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Natural convection in a sloping porous layer

Published online by Cambridge University Press:  29 March 2006

S. A. Bories  and
M. A. Combarnous
S. A. Bories
Affiliation:
Groupe d'Etude I.F.P.-I.M.F. sur les Milieux Poreux, 2 Rue Camichel, Toulouse, France
M. A. Combarnous
Affiliation:
Groupe d'Etude I.F.P.-I.M.F. sur les Milieux Poreux, 2 Rue Camichel, Toulouse, France
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Abstract

This paper describes an experimental and theoretical study of thermal convection in a sloping porous layer. The saturated layer is bounded by two parallel impermeable planes maintained at different temperatures. Several types of flows were observed: a unicellular movement and a juxtaposition of longitudinal coils or of polyhedral cells.

A theoretical analysis has been made using the standard bases of the linear theory of stability and by taking into account some assumptions suggested by experimental observations. The critical conditions for the transition between unicellular and polycellular flows has been determined. For flow in longitudinal coils or with polyhedral cells the average heat transfer depends mainly on the filtration Rayleigh number and on the slope of the layer.

The experimental study was made in a Rayleigh number range 0–800 and for various slopes (0–90°). For both the transition criterion and the heat transfer, a good fit was observed between the experimental and theoretical results. For maximum slope, i.e. 90°, a correlation which connects the Nusselt number with both the Rayleigh number and the vertical extent of the model is proposed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 57 , Issue 1 , 23 January 1973 , pp. 63 - 79
Copyright
© 1973 Cambridge University Press

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References

Aziz, K. & Combarnous, M. A. 1970 Prediction theorique du transfert de chaleur par convection naturelle dans une couche horizontale. C.R. Acad. Sci. B 271, 813.Google Scholar
Aziz, K., Holst, P. H. & Karra, P. S. 1968 Natural convection in porous media. 19th Annual Meeting Petroleum Society C.I.M. (Calgary). Paper, no. 6813.Google Scholar
Bories, S. A. 1970a Sur les mecanismes fondamentaux de la convection naturelle en milieu poreux. Ph.D. thesis, University of Toulouse.
Bories, S. A. 1970b Sur les mécanismes fondamentaux de la convection naturelle en milieu poreux. Revue Gén. Therm. 9 (108), 1377–1402.Google Scholar
Caltagirone, J. P., Cloupeau, M. & Combarnous, M. A. 1971 Convection naturelle fluctuante dans une couche poreuse horizontale. C.R. Acad. Sci. B 273, 833–836.Google Scholar
Catton, I. 1966 Natural coiivection in horizontal liquid layers. Phys. Fluids, 9, 2521–2522.Google Scholar
Chan, B. K. C., Ivey, C. M. & Barry, J. M. 1970 Natural convection in enclosed porous media with rectangular boundaries. J. Heat Transfer, 2, 21–27.Google Scholar
Combarnous, M. A. 1970a Convection naturelle et convection mixte en mileu poreux. Ph.D. thesis, University of Paris.
Combarnous, M. A. 1970b Convection naturelle et mixte dans m e couche poreuse horizontale. Revue Gén. Therm. 9, 1355–1376.Google Scholar
Hart, J. E. 1971a Stability of the flow in differentially heated inclined box. J. Fluid Mech. 47, 547–576.Google Scholar
Hart, J. E. 1971b Transition to a wavy vortex regime in convective flow between inclined plates. J. Fluid Mech. 48, 265–271.Google Scholar
Holst, P. H. 1970 A theoretical and experimental investigation in porous media. Ph.D. thesis, University of Calgary.
Horton, C. W. & Rogers, F. T. 1945 Convection currents in a porous medium. J. Appl. Phys. 16, 367–370.Google Scholar
Kaneko, T. 1972 An experimental investigation of natural convection in porous media. M.S. thesis. University of Calgary.
Katto, Y. & Masuoka, T. 1967 Criterion for onset of convective flow in a fluid in a porous medium. Int. J. Heat Mass Transjer, 10, 297–309.Google Scholar
Klarsfeld, S. M. 1970 Champs de temperature associes aux mouvements de convection naturelle dans un milieu poreux limité. Revue Gén. Therm. 9 (108), 1403–1424.Google Scholar
Lapwood, E. R. 1948 Convection of a fluid in a porous medium. Proc. Carnb. Phil. Soc. 44, 508–521.Google Scholar
Nield, D. A. 1968 Onset of thermohaline convection in a porous medium. Wat. Resour. Res. 4, 353–360.Google Scholar
Schneider, K. J. 1963 Die Wlirmaleitfahigkeit Korniger Stoffe und ihre Beeinflussung durch Freie Konvektion. Ph.D. thesis, Technischen Hochschule, Karlsruhe.
Unny, T. E. 1972 Thermal instability in differential heated inclined fluid layers. J. Appl. Mech. 39, 41–46.Google Scholar
Vlasuk, M. P. 1972 Heat transfer with natural convection in permeable porous medium. IVth All-Union Heat and Mass Transfer Conference (Minsk), paper no. 1–49.Google Scholar
Westbrook, D. It. 1969 Stability of convective flow in a porous medium. P h p. Fluids, 12, 1547.Google Scholar
Wooding, R. A. 1957 Steady state free thermal convection of liquid in a saturated permeable medium. J. Fluid Mech. 2, 273–285.Google Scholar