partially porous cavity

References:

[1] D. B. Ingham, I. Pop, Transport Phenomena in Porous Media, Pergamon,
Oxford,1998.
[2] K. Vafai, Handbook of Porous Media, Marcel Dekker, New York, 2000.
[3] I. Pop, D.B. Ingham, Convective Heat Transfer: Mathematical and
Computational Modeling of Viscous Fluid and Porous Media, Pergamon,
Oxford, 2001.
[4] M. Mharzi, M. Daguenet, S. Daoudi, "Thermosolutal natural convection
in a vertically layered fluid-porous medium heated from the side". Energy
Conversion and Management, Vol.41, pp.1065-1090, 2000.D. Seguin,
"Etude expérimentale dans les milieux poreux", Thèse de Doctorat, EPSI
de Nantes, 1997
[5] O. Rahli, K. Bouhadef, "Convection naturelle thermosolutale dans une
cavité compartimentée par une cloison poreuse". 6éme Congrès de
Mécanique, Tanger, 2003
[6] N. H. Saeid, I. Pop, "Transient free convection in a square cavity filled
with porous medium", Int. J. Heat Mass Transfer 47 (2004) 1917-1924.
[7] E. Baez, A. Nicolas, "2D natural convection flows in tilted cavities:
Porous media and homogeneous fluids". International Journal of Heat
and Mass Transfer 49, pp4773-4785, 2006.
[8] R. Bennacer, A. Tobbal, H. Beji, & B. Vasseur, "Double diffusive
convection in vertical enclosure filled with anisotropic porous media",
Int. J. Therm. Sci. Vol. 40, pp 30-41, 2001.
[9] N. J. Rabadi., E. M. Hamdan, "Free convection from inclined permeable
walls embedded in variable permeability porous media with lateral mass
flux". Journal of Petroleum Science and Engineering 26, pp 241-251,
2000.
[10] E. Magyari, B. Keller, "Exact analytic solutions for free convection
boundary layers on a heated vertical plate with lateral mass flux
embedded in a saturated porous medium". Heat and Mass Transfer 36,
pp. 109-116, 2000.
[11] M. A. El Hakiem., "Combined convection in non-Newtonian fluid along
a non-isothermal vertical plate in a porous medium with lateral mass
flux". Heat and Mass Transfer 37, pp379- 385, 2001.
[12] B.V. Rathish Kumar, S.V.S.S.N.V.G. Krishna Murthy, "Mixed
convection in a non-Darcian fluid saturated square porous enclosure
under multiple suction effect" International Journal of heat and mass
transfer, 53 (2010) 5764-5773.
[13] M. P. Cheng, "The influence of lateral mass flux on free convection
boundary layers in saturated porous medium". International Journal of
Heat and Mass Transfer 20, pp201-206, 1977.