This study deals with natural convection driven by combined thermal and solutal buoyancy forces in a binary fluid. The consequence of thermosolutal convection on heat and mass transfer is examined in a confined enclosure partially filled with a porous medium. The mathematical description of the problem makes use of a one-domain formulation of the conservation equations. The presented numerical results quantitatively show the significant influence of the presence of a relatively thin porous layer on the flow structure and on heat and species transfer in the enclosure. The paper is dedicated to the analysis of the influence of the thickness and permeability of the porous layer in a range of governing parameters. For a low permeability porous layer, the numerical results are compared to an analysis based on simple scaling laws, which provide a good interpretation in terms of the wall transfer decrease with the porous layer thickness. The effect of permeability is investigated and it is shown that flow penetration in the porous layer induces a specific behavior of the flow structure and average heat transfer in the enclosure.
Issue Section:
Porous Media
1.
Arquis
E.
Caltagirone
J.-P.
1984
, “Sur les Conditions Hydrodynamiques au Voisinage d’une Interface Milieu Fluide-Milieu Poreux: Application a la Convection Naturelle
,” C. R. Acad. Sc.
, Vol. 299–11
, pp. 1
–4
.2.
Beavers
G. S.
Joseph
D. D.
1967
, “Boundary Conditions at a Naturally Permeable Wall
,” J. Fluid Mech.
, Vol. 30
, pp. 197
–207
.3.
Beavers
G. S.
Sparrow
E. M.
Magnuson
R. A.
1970
, “Experiments on Coupled Parallel Flows in a Channel and a Bounding Porous Medium
,” Trans. of ASME Journal of Basic Engineering
, Vol. 92
, pp. 843
–848
.4.
Beavers
G. S.
Sparrow
E. M.
Masha
B. A.
1974
, “Boundary Condition at a Porous Surface Which Bounds a Fluid Flow
,” AIChE Journal
, Vol. 20-3
, pp. 596
–597
.5.
Beckermann
C.
Ramadhyani
S.
Viskanta
R.
1987
, “Natural Convection Flow and Heat Transfer Between a Fluid Layer and a Porous Layer Inside a Rectangular Enclosure
,” ASME JOURNAL OF HEAT TRANSFER
, Vol. 109
, pp. 363
–370
.6.
Beckermann
C.
Viskanta
R.
Ramadhyani
S.
1988
, “Natural Convection in Vertical Enclosures Containing Simultaneously Fluid and Porous Layers
,” J. Fluid Mech.
, Vol. 186
, pp. 257
–284
.7.
Bejan, A., 1995, Convection heat transfer, 2nd ed., John Wiley & Sons Inc., NY.
8.
Be´nard
C.
Be´nard
R.
Bennacer
R.
Gobin
D.
1996
, “Melting Driven Thermo-Haline Convection
,” Phys. Fluid A
, Vol. 8
, pp. 112
–130
.9.
Bergman
T. L.
Srinivasan
R.
1989
, “Numerical Simulation of Soret-Induced Double Diffusion in an Initially Uniform Concentration Binary Liquid
,” Int. J. Heat Mass Transfer
, Vol. 32
, pp. 679
–687
.10.
Brinkman
H. C.
1947
, “A Calculation of the Viscous Force Exerted by a Flowing Fluid on a Dense Swarm of Particles
,” Appl. Sci. Res.
, Vol. A1
, pp. 27
–34
.11.
Chen
F.
Chen
C. F.
1992
, “Double-Diffusive Fingering Convection in a Porous Medium
,” Int. J. Heat Mass Transfer
, Vol. 36-3
, pp. 793
–807
.12.
Ettefagh
J.
Vafai
K.
Kim
S. J.
1991
, “Non-Darcian Effects in Open-Ended Cavities Filled With a Porous Medium
,” ASME JOURNAL OF HEAT TRANSFER
, Vol. 113
, pp. 747
–756
.13.
Givler
R. C.
Altobelli
S. A.
1994
, “A Determination of the Effective Viscosity for the Brinkman-Forchheimer Flow Model
,” J. Fluid Mech.
, Vol. 258
, pp. 355
–370
.14.
Gobin
D.
Bennacer
R.
1996
, “Cooperating Thermosolutal Convection in Enclosures: 1. Scale Analysis and Mass Transfer; 2. Heat Transfer and Flow Structure
,” Int. J. Heat Mass Transfer
, Vol. 39–13
, pp. 2671
–2681
.15.
Goyeau
B.
Songbe
J.-P.
Gobin
D.
1996
, “Numerical Study of Double-Diffusive Natural Convection in a Porous Cavity Using the Darcy-Brinkman Formulation
,” Int. J. Heat Mass Transfer
, Vol. 39-7
, pp. 1363
–1378
.16.
