Journal of Fluid Mechanics

Natural convection in a sloping porous layer

S. A.  Bories a1 and M. A.  Combarnous a1
a1 Groupe d'Etude I.F.P.-I.M.F. sur les Milieux Poreux, 2 Rue Camichel, Toulouse, France

Article author query
bories sa   [Google Scholar] 
combarnous ma   [Google Scholar] 


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.

(Published Online March 29 2006)
(Received February 1 1972)
(Revised June 26 1972)