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We report a numerical study of Rayleigh--B\'enard convection through randomporous media using pore-scale modelling, focusing on the Lagrangian dynamics offluid particles and heat transfer for varied porosities $\phi$. Due to theinteraction between the porous medium and the coherent flow structures, theflow is found to be highly heterogeneous, consisting of convection channelswith strong flow strength and stagnant regions with low velocities. Themodifications of flow field due to porous structure have a significantinfluence on the dynamics of fluid particles. Evaluation of the particledisplacement along the trajectory reveals the emergence of anomalous transportfor long times as $\phi$ is decreased, which is associated with the long-timecorrelation of Lagrangian velocity of the fluid. As porosity is decreased, thecross-correlation between the vertical velocity and temperature fluctuation isenhanced, which reveals a mechanism to enhance the heat transfer in porousmedia convection.

Lagrangian dynamics and heat transfer in porous media convection