The buoyancy-driven transient double-diffusive convection in a square cavity filled with water-saturated porous medium is studied numerically. While the right and left side wall temperatures vary linearly from θa to θo and θo to θb, respectively, with height, the top and bottom walls of the cavity are thermally insulated. The species concentration levels at the right and left walls are c1 and c2, respectively, with c1>c2. The Brinkman–Forchheimer extended Darcy model is considered to investigate the average heat and mass transfer rates and to study the effects of maximum density, the Grashof number, the Schmidt number, porosity, and the Darcy number on buoyancy-induced flow and heat transfer. The finite volume method with power law scheme for convection and diffusion terms is used to discretize the governing equations for momentum, energy, and concentration, which are solved by Gauss–Seidel and successive over-relaxation methods. The heat and mass transfer in the steady-state are discussed for various physical conditions. For the first time in the literature, the study of transition from stationary to steady-state shows the existence of an overshooting between the two cells and in the average Nusselt number. The results obtained in the steady-state regime are presented in the form of streamlines, isotherms, and isoconcentration lines for various values of Grashof number, Schmidt number, porosity and Darcy number, and midheight velocity profiles. It is found that the effect of maximum density is to slow down the natural convection and reduce the average heat transfer and species diffusion. The strength of convection and heat transfer rate becomes weak due to more flow restriction in the porous medium for small porosity.

1.
Han
,
H.
, and
Kuehn
,
T. H.
, 1991, “
Double-Diffusive Natural Convection in a Vertical Rectangular Enclosure-II: Numerical Study
,”
Int. J. Heat Mass Transfer
0017-9310,
34
, pp.
461
471
.
2.
Beghein
,
C.
,
Haghighat
,
F.
, and
Allard
,
F.
, 1992, “
Numerical Study of Double-Diffusive Natural Convection in a Square Cavity
,”
Int. J. Heat Mass Transfer
0017-9310,
35
, pp.
833
846
.
3.
Nithiarasu
,
P.
,
Sundararajan
,
T.
, and
Seetharamu
,
K. N.
, 1997, “
Double-Diffusive Natural Convection in a Fluid Saturated Porous Cavity With a Freely Convecting Wall
,”
Int. Commun. Heat Mass Transfer
0735-1933,
24
(
8
), pp.
1121
1130
.
4.
Kandaswamy
,
P.
, and
Kumar
,
K.
, 1999, “
Buoyancy-Driven Nonlinear Convection in a Square Cavity in the Presence of a Magnetic Field
,”
Acta Mech.
0001-5970,
136
, pp.
29
39
.
5.
Sundaravadivelu
,
K.
, and
Kandaswamy
,
P.
, 2000, “
Double Diffusive Nonlinear Convection in a Square Cavity
,”
Fluid Dyn. Res.
0169-5983,
27
, pp.
291
303
.
6.
Khanafer
,
K.
, and
Vafai
,
K.
, 2002, “
Double-Diffusive Mixed Convection in a Lid-Driven Enclosure Filled With a Fluid Saturated Porous Medium
,”
Numer. Heat Transfer, Part A
1040-7782,
42
, pp.
465
486
.
7.
Saeid
,
N. H.
, and
Pop
,
I.
, 2004, “
Maximum Density Effects on Natural Convection From a Discrete Heater in a Cavity Filled With a Porous Medium
,”
Acta Mech.
,
171
, pp.
203
212
. 0001-5970
8.
Sezai
,
I.
, and
Mohamad
,
A. A.
, 1999, “
Three Dimensional Double Diffusive Convection in a Porous Cubic Enclosure Due to Opposing Gradients of Temperature and Concentration
,”
J. Fluid Mech.
0022-1120,
400
, pp.
333
353
.
9.
Sezai
,
I.
, and
Mohamad
,
A. A.
, 2000, “
Double Diffusive Convection in a Cubic Enclosure With Opposing Temperature and Concentration Gradients
,”
Phys. Fluids
1070-6631,
12
(
9
), pp.
2210
2223
.
10.
Mohamad
,
A. A.
,
Bennacer
,
R.
, and
Azaiez
,
J.
, 2004, “
Double Diffusion Natural Convection in a Rectangular Enclosure Filled With Binary Saturated Porous Media: The Effect of Lateral Aspect Ratio
,”
Phys. Fluids
1070-6631,
16
(
1
), pp.
184
199
.
11.
Mohamad
,
A. A.
, and
Bennacer
,
R.
, 2002, “
Double Diffusion Natural Convection in an Enclosure Filled With Saturated Porous Medium and Subjected to Cross Gradients: Stably Stratified Fluid
,”
Int. J. Heat Mass Transfer
,
45
, pp.
3725
3740
. 0017-9310
12.
Vafai
,
K.
, 2005,
Handbook of Porous Media
,
2nd ed.
,
Dekker
,
New York
.
13.
Nield
,
D. A.
, and
Bejan
,
A.
, 2006,
Convection in Porous Media
,
3rd ed.
,
Springer
,
New York
.
14.
Patankar
,
S. V.
, 1980,
Numerical Heat Transfer and Fluid Flow
,
Hemisphere
,
Washington, DC
.
15.
Rudraiah
,
N.
,
Barron
,
R. M.
,
Venkatachalappa
,
M.
, and
Subbaraya
,
C. K.
, 1995, “
Effect of a Magnetic Field on Free Convection in a Rectangular Enclosure
,”
Int. J. Eng. Sci.
0020-7225,
33
(
8
), pp.
1075
1084
.
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