Heat and Mass Transfer in a Saturated Porous Medium Confined in Cylindrical Annular Geometry

This paper reports the numerical simulation of doublediffusive
natural convection flows within a horizontal annular filled
with a saturated porous medium. The analysis concerns the influence
of the different parameters governing the problem, namely, the
Rayleigh number Ra, the Lewis number Le and the buoyancy ratio N,
on the heat and mass transfer and on the flow structure, in the case of
a fixed radius ratio R = 2. The numerical model used for the
discretization of the dimensionless equations governing the problem
is based on the finite difference method, using the ADI scheme. The
study is focused on steady-state solutions in the cooperation situation.





References:
[1] M. Mamou, P. Vasseur and M. Hasnaoui, "On numerical stability
analysis of double diffusive convection in confined enclosures," Journal
of Fluid Mechanics, Vol. 433, pp. 209-250, 2001.
[2] D. B. Rafael, E. Crespo del Arco, P. Bontoux and J. Ouazzani,
"Convection and instabilities in differentially heated inclined shallow
rectangular boxes," C. R. Acad. Sci. Paris, t. 326, Serie II B, pp. 711-
718, 1998.
[3] D. Gobin and R. Bennacer, "Cooperating thermosolutal convection in
enclosures - II. Heat transfer and flow structure," Int. J. Heat Mass
Transfer, Vol. 39, No. 13, pp. 2683-2697, 1996.
[4] O. V. Trevisan and A. Bejan, "Natural convection with combined heat
and mass transfer buoyancy effects in a porous medium," Int. J. Heat
Mass Transfer, Vol. 38, No. 8, pp. 1597-1611, 1985.
[5] F. Alavyon, "On natural convection in vertical porous enclosures due to
prescribed fluxes of heat and mass at the vertical boundaries," Int. J.
Heat Mass Transfer, Vol. 36, No. 10, pp. 2479-2498, 1993.
[6] M. Hasnaoui, P. Vasseur, E. Bilgen and L.Robillard, "Analytical and
numerical study of natural convection heat transfer in a vertical porous
annulus," Chen. Eng. Comm., Vol. 136, pp. 77-94, 1995.
[7] M. Marcoux, M.-C Charrier-Mojtabi and M. Azaiez, "Double diffisive
convection in an annular vertical porous layer," Int. J. Heat and Mass
Transfer, Vol. 42, pp. 2313-2315, 1999.
[8] H. Beji, R. Bennacer and R. Duval, "Double-diffisive natural convection
in a vertical porous annulus," Num. Heat Transfer, Part A, Vol. 36, pp.
153-170, 1999.
[9] P. W. Shipp, M. Shoukri, and M. B. Carver, "Double diffusive natural
convection in a closed annulus," Num. Heat Transfer, Vol. 24, pp. 339–
356, 1993.
[10] S. Chen, J. Tolke, and M. Krafczyk, "Numerical investigation of doublediffusive
(natural) convection in vertical annuluses with opposing
temperature and concentration gradients," Int. J. Heat Fluid Flow, Vol.
31, pp. 217-226, 2010.
[11] J. Belabid and A.Cheddadi, "Comparative Numerical Simulation of
Natural Convection in a Porous Horizontal Cylindrical Annulus,"
Applied Mechanics and Materials, Vol. 670 - 671, pp. 613 - 616, 2014.
[12] F. A. Hamad and M. K. Khan, "Natural Convection Heat Transfer in
Horizontal and Inclined Annulus of Different Diameter Ratios," Energy
Convers. Mgmt, Vol. 39, No. 8, pp. 797-807, 1998.
[13] H. H. Bau, G. McBlane, and I. Sarferstein, "Numerical simulation of
thermal convection in an eccentric annulus containing porous media",
ASME 83 WA/HT 34, 1983.
[14] M. C. Charrier-Mojtabi, "Numerical simulation of two- and three
dimensional free convection flows in a horizontal porous annulus using
a pressure and temperature formulation," Int. J. Heat Mass Transfer. Vol.
40, No. 7, pp. 1521-1533, 1997.
[15] G. Desrayaud, A. Fichera, M. Marcaux, and A. Pagano, "An analytical
solution for the stationary behaviour of binary mixtures and pure fluids
in a horizontal annular cavity," Int. J. Heat and Mass Transfer, Vol. 49,
pp. 3253-3263, 2006.
[16] Z. Alloui, and P. Vasseur, "Natural convection in a horizontal Annular
porous cavity saturated by a binary mixture," Computational Thermal
Sciences, Vol. 3(5), pp. 407-417, 2011.