Natural convection past inclined porous layers

This paper describes a study of combined Rayleigh-Bénard convection and Tollmien-Schlichting type of instability of a fluid in an inclined layer bounded by two permeable beds. Several types of flows, depending on the value of the Prandtl number, Pr, are studied using a fast convergent power series technique. Two different convective movements, longitudinal and transverse rolls, based on different Prandtl numbers, are reported. The effect of slip at the nominal surface is to augment the instability and change the critical Grashof number, Gr, and critical Rayleigh number, Ra, markedly for small permeability parameter σ , being independent of Gr and Ra for large σ . The effect of inclination Φ is to inhibit the onset of instability in the case of air and to augment it in the case of mercury. It is shown that at maximum inclination (i.e.,Φ =π/2), the instability sets in as transverse rolls, irrespective of the value of Pr. In the case of mercury, the transverse rolls exist for all Φ, whereas in the case of air, they are limited only to certain Φ. The cell pattern changes dramatically in the range Φ=π/6-π/4