Onset of convection in a horizontal porous layer is investigated including the effects of through-flow and a uniformly distributed internal heat generation for different types of hydrodynamic boundary conditions. The instability parameter is either a Darcy-external or Darcy-internal Rayleigh number which has been determined numerically using Galerkin technique. When the boundary conditions at the top and bottom are not identical, it is found that a small amount of through-flow in one particular direction destabilizes the system in the absence of heat generation. However, in the presence of an internal heat generation, through-flow in one direction destabilizes the system even if the boundary conditions at the two boundaries are of the same type and the destabilization is found to be more with the increase in internal Rayleigh number.

Onset of convection in a porous layer with net through-flow and internal heat generation

Stability of a suspension of gyrotactic microorganisms in superimposed fluid and porous layers

The onset of Darcy‐Brinkman convection in a porous medium layer with vertical throughflow and variable gravity field effects

Natural convection in fluid–superposed porous layers heated locally from below

This paper is concerned with the question of the beginning of convective motion in a fluid saturated porous layer, containing a salt in solution, heated below and salted above and below. This model has a single temperature and employs the Darcy theory in the micropores, the Brinkman theory, however, being utilized in the macropores. The effect of slip boundary conditions on the stability of the model is also studied. General boundary conditions regarding temperature and salt are also taken into account. It will be shown that the linear instability threshold is the same as that of nonlinear stability if the layer is salted from above, indicating that the linear theory entirely captures the physics of the onset of thermal convection. In the case of salting from below, the behavior of the transition from stationary to oscillatory convection is investigated in detail, as the boundary conditions change from prescribed temperature and salt concentration toward those of prescribed heat flux and salt flux. The nonlinear stability threshold does not coincide with that of linear instability; thus, regions of possible subcritical instability are still present. We believe that the problem presented in this paper has not been addressed before and that its study will have great scientific value and impact.

Bidispersive double diffusive convection with relatively large macropores and generalized boundary conditions

We implement a linear stability analysis of the convective instability in superposed horizontal fluid and porous layers with throughflow in the vertical direction. It is found that in such a physical configuration both stabilizing and destabilizing factors due to vertical throughflow can be enhanced so that a more precise control of the buoyantly driven instability in either a fluid or a porous layer is possible. For ζ = 0.1 (ζ, the depth ratio, defined as the ratio of the fluid-layer depth to the porous-layer depth), the onset of convection occurs in both fluid and porous layers, the relation between the critical Rayleigh number Rcm and the throughflow strength γm is linear and the Prandtl-number (Prm) effect is insignificant. For ζ ≥ 0.2, the onset of convection is largely confined to the fluid layer, and the relation becomes Rcm ∼ γ2m for most of the cases considered except for Prm = 0.1 with large positive γm where the relation Rcm ∼ γ3m holds. The destabilizing mechanisms proposed by Nield (1987 a, b) due to throughflow are confirmed by the numerical results if considered from the viewpoint of the whole system. Nevertheless, from the viewpoint of each single layer, a different explanation can be obtained.

/pdf/throughflow-effects-on-convective-instability-in-superposed-4xjcqozetc.pdf

Throughflow effects on convective instability in superposed fluid and porous layers

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Throughflow effects on convective instability in superposed fluid and porous layers