Analysis of Heat and Mass Transfer in a Porous Cavity Containing Water near Its Density Maximum
Murugan Muthtamilselvan
DOI: 10.4236/am.2011.28127   PDF   HTML     4,977 Downloads   10,025 Views   Citations


A numerical study is performed on steady natural convection inside a porous cavity with cooling from the side walls. The governing equations are solved by finite volume method. Representative results illustrating the effects of the thermal Rayleigh number, density inversion parameter, buoyancy ratio and Schmidt number on the contour maps of the fluid flow, temperature and concentration are reported. It is found that the number of cells which form in the cavity varies primarily with the density inversion parameter and is always even due to the symmetry imposed by the cold sidewalls. In addition that the flow becomes weaker as the Darcy number decreases from the pure fluid limit towards the Darcy-flow limit.

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M. Muthtamilselvan, "Analysis of Heat and Mass Transfer in a Porous Cavity Containing Water near Its Density Maximum," Applied Mathematics, Vol. 2 No. 8, 2011, pp. 927-934. doi: 10.4236/am.2011.28127.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] D. A. Nield and A. Bejan, “Convection in Porous Media (Third Edition),” Springer-Verlag, New York, 2006.
[2] K. Vafai, “Handbook of Porous Media,” 2nd Edition, Marcel Dekker Inc., New York, 2005. doi:10.1201/9780415876384
[3] F. Alavyoon, “On Natural Convection in Vertical Porous Enclosures Due to Prescribed Fluxes of Heat and Mass Transfer at the Vertical Boundaries,” International Journal of Heat and Mass Transfer, Vol. 36, No. 10, 1993, pp. 2479-2498. doi:10.1016/S0017-9310(05)80188-7
[4] M. Mamou, P. Vasseur and E. Bilgen, “Multiple Solution for Double-Diffusive Convection on a Vertical Porous Enclosure,” International Journal of Heat and Mass Transfer, Vol. 38, No. 10, 1995, pp. 1787-1798. doi:10.1016/0017-9310(94)00301-B
[5] M. Nishimura, M. Wakamatsu and A. M. Morega, “Oscillatory Double-Diffusive Convection in a Rectangular Enclosure with Combined Horizontal Temperature and Concentration Gradients,” International Journal of Heat and Mass Transfer, Vol. 41, No. 11, 1998, pp. 1601-1611. doi:10.1016/S0017-9310(97)00271-8
[6] I. Sezai and A. A. Mohamad, “Three-Dimensional Double-Diffusive Convection in a Porous Cubic Enclosure Due to Opposing Gradients of Temperature and Concentration,” The Journal of Fluid Mechanics, Vol. 400, 1999, pp.333-353. doi:10.1017/S0022112099006540
[7] M. W. Nansteel, K. Medjani and D. S. Lin, “Natural convection of Water near Its Density Maximum in Ractangular Enclosure: Low Rayleigh Number Calculations,” Physics of Fluids, Vol. 30, No. 2, 1987, pp. 312-317. doi:10.1063/1.866379
[8] A. Mahidjiba, L. Robillard and P. Vasseur, “On Set of Convection in a Horizontal Anisotropic,” International Communications in Heat and Mass Transfer, Vol. 27, No. 6, 2000, pp. 765-774. doi:10.1016/S0735-1933(00)00157-3
[9] R. Bennacer, A. Tobbal, H. Beji and P. Vasseur, “Double Diffusive Convection in a Vertical Enclosure Filled with Anisotropic Porous Media,” International Journal of Thermal Sciences, Vol. 40, No. 1, 2001, pp. 30-41. doi:10.1016/S1290-0729(00)01185-6
[10] M. Muthtamilselvan, M. K. Das and P. Kandaswamy, “Convection in a Lid-Driven Heat Generating Porous Cavity with Alternative Thermal Boundary Conditions,” Transport in Porous Media, Vol. 82, No. 2, 2010, pp. 337-346. doi:10.1007/s11242-009-9429-7
[11] S. V. Patankar, “Numerical Heat Transfer and Fluid Flow,” Hemisphere, Washington DC, 1980.
[12] T. Hayase, J. A. C. Humphrey and R. Grief, “A Consistently Formulated QUICK Scheme for Fast and Stable Convergence Using Finite-Volume Iterative Procedures,” Journal of Computational Physics, Vol. 98, No. 1, 1992, pp. 108-118. doi:10.1016/0021-9991(92)90177-Z
[13] P. Kandaswamy, M. Muthtamilselvan and J. Lee, “Prandtl Number Effects on Mixed Convection in a Lid- Driven Porous Cavity,” Journal of Porous Media, Vol. 11, 2008, pp. 791-801. doi:10.1615/JPorMedia.v11.i8.70

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