Stability of natural convection in superposed fluid and porous layers: Equivalence of the one- and two-domain approaches

International Journal of Heat and Mass Transfer

Volumn 52, Issue 1-2, 2009, Pages 533-536

  Hirata, S C ^a   Goyeau, B ^b   Gobin, D ^a   Chandesris, M ^c   Jamet, D ^c  

^a Centre National de la Recherche Scientifique   (France)

^b ECOLE CENTRALE PARIS   (France)

^c DEN/DER/SSTH   (France)

Author keywords

Fluid porous interface; Linear stability; Natural convection

Indexed keywords

DIFFERENTIATION (CALCULUS); ELECTRIC FIELD EFFECTS; FLUID DYNAMICS; HEAT CONVECTION; MULTIPHASE FLOW; NATURAL CONVECTION; POROUS MATERIALS; TWO PHASE FLOW;

DOMAIN APPROACHES; DOMAIN FORMULATIONS; EFFECTIVE DIFFUSIVITIES; FLUID LAYERS; INTERFACIAL REGIONS; LINEAR STABILITY; MACROSCOPIC PROPERTIES; MARGINAL STABILITIES; MODELING APPROACHES; POROUS LAYERS; POROUS MEDIUMS; STABILITY ANALYSES; TWO-PHASE FLOWS;

PHASE INTERFACES;

EID: 57049153462     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2008.07.045     Document Type: Article

References (21)

1. Kataoka I. Local instant formulation of two-phase flow. Int. J. Multiphase Flow 12 5 (1986) 745-758
2. Nield D.A. Onset of convection in a fluid layer overlying a layer of a porous medium. J. Fluid Mech. 81 (1977) 513-522
3. Nield D.A. The boundary correction for the Rayleigh-Darcy problem: limitations of the Brinkman equation. J. Fluid Mech. 128 (1983) 37-46
4. Chen F., and Chen C.F. Onset of finger convection in a horizontal porous layer underlying a fluid layer. J. Heat Transfer 110 (1988) 403-409
5. Carr M., and Straughan B. Penetrative convection in a fluid overlying a porous layer. Adv. Water Resour. 26 (2003) 263-276
6. Carr M. Penetrative convection in a superposed porous-medium-fluid layer via internal heating. J. Fluid Mech. 509 (2004) 305-329
7. Beavers G.S., and Joseph D.D. Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30 (1967) 197-207
8. Beavers G.S., Sparrow E.M., and Magnuson R.A. Experiments on coupled parallel flows in a channel and a bounding porous medium. J. Basic Eng. 92 (1970) 843-848
9. Brinkman H.C. A calculation of the viscous force exerted by flowing fluid on a dense swarm of particles. Appl. Sci. Res. A1 (1947) 27-34
10. Neale G., and Nader W. Practical significance of Brinkman's extension of Darcy's law: Coupled parallel flow within a channel and a bounding porous medium. Can. J. Chem. Eng. 52 (1974) 475-478
11. Desaive T., Lebon G., and Henneberg M. Coupled capillary and gravity-driven instability in a liquid film overlying a porous layer. Phys. Rev. E 64 (2001) 066304
12. Hirata S.C., Goyeau B., Gobin D., Carr M., and Cotta R.M. Linear stability analysis of natural convection in superposed fluid and porous layers: influence of interfacial modelling. Int. J. Heat Mass Transfer 50 7-8 (2007) 1356-1367
13. Arquis E., and Caltagirone J. Sur les conditions hydrodynamiques au voisinage d'une interface milieu fluide-milieu poreux: application à la convection naturelle. C.R. Acad. Sci. 299-II (1984) 1-4
14. Zhao P., and Chen C.F. Stability analysis of double-diffusive convection in superposed fluid and porous layers using a one-equation model. Int. J. Heat Mass Transfer 44 (2001) 4625-4633
15. Schwartz L. Méthodes Mathématiques Pour Les Sciences Physiques (1961), Hermann, Paris
16. Cotta R.M. Integral Transforms in Computational Heat and Fluid Flow (1993), CRC Press, Boca Raton, FL
17. Whitaker S. The Method of Volume Averaging (1999), Springer, New York
18. Hirata S.C., Goyeau B., and Gobin D. Stability of natural convection in superposed fluid and porous layer: influence of the interfacial jump boundary condition. Phys. Fluids 19 (2007) 058102
19. Hirata S.C., Goyeau B., Gobin D., and Cotta R.M. Stability of natural convection in superposed fluid and porous layers using integral transforms. Numer. Heat Transfer 50 5 (2006) 409-424
20. Chandrasekhar S. Hydrodynamic and Hydromagnetic Stability (1961), Oxford University Press, London
21. S.C. Hirata, Stabilité de la convection thermique et/ou solutale en couches fluide et poreuse superposées, Ph.D. Thesis, Université de Paris, VI, 2007.