Impurity transport in developed Rayleigh–Bénard convection

• Dual-porosity model for impurity transport in Rayleigh–Bénard convection is proposed.
• For the chain of rolls the subdiffusion and the classical diffusion are described.
• Concentration profile at far distances is evaluated.
• An estimate for effective diffusivity at large Rayleigh number is considered.
• Expression for effective diffusivity for transport in lattice of hexagons is proposed.

A model similar to the dual-porosity model is proposed, which describes impurity transport in developed Rayleigh–Bénard convection. The transport characteristics are considered for the two flow configurations (a chain of rolls and a lattice of hexagons) and for a wide interval of Rayleigh number values (when the flow is steady or time-dependent). For the chain of rolls subdiffusion at small times and the classical diffusion with effective diffusivity at large times are described. Concentration profile at distances much greater than the impurity cloud size is evaluated. Dependence of effective diffusivity on characteristics of flow fluctuations at large Rayleigh number is considered.