Density inversion phenomenon in porous penetrative convection

Penetrative convection in a bi‐disperse porous medium

“…if $$$ {c}_1\to 1 $$$ and $$$ {c}_2\to 0 $$$, the bi‐disperse porous medium approximates a monodispersive one. In the limit case for $$$ {c}_1\to 1 $$$ and $$$ {c}_2\to 0 $$$, we recovered the results found in [15], where the Authors analyzed the onset of penetrative convection in a single porosity material.…”

“…if c 1 → 1 and c 2 → 0, the bi-disperse porous medium approximates a monodispersive one. In the limit case for c 1 → 1 and c 2 → 0, we recovered the results found in [15], where the Authors analyzed the onset of penetrative convection in a single porosity material. To evaluate the role of the double porosity structure, we perform numerical simulations for quoted values of the dimensionless permeability ratio and the dimensionless momentum transfer coefficient, namely Accounting for the discussion made in [36], we analyzed the behavior of the linear instability threshold  L , local stability threshold  N , and global stability threshold  E with respect to K r ∈ [0, 10] or very large K r and 𝛾 ∈ [0, 1] or very small 𝛾, and for fixed upper plane temperature T U = 4 and T U = 6 (see Figures 4 and 5).…”

“…This physical evidence will be proved in the subsequent mathematical analysis. The thermodynamic consistency of Equation ( 1) was discussed in [15] and analyzed more in general in [16,17]. Penetrative convection in porous media was studied under anisotropic or double-diffusive effects in [18][19][20] and in presence of throughflow for the onset of penetrative convection [21].…”

The onset of anisotropic Darcy–Brinkman penetrative convection with local thermal nonequilibrium due to heat generation and extraction

“…Roberts 2 made a significant contribution to our understanding of penetrative convection in a fluid layer that has been uniformly heated internally. One could consult the study of Borujerdi et al, 3 Kuznetsov and Nield, 4 Nandal and Mahajan, 5 Arnone and Capone, 6 and Naveen Kumar et al 7 to understand the effects of heat generation in a porous medium. Even though penetrative convection in the two examples has been widely researched, one involves internal heating, and the other is anticipated to have a nonlinear density function.…”

Compressibility effect on Darcy porous convection

“…The mathematical models describing the onset of convective motions in horizontal layers of fluids heated from below are well known for both clear fluids and fluid-saturated porous media (see [1,2] and references therein) and have been widely analysed under various assumptions: in [3,4,5] the authors analysed the effect of the local thermal non-equilibrium hypothesis on the onset of convection in horizontal porous layers; in [6] the Darcy-Bénard problem for Bingham fluids has been studied, while in [7,8] the authors examined the onset of convection in an inclined horizontal layer of porous medium; convective instabilities in horizontal layers of bi-disperse porous media have been analysed in [9,10,11,12,13], the onset of penetrative convection has been studied in [14,15,16]. Usually, the fluid is assumed as Newtonian and incompressible.…”