Double diffusive natural convection in a partially layered cavity with inner solid conductive body

Document Type : Article


Mechanical Engineering Department, Engineering College, University of Basrah, Basrah, Iraq


This paper investigates the double–diffusive natural convection in partially layered square cavity. The cavity composed of porous layer on the left and fluid layer on the right. A conductive solid body is included inside the cavity to control the natural convection. The left wall is kept at constant high temperature and adjusted with high concentration, while the right wall is kept at low temperature and low concentration. The horizontal walls are thermally insulated. The 2-dimensional governing equations have been solved using up-wind scheme finite difference method. The Parndtl number and buoyancy ratio are fixed at 6.26 and 1, respectively. The problem has been governed by five parameters namely, Lewis number (Le = 1–50), Rayleigh number Ra (103-106), Darcy number (10-9-1), aspect ratio of the body relative to the cavity A (0.3, 0.5) and the position of the body. The results have showed that locating the solid body close to the mid height of the left wall gives maximum convective heat transfer, while minimum heat transfer is associated when the solid body is located at the cavity center. It is also found that the Nusselt and Sherwood numbers behave contradictory with the location of the solid body.


Main Subjects

1. Ingham, D.B. and Pop, I. (Eds.), Transport Phenomena
in Porous Media II, 1st Ed., Pergamon (2002).
2. Baytas, A.C, Baytas, A.F., Ingham, D.B., and Pop,
I. \Double di usive natural convection in an enclosure
lled with a step type porous layer: Non-Darcy
Int. J. Therm. Sci., 48, pp. 665-673 (2009).
3. Hirata, S.C., Goyeau, B., and Gobin, D. \Stability of
thermosolutal natural convection in superposed
and porous layers", Transp. Porous Media, 78, pp. 525-
536 (2009).
4. Islam, A.W., Sharif, A.R., and Carlson, E.S. \Numerical
investigation of double di usive natural convection
of CO2 in a brine saturated geothermal reservoir",
Geothermics, 48, pp. 101-111 (2013).
5. Hadidi, N., Bennacer, R., and Ould-amer, Y. \Twodimensional
thermo-solutal natural convective heat
and mass transfer in a bi-layered and inclined porous
enclosure", Energy, 93, pp. 2582-2592 (2015).
6. Mharzi, M., Daguenet, M., and Daoudi, S. \Thermosolutal
natural convection in a vertically layered
medium heated from the side", Energy Conversion
and Management, 41, pp. 1065-1090 (2000).
7. Bennacer, R., Beji, H., and Mohamad, A.A. \Double
di usive convection in a vertical enclosure inserted
with two saturated porous layers con ning a
layer", Int. J. Therm. Sci., 42, pp. 141-151 ( 2003).
8. Gobin, D., Goyeau, B., and Neculae, A. \Convective
heat and solute transfer in partially porous cavities",
Int. J. Heat Mass Transfer, 48, pp. 1898-1908 (2005).
9. Outaleb, Y., Bouhadef, K., and Rahli, O. \Double
di usive convection in a partially porous cavity under
suction/injection e ects", World Academy of Science,
Engineering and Technology, 55, pp. 883-887 (2011).
10. Hadidi, N, Ould-Amer, Y., and Bennacer, R. \Bilayered
and inclined porous collector: Optimum heat
and mass transfer", Energy, 51, pp. 422-430 (2013).
11. Hadidi, N. and Bennacer, V. \Three-dimensional
double di usive natural convection across a cubical
enclosure partially lled by vertical porous layer", Int.
J. Therm. Sci., 101, pp. 143-157 (2016).
12. House, J.M., Beckermann, C., and Smith, T.F. \E ect
of a centered conducting body on natural convection
heat transfer in an enclosure", Numer. Heat Transfer,
A, 18, pp. 213-225 (1990).
13. Ha, M.Y. and Jung, M.J. \A numerical study on
three-dimensional conjugate heat transfer of natural
convection and conduction in a di erentially heated cubic
enclosure with a heat-generating cubic conducting
body", Int. J. Heat Mass Transfer, 43, pp. 4229-4248
14. Lee, J.R. and Ha, M.Y. \A numerical study of natural
convection in a horizontal enclosure with a conducting
body", Int. J. Heat Mass Transfer, 48, pp. 3308-3318
15. Braga, E.J. and de Lemos, M.J.S. \Heat transfer in
enclosures having a xed amount of solid material simulated
with heterogeneous and homogeneous models",
Int. J. Heat Mass Transfer, 48, pp. 4748-4765 (2005).
16. Braga, E.J. and de Lemos, M.J.S. \Laminar natural
convection in cavities lled with circular and square
rods", Int. Commun. Heat Mass Transfer, 32, pp.
1289-1297 (2005).
17. Merrikh, A.A. and Lage, J.L. \Natural convection in
an enclosure with disconnected and conducting solid
blocks", Int. J. Heat Mass Transfer, 48, pp. 1361-1372
18. Das, M.K. and Reddy, K.S.K. \Conjugate natural
convection heat transfer in an inclined square cavity
containing a conducting block", Int. J. Heat Mass
Transfer, 49, pp. 4987-5000 (2006).
19. Zhao, F., Liu, D., and Tang, G. \Conjugate heat
transfer in square enclosure", Heat Mass Transfer, 43,
pp. 907-922 (2007).
20. Sheremet, M.A., Oztop, H.F., Pop, I., and Abu-
Hamdeh, N. \Analysis of entropy generation in natural
convection of nano
uid inside a square cavity having
hot solid block: Tiwari and Das' Model", Entropy, 18,
pp. 1-15 (2016).
21. Sivaraj, C. and Sheremet, M.A. \MHD natural convection
in an inclined square porous cavity with a heat
conducting solid block", Journal of Magnetism and
Magnetic Materials, 426, pp. 351-360 (2017).
22. Chamkha, A.J., Selimefendigil, F., and Ismael, M.A.
\Mixed convection in a partially layered porous cavity
with an inner rotating cylinder", Numer. Heat Transfer,
A, 69, pp. 659-675 (2016).
23. Selimefendigil, F., Ismael, M.A., and Chamkha, A.J.
\Mixed convection in superposed nano
uid and porous
layers in square enclosure with inner rotating cylinder",
Int. Journal of Mechanical Sciences, 124(125),
pp. 95-108,(2017).
24. Chamkha, A.J. and Ismael, M.A. \Natural convection
in di erentially heated partially porous layered cavities
lled with nano
uid", Numer. Heat Transfer, A, 65,
pp. 1089-1113 (2014).
25. Sheremet, M.A. and Trifonova, T.A. \Unsteady conjugate
natural convection in a vertical cylinder containing
a horizontal porous layer: Darcy model and
brinkman extended Darcy model", Transp. Porous
Med., 101, pp. 437-463 (2014).
26. M-Juan, Y., B-Ming, Y., Bin, Z., and M-Tao, H.A.
\Geometry model for tortuosity of streamtubes in
porous media with spherical particles", Chines Physics
Letters, 22, pp. 1464-1467 (2005).
M.A. Ismael and H.S. Ghalib/Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 2643{2659 2659
27. Holman, J.P., Heat Transfer, McGraw Hill, New York,
10th Ed. (2010).