Natural convection in porous media: the role of porosity and conductivity ratios in the transition from laminar to inertial convection

We study natural convection in porous media using a lattice Boltzmann method that recovers the incompressible Navier–Stokes–Fourier dynamics. The porous structure consists of a staggered two-dimensional cylinder array with half-cylinders at the walls, forming a Darcy continuum at the domain scale. Hydrodynamic reference simulations reveal distinct flow regimes: laminar (Darcy), steady inertial (Forchheimer) and vortex shedding. We then analyse the effects of porosity and solid-to-fluid conductivity ratio ( $k_s/k_{\!f}$ ) on natural convection. At low porosity ( $\varphi = 33\,\%$ ), convection is highly sensitive to thermal coupling, particularly for insulating solids, whereas conductive matrices buffer this effect through lateral diffusion. Increasing porosity ( $\varphi = 43\,\%$ ) smooths the transition as solid and fluid phases become more balanced. Across the explored range, two inertial regimes emerge governed by plume-scale confinement. The transition from Darcy to inertia-driven convection begins once the dynamics resembles the Forchheimer regime of the reference simulations. Based on our data, the system is governed by the confinement parameter $\varLambda$ , which relates the plume-neck width, equivalent to the thermal boundary-layer thickness, to the pore scale: for $\varLambda \gtrsim 1$ , the dynamics follows Forchheimer scaling, while for $\varLambda \lt 1/2$ it shifts toward Rayleigh–Bénard behaviour. Comparison with experimental data shows the same trend: the nominal Darcy–Rayleigh-to-porous-Prandtl ratio, $Ra^*/\textit{Pr}_{\!p} \approx 1$ , holds for $\varLambda \gt 10$ , but weaker confinement causes earlier departure. Finally, we revise benchmark Nusselt numbers for a cavity with square obstacles, showing that the reference by Merrikh & Lage (2005 Intl J. Heat Transfer 48(7), 1361–1372) misrepresents trends due to improper normalisation.