Goyeau
B.
Benihaddadene
T.
Gobin
D.
Quintard
M.
1997
, “Averaged Momentum Equation for Interdendritic Flow During Solidification
,” Transport in Porous Media
, Vol. 28
, pp. 19
–50
.17.
Kaviany, M., 1995, Principles of Heat Transfer in Porous Media, Springer-Verlag Inc., NY.
18.
Koplik
J.
Levine
H.
Zee
A.
1983
, “Viscosity Renormalization in the Brinkman Equation
,” Phys. Fluids
, Vol. 26–10
, pp. 2864
–2870
.19.
Lauriat
G.
Prasad
V.
1987
, “Natural Convection in a Vertical Porous Cavity: a Numerical Study for Brinkman-Extended Darcy Formulation
,” ASME JOURNAL OF HEAT TRANSFER
, Vol. 109
, pp. 688
–696
.20.
Le Breton
P.
Caltagirone
J. P.
Arquis
E.
1991
, “Natural Convection in a Square Cavity With Thin Porous Layers on its Vertical Walls
,” ASME JOURNAL OF HEAT TRANSFER
, Vol. 113
, pp. 892
–898
.21.
Lundgren
T. S.
1972
, “Slow Flow Through Stationary Random Beds and Suspensions of Spheres
,” J. Fluid Mech.
, Vol. 51
, pp. 273
–299
.22.
Neale
G.
Nader
W.
1974
, “Practical Significance of Brinkman,’ Extension of Darcy, Law: Coupled Parallel Flows Within a Channel and a Bounding Porous Medium
,” The Canadian Journal of Chemical Engineering
, Vol. 52
, pp. 475
–478
.23.
Nield
D. A.
1991
, “The Limitation of the Brinkman-Forchheimer Equation in Modeling Flow in a Saturated Porous Medium and at an Interface
,” Int. J. Heat Fluid Flow
, Vol. 12
, pp. 269
–272
.24.
Nield, D. A., and Bejan, A., 1992, Convection in porous media, Springer-Verlag New York Inc., NY.
25.
Ochoa-Tapia
J. A.
Whitaker
S.
1995
, “Momentum Transfer at the the Boundary Between a Porous Medium and a Homogeneous Fluid—I. Theoretical Development
,” Int. J. Heat Mass Transfer
, Vol. 38
, pp. 2635
–2646
.26.
Prescott
P.
Incropera
F. P.
1996
, “Convection Heat and Mass Transfer in Alloy Solidification
,” Adv. in Heat Transfer
, Vol. 28
, pp. 231
–338
.27.
Saffman
P. G.
1971
, “On the Boundary Condition at the Surface of a Porous Medium
,” Studies in Applied Mathematics L
, Vol. 2
, pp. 93
–101
.28.
Sahraoui
M.
Kaviany
M.
1992
, “Slip and No-Slip Velocity Boundary Conditions at the Interface of Porous, Plain Media
,” Int. J. Heat Mass Transfer
, Vol. 35-4
, pp. 927
–943
.29.
Sathe
S. B.
Lin
W. Q.
Tong
T. W.
1988
, “Natural Convection in Enclosures Containing an Insulation With Permeable Fluid-Porous Interface
,” Int. J. Heat Fluid Flow
, Vol. 9–4
, pp. 389
–395
.30.
Song
M.
Viskanta
R.
1994
, ’Natural Convection Flow and Heat Transfer Within a Rectangular Enclosure Containing a Vertical Porous Layer
,” Int. J. Heat Mass Transfer
, Vol. 37–16
, pp. 2425
–2438
.31.
Turki, S., and Lauriat, G., 1990, “An Examination of Two Numerical Procedures for Natural Convection in Composite Enclosures,’ Numerical Heat Transfer proceedings of AIAA-ASME Thermophysics and Heat Transfer Conference, HTD No. 130, pp. 107–113.
32.
Vafai
K.
Kim
S. J.
1990
, “Fluid Mechanics of the Interface Region Between a Porous Medium and a Fluid Layer-An Exact Solution
,” Int. J. Heat Fluid Flow
, Vol. 11-3
, pp. 254
–256
.33.
Vafai
K.
Kim
S. J.
1995
, “On the Limitations of the Brinkman-Forch-heimer-Extended Darcy Equation
,” Int. J. Heat Fluid Flow
, Vol. 16-1
, pp. 11
–15
.34.
Webster
I. T.
Norquay
S. J.
Ross
F. C.
Wooding
R. A.
1996
, “Solute Exchange by Convection Within Estuarine Sediments
,” Estuarine, Coastal and Shelf Science
, Vol. 42
, pp. 171
–183
.
This content is only available via PDF.
Copyright © 1998
by The American Society of Mechanical Engineers
You do not currently have access to this content.
