The object of this study is the heat transfer associated to a buoyancy-induced flow developing in a rectangular cavity, partly filled with porous medium, with given heat flux from the sides. Numerical experiments show the existence of a quasi parallel solution away from the top and bottom end walls, characterized by a linear vertical temperature profile. Analytical expressions are derived for the velocity and temperature which, combined with an energy balance, enable us to relate the stratification to the other governing parameters. Influence of the porous layer’s permeability and width, and of the Rayleigh number on the flow structure and heat transfer is thoroughly investigated, and summarized in simple relationships.
Issue Section:
Porous Media
1.
Lauriat
, G.
, and Prasad
, V.
, 1987
, “Natural Convection in a Vertical Porous Cavity: A Numerical Study for Brinkman-Extended Darcy Formulation
,” ASME J. Heat Transfer
, 109
, pp. 688
–696
.2.
Vafai
, K.
, and 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
11-3
, pp. 254
–256
.3.
Beckerman
, C.
, Viskanta
, R.
, and Ramadhyani
, S.
, 1988
, “Natural Convection in Vertical Enclosures Containing Simultaneously Fluid and Porous Layer
,” J. Fluid Mech.
, 186
, pp. 257
–284
.4.
Le Breton
, P.
, Caltagirone
, J. P.
, and Arquis
, E.
, 1991
, “Natural Convection in a Square Cavity With Thin Porous Layers on its Vertical Walls
,” ASME J. Heat Transfer
, 113
, pp. 892
–898
.5.
Gobin
, D.
, Goyeau
, B.
, and Songbe
, J.-P.
, 1998
, “Double Diffusive Natural Convection in a Composite Fluid-Porous Layer
,” ASME J. Heat Transfer
, 120
, pp. 234
–242
.6.
Nield, D., and Bejan, A., 1998, Convection in Porous Media, 2nd edition, Springer-Verlag, New York.
7.
Weisman, C., Le Que´re´, P., and Firdaouss, M., 1999, “Sur une solution exacte de la convection naturelle en cavite´ partiellement remplie d’un milieu poreux,” C. R. Acad Sc. Paris, Vol. 327-II B, pp. 235–240.
8.
Bergholz
, R. F.
, 1978
, “Instability of Steady Natural Convection in a Vertical Fluid Layer
,” J. Fluid Mech.
, 84
, pp. 743
–768
.9.
Kimura
, S.
, and Bejan
, A.
, 1984
, “The Boundary Layer Natural Convection Regime in a Rectangular Cavity with Uniform Heat Flux from the Side
,” ASME J. Heat Transfer
, 106
, pp. 98
–103
.10.
Trevisan
, O. V.
, and Bejan
, A.
, 1986
, “Mass and Heat Transfer by Natural Convection in a Vertical Slot Filled With Porous Medium
,” Int. J. Heat Mass Transf.
, 29
, pp. 403
–415
.11.
Gill
, A. E.
, 1966
, “The Boundary-Layer Regime for Convection in a Rectangular Cavity
,” J. Fluid Mech.
, 26
, pp. 515
–536
.12.
Weber
, J. E.
, 1974
, “The Boundary-Layer Regime for Convection in a Vertical Porous Layer
,” Int. J. Heat Mass Transf.
, 18
, pp. 569
–573
.13.
Amiri
, A.
, and Vafai
, K.
, 1994
, “Analysis of Dispersion Effects and Non-Thermal Equilibrium, Non-Darcian, Variable Porosity Incompressible Flow Through Porous Media
,” Int. J. Heat Mass Transf.
, 37
, No. 6
, pp. 939
–954
.14.
Amiri
, A.
, Vafai
, K.
, and Kuzay
, T. M.
, 1995
, “Effects of Boundary Conditions on Non-Darcian Heat Transfer Through Porous Media and Experimental Comparisons
,” Numer. Heat Transfer, Part A
, 27
, pp. 651
–664
.15.
Beck
, J. L.
, 1972
, “Convection in a Box of Porous Material Saturated With Fluid
,” Phys. Fluids
, 15
, No. 8
, pp. 1377
–1383
.16.
Alazmi
, B.
, and Vafai
, K.
, 2000
, “Analysis of Variance Within the Porous Media Transport Models
,” ASME J. Heat Transfer
, 122
, pp. 303
–326
.17.
Amahmid
, A.
, Hasnaoui
, M.
, and Vasseur
, P.
, 1999
, “Etude analytique et nume´rique de la convection naturelle dans une couche poreuse de Brinkman doublement diffusive
,” Int. J. Heat Mass Transf.
, 42
, pp. 2991
–3005
.18.
Givler
, R. C.
, and Altobelli
, S. A.
, 1994
, “A Determination of the Effective Viscosity for the Brinkman-Forchheimer Flow Model
,” J. Fluid Mech.
, 258
, pp. 355
–370
.19.
Alazmi
, B.
, and Vafai
, K.
, 2001
, “Analysis of Fluid Flow and Heat Transfer Interfacial Conditions Between a Porous Medium and a Fluid Layer
,” Int. J. Heat Mass Transf.
, 44
, pp. 1735
–1740
.20.
Ochoa-Tapia
, J.
, and Whitaker
, S.
, 1995
, “Momentum Transfer at the Boundary Between a Porous Medium and a Homogeneous Fluid: I—Theoretical Development
,” Int. J. Heat Mass Transf.
, 38
, No. 14
, pp. 2635
–2646
.21.
Ochoa-Tapia
, J.
, and Whitaker
, S.
, 1995
, “Momentum Transfer at the Boundary Between a Porous Medium and a Homogeneous Fluid: II—Comparison With Experiment
,” Int. J. Heat Mass Transf.
, 38
, No. 14
, pp. 2647
–2655
.22.
Le Breton, P., 1991, “Etude nume´rique et expe´rimentale de la convection naturelle laminaire et turbulente en cavite´ partiellement occupe´e d’un milieu poreux,” Ph.D., Univ. Bordeaux.
23.
Bejan, A., 1984, Convection Heat Transfer, John Wiley and Sons, New York.
24.
Straughan
, B.
, 2001
, “A Sharp Nonlinear Stability Threshold in Rotating Porous Convection
,” Proc. R. Soc. London, Ser. A
, 457
, pp. 87
–93
.25.
Kaviany, M., 1991, Principles of Heat Transfer in Porous Media, Springer-Verlag, New York.
26.
Temam, R., 1979, Navier-Stokes Equations, North-Holland, Amsterdam.
27.
Le Que´re´
, P.
, 1991
, “Accurate Solutions to the Square Differentially Heated Cavity at High Rayleigh Number
,” Comput. Fluids
, 20
, pp. 19
–41
.Copyright © 2002
by ASME
You do not currently have access to this content